@sudden harbor Has your question been resolved?
#help-49
midnight plankBOT
midnight plankBOT
midnight patio
midnight plankBOT
midnight patio
help meeeeee
delicate sage
any T queetion
?
delicate sage
Okk
Let's start with the 1st t
Lets there be two sets [A,B,C,D] and [1,2,3,4]
Total possible combinations is 4c1 × 4c1
Or 16
delicate sage
Now just calculate the probabilities for A,B,C,D and 1,2,3,4
delicate sage
can i get help with the second T
Ok as you say
Probability of winning is 3/8
Do I need to explain this ?
So in 400 games expectation should be 400×3/8
,calc 400*3/8
grand pondBOT
Result:
150
oh
delicate sage
So we see there is a reason to suspect
delicate sage
Which question?
midnight patio
Which question?
bottom left
delicate sage
So we see there is a reason to suspect
..
midnight patio
i dont think it would be a good prove
midnight patio
oh
delicate sage
So it's a formula based proof
I don't think they want you to , write something more mathematical, they only want English and an explanation
midnight plankBOT
@midnight patio Has your question been resolved?
brisk crag
7-10
should 7 be be 0, 1, 0, -3 and domain is -inf, inf and range is -inf, 1
midnight plankBOT
7-10
should 7 be be 0, 1, 0, -3 and domain is -inf, inf and range is -inf, 1
@brisk crag Has your question been resolved?
modern sapphire
yes, thats correct
brisk crag
Can you help me with it, I dont understand
modern sapphire
For domain: What can you say about the lines?
brisk crag
they are disconnected
modern sapphire
thats relevantfor function definition, but for defining the domain itself, its not
so you can just write the union of the two to say the domain is entire real numbers
brisk crag
So I think of them as connected?
modern sapphire
Or, the domain is just (-inf, inf)
modern sapphire
So I think of them as connected?
Yes, coz in the end it is still a single function
modern sapphire
Now, onwards to the range: What can you say about it?
modern sapphire
But the range will be different right?
ofc
brisk crag
All though they are discontinued I can also do -inf, inf because they both go down and up continuously
modern sapphire
do they go down tho?
modern sapphire
you have to chek whats the value of x for say y = -2
brisk crag
So [1 inf and [-2, inf
modern sapphire
its still wrong
modern sapphire
you have to chek whats the value of x for say y = -2
.
brisk crag
1
modern sapphire
y(1) = 1
you can see that from the figure
thats what the thick dot on left line means
brisk crag
Im lost
modern sapphire
At x = 1, you can see theres two lines, but the line on left has a thick dot at (1,1) and the one on right has a hollow circle at (1,-2)
brisk crag
yes
modern sapphire
that means the function at x = 1 is defined as 1
and not -2
the filled circle and hollow circle is the graphical notation that says this
so technically, there is no preimage for the value y = -2
Now can you say how that changes the range?
modern sapphire
nope, fory = -1.9 theres still a valid preimage x
the hollow is only for single point 1,-2
it doesnt say anything about the other points
modern sapphire
So [1 inf and [-2, inf
this one is almost correct
can you modify it just bit based on this preceeding discussion?
brisk crag
[1, inf) and (-1, inf)?
modern sapphire
nope
modern sapphire
sure
brisk crag
[1, inf) -2<x<inf
modern sapphire
yep
brisk crag
Can i write that in interval?
modern sapphire
so instead of [-2, inf) you need (-2, inf)
modern sapphire
you know the difference [ and ( right?
modern sapphire
Nono, specifically, it means for a set [a,b] the point a is within the set
and (a,b] means a is not in it but all the rest of the points of [a,b] are
brisk crag
include/exclude
modern sapphire
yes
modern sapphire
[1, inf) -2<x<inf
ofc, once again you have to take the union of two sets here
brisk crag
One last thing, so the functional values for 9 are
0
1
2
3
brisk crag
ofc, once again you have to take the union of two sets here
wdym?
modern sapphire
the range can be written as a single set, and its not a piecewise thing since f(x) is defined as a single function
so do [1,inf) U (-2,inf)
brisk crag
What does u mean again?
modern sapphire
One last thing, so the functional values for 9 are
0
1
2
3
😦
modern sapphire
What does u mean again?
set union
modern sapphire
One last thing, so the functional values for 9 are
0
1
2
3
yeah now its right
modern sapphire
Alright tysm
npnp
brisk crag
Like really difficult teasers?
modern sapphire
Are there any diffcult subjects in pre calc?
hmm, thats I believe entirely a matter of opinion
brisk crag
Can I hear your opinion?
modern sapphire
personally, I struggled a bit with calculating limits
the rest was pretty easy for me
brisk crag
Do you happen to have notes you can send?
midnight plankBOT
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inner galleon
I'm currently doing revision and have the answer (third pic), but I don't get how the values are derived. Where did the 30 in data likelihood "low" come from? I thought it would be a 70
midnight plankBOT
I'm currently doing revision and have the answer (third pic), but I don't get ho...
@inner galleon Has your question been resolved?
midnight plankBOT
@inner galleon Has your question been resolved?
inner galleon
<@&286206848099549185> hi sorry for the ping I still havent figured it out :")
inner galleon
.close
midnight plankBOT
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fair kayak
Guys, what i got so far is
6a+b=4
Am i doing it right?
midnight plankBOT
Guys, what i got so far is
6a+b=4
Am i doing it right?
last slate
Guys, what i got so far is
6a+b=4
Am i doing it right?
work = rate * time?
1 work = (rate of A +rate of B) * 4 days
make another equation with the second sentence and solve the simultaneous eq
feral sigil
No y is negative it's wrong
last slate
Ohh that makes sense
he was wrong
fair kayak
Ohh
last slate
Wait what formula is this?
hmm wdym?
fair kayak
Is that a physics formula?
last slate
Time taken by A and B to complete their work = four days
Time taken by B to complete his work = 6+ than time taken by a
Let The work done by A be x
work done in one day=
1/4=1/6+1/x+1/x
=1/4=1/6+2/x
=1/4-1/6=2/x
6/24-4/24=2/x
2/24=2/x
cross multoply
2x=24(2)
=x=24
.
idk if this is right
fair kayak
Is that a physics formula?
It seems familiar to me but i can’t remember it
last slate
Is that a physics formula?
well does it not make intuitive sense? also no it’s used to solve “work rate problems”
fallen aurora
Time taken by A and B to complete their work = four days
Time taken by B to comp...
!nosols
midnight plankBOT
Time taken by A and B to complete their work = four days
Time taken by B to comp...
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
last slate
It seems familiar to me but i can’t remember it
it kinda is sure
last slate
Time taken by A and B to complete their work = four days
Time taken by B to comp...
is this correct ?
last slate
It seems familiar to me but i can’t remember it
Look if it takes 2 hours for A to finish 1 “unit” of work, then how long does it take for him to finish half the work?
fair kayak
Look if it takes 2 hours for A to finish 1 “unit” of work, then how long does it...
1 hour
last slate
it’s the same principle here tbh
OHHJ I GOT IY
it’s like speed = distance/ time
I GOT IY
I GOT IT
only the physical implication has changed
speed = rate
distance = unit of work done
time = well time lol
last slate
@last slate
so makes sense?
hey how
should i practice eight grade maths
higher lvl
last slate
should i practice eight grade maths
this is dino’s channel
if u want help, you make your own channel
how?
fair kayak
Anyways, thanks everyone for ur help!!!
fair kayak
work = rate * time?
Thank u smm kiz
last slate
post your question there
last slate
Thank u smm kiz
did u solve it though?
fair kayak
I’m understanding it
last slate
so do you know how to make the very first equation from the first sentence?
last slate
but there are two people so you would give them
different rates
cuz one person could be more efficient than the other
last slate
(A+B)*4 = 1
yes
second sentence?
you have two unknowns thus u need two equations to uniquely solve for it
also wait
what’s the question?
i forgot but u just posted a statement lol
last slate
Work = rate x time
1 = B*(6A)
not quite, remind yourself what A and B actually meant
fair kayak
1/B = 4+6a?
fair kayak
Bx = 1
last slate
If B takes 7 days …. he takes 6 more days than if A did the task on his own
fair kayak
yeah and if B takes x days, how long does A take?
X-6
last slate
Thank youuu soso much <@456226577798135808>
np
did you solve it though?
1 = A (x -6)
fair kayak
I got -1 for A
grand pondBOT
last slate
The first solution is not right, why?
As in, it doesn’t work in the context of our problem
Remind yourself again what A and B means physically
fair kayak
Oooooo
fair kayak
Okayy i’ll try understanding this again
last slate
No
the rate
but the rate describes how much work he does in a given time right?
So a rate or 1/5 for example, in this context, would mean 1 work in 5 hours
i mean falling back to what we described. Work = rate * time so rate = Work / Time
so now if u look back at this
The first equation says A = -1/4
what does that mean?
fair kayak
but the rate describes how much work he does in a given time right?
Yess
fair kayak
what does that mean?
1 unit in more than 4 days?
last slate
it days -1/4
says*
which means he does -1 unit of work in 4 hours
which makes no sense (well it could make sense, he could just be undoing the work the other guy is doing)
but the reason why it doesn’t work is cuz this dude apparently can finish one work himself
so if all he’s doing is obstructing, he wouldn’t have been able to finish the work
so A = -1/4 makes no sense in this context
last slate
so now if u look back at this
your answer is whatever A is in the second line of the solutions
well not the value of A but what does 1/6 mean and what your question asks you to do
fair kayak
anyway i have to go
Okayyy thank you sooo muchh
fair kayak
well not the value of A but what does 1/6 mean and what your question asks you t...
Yesyesss thanks for being so patient
.close
midnight plankBOT
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Available help channel!
twilit field
Just wanted to ensure how I would solve such a problem, is right
midnight plankBOT
Just wanted to ensure how I would solve such a problem, is right
grand pondBOT
ƒ(why am i here )= I don't know
carmine sigil
I don't believe so
onyx plover
Where did the three go?
grand pondBOT
ƒ(why am i here )= I don't know
twilit field
so $x= \frac{3}{4}+ \frac{r}{2} - \frac{0s}{4}$
grand pondBOT
ƒ(why am i here )= I don't know
carmine sigil
You can just turn 0s into 0 you know.
last slate
can someone say why 180=179'59''60
midnight plankBOT
can someone say why 180=179'59''60
dreamy lichen
can someone say why 180=179'59''60
do you mean 180° = 179° 59' 60''?
delicate sage
Just like 1 hr = 59 min 60s
summer ravine
yea
last slate
yes
summer ravine
60*60
dreamy lichen
60'' = 1', 59' + 1' = 60', 60' = 1°, 179° + 1° = 180°
last slate
?
summer ravine
can someone say why 180=179'59''60
first of all, specify what is in degrees and what is in minutes or seconds
summer ravine
no way
last slate
so it took theta as
summer ravine
!original
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
summer ravine
yea
lavish venture
60'' = 1', 59' + 1' = 60', 60' = 1°, 179° + 1° = 180°
^
summer ravine
he didn't label it correctly
dreamy lichen
do you mean 180° = 179° 59' 60''?
that's why I asked this
last slate
summer ravine
which one
last slate
lit it be supllmement
last slate
was this yes answer to my question btw?
ye
lavish venture
60 seconds is a minute
last slate
ye
dreamy lichen
and that gives you the missing minute
lavish venture
if i told you to dm me in 1 minute and 60 seconds
last slate
hmmm ok
lavish venture
would that not be 2 minutes?
last slate
it makes sense now
the 60 gets converted into one
and then it gets converted onto one again
which adds up to 180
Thank you so much
😇
.close
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sudden harbor
midnight plankBOT
sudden harbor
I don't understand how to derive rev and profit from the functions given
midnight plankBOT
@sudden harbor Has your question been resolved?
tacit lance
midnight plankBOT
tacit lance
how do I solve this?
I tried substituting $a^{x} + b^{x} = t$ but that didn't do anything
grand pondBOT
furyolen
cedar coral
why not expand the parenthesis and separate the integral in three?
tacit lance
o poop
goddamn
nvm
I did expand it but I only seperated it into 2
tyty
.close
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cyan dagger
Where is this x^2 coming from?
midnight plankBOT
Where is this x^2 coming from?
grand pondBOT
speedydelete
merry skiff
now you can multiply both parts of the fraction by x
which is $\frac{x^2(1 - \cos x)}{(\sin^2 3x) x}$
grand pondBOT
speedydelete
merry skiff
then, you can split it into 2 fractions like this
cyan dagger
How come we multiply it by x?
merry skiff
$\frac{x^2}{\sin^2 3x} \cdot \frac{(1 - \cos x)}{x}$
grand pondBOT
speedydelete
merry skiff
How come we multiply it by x?
probably for the next part of the thing
cyan dagger
This is the full problem if that helps
Oh I think I get why it was multiplied by x
It was to apply the rule where limit approaching 0 for f(x) = sin theta/theta = 1
Maybe?
Idk it just randomly jumped to x^2 without explaining why so I didn't get it.
.close
idle valley
midnight plankBOT
idle valley
why is this not decreasing at an increasing rate?
hard shard
,rccw
grand pondBOT
hard shard
what is this graph
hard shard
!xy
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
idle valley
all good
ocean hazel
why is this not decreasing at an increasing rate?
increasing rate means f' is increasing or getting less negative
but the slopes get more and more negative
hard shard
if you take derivatives at certain points, the derivative will become a bigger negative number
ocean hazel
so its decreasing at a decreasing rate
idle valley
increasing rate means f' is increasing or getting less negative
Why? If you are on a roller coaster and progressively go more down, you are going down at an increasing rate
ocean hazel
2024 ap calc bc frq had the same problem and it was pretty controversial
hard shard
you are going down at a going down rate
idle valley
you are going down at a going down rate
going down at an increasing rate. You are going in the negative direction at increasing “speed”
going down increasingly quick
i have a test on this tmr and my teacher is russian and i can’t understand her 💀
hard shard
like jash said, its controversial, so i would advise avoiding the confusing wording
oh
idle valley
like jash said, its controversial, so i would advise avoiding the confusing word...
how do i avoid that?
hard shard
most people would look at the graph of the derivative and mkae their assumption from there
idle valley
also i don’t want to do what she wants me to do on the test but then get it wrong on the ap exam
hard shard
just consider concave down as "__creasing at a decreasing rate"
both in and de work there
then concave up is "in/decreasing at an increasing rate"
the thing is you definitely understand whats going on, its just an ambiguous wording which one way has been chosen as standard
idle valley
the thing is you definitely understand whats going on, its just an ambiguous wor...
yeah and my friends are all calling me stupid for thinking it’s wrong 💀
I like understanding the whys in math, and conceptualizing it. Conceptually this is hard to make sense of.
hard shard
i think it would be easier for you to understand if you think of it as "the derivative is decreasing"
since it becomes more negative
idle valley
i think it would be easier for you to understand if you think of it as "the deri...
The funny thing is, This makes more sense and we haven’t been taught derivatives
hard shard
then if you have a positive derivative, you say "increasing at a decreasing rate" and negative derivative is "decreasing at a decreasing rate"
idle valley
then if you have a positive derivative, you say "increasing at a decreasing rate...
or gets “progressively more negative”
and or positive
hard shard
or gets “progressively more negative”
yeah thats good
hard shard
the idea of "negative at a negative rate" is up to interpretation though
youre welcome
idle valley
.close
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zealous abyss
I am trying to calculate the radius of a circle needed to create an arc between two straight lines at a 132° angle from each other, with a known distance. I would like the circle to intersect each straight line tangent to the arc. I’m sure there’s a formula for this, but I just can’t wrap my head around getting the exact arc. I’ve drawn in all of the known dimensions and where the arc needs to be located. Any help would be appreciated. Let me know if there’s anything else I need to add.
midnight plankBOT
I am trying to calculate the radius of a circle needed to create an arc between ...
midnight plankBOT
@zealous abyss Has your question been resolved?
zealous abyss
It has not
I believe this is another way to put the problem
<@&286206848099549185>
small jasper
Search up the intersecting chords theorem
zealous abyss
That looks like it will help. Thank you so much.
small jasper
That looks like it will help. Thank you so much.
midnight plankBOT
If you are done with this channel, please mark your problem as solved by typing .close
zealous abyss
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rocky ether
for part 3, how would you find |R3|?
midnight plankBOT
for part 3, how would you find |R3|?
floral apex
R is for Radius
Usually, you'd use the ratio test
Really, it should be positive, the | | are extraneous
Does that help?
rocky ether
yeah i setup |R3| = |(x-1)^4 / 4! * f''''(x)|
but there's also the other way to find R3 which is just R3 <= 1^(2*4+1)/(9!)
floral apex
R isnt remainder
its a radius
They aren't asking you to find the error in the approximation, they're asking you to propose a range of x values outside of which the sum must diverge
wait
am i stupid 
rocky ether
how come it's setup like the remainder
floral apex
hmm idk probably because i might be stupid
rocky ether
😭 😭
floral apex
I'm having a hard time understanding the question
rocky ether
yeah i'm not rly sure about it either
floral apex
Why would the sum not exist?
I mean, why would it not existing have anything to do with the 3rd term
maybe they mean
rocky ether
i saw people online who were calculating the error, but did it in some weird ways
floral apex
Provide a range, |R3| > |S-S3|, which bounds the error on the actual sum
or something like that
rocky ether
i thought error bound only gave an upper bound
floral apex
Taylor remainder? Yea, it does
which is what you want
a bound on the truncation error
rocky ether
how would there be an interval if the error is only a number and not an interval?
floral apex
At least I think that's what this problem is asking
floral apex
how would there be an interval if the error is only a number and not an interval...
lemme scribble so i can make sure i say it in a way that is reasonable
rocky ether
🙏
floral apex
🙏
I think, you'd think of it this way
Say that we name the exact error E
then S_3 + E = S
rocky ether
yeah
floral apex
or, more naturally, S - S3 = E
we can also create a bound, using some remainder bound R
R is a bound, so it will over estimate the magnitude of the error, since its as big as it can possible be
we can write this symbolically as |E| < |R|
then $|S-S_3| = |E| < |R|$
grand pondBOT
jan Niku
floral apex
i guess that should be <= but you get what i mean
rocky ether
yeah
floral apex
I think the implied interval is [S3 -R, S3 +R]
implied that this interval contains S
but its not written like that
floral apex
**jan Niku**
its written in this way
rocky ether
cuz there's like this
floral apex
but how would you find R?
you would use what you did before, at least thats what you'd use, id have to do more math to check its correct
yea
this is it
rocky ether
and |R| <= a_(n+1)
rocky ether
and |R| <= a_(n+1)
is it different from this?
floral apex
I could link a video or something if you want
floral apex
is it different from this?
The idea is that the error you lose by truncation the ENTIRE rest of the series can be bounded by using just the next term
thats why its a cool theorem
I think what you wrote there is saying more or less the same thing
assuming a_n is the sequence thats handling everything thats not x-involved in the series
rocky ether
for what i wrote i was using a_n = (-1)^n * x^(2n+1) /(2n+1)!
so i'd get 1/9! as the maximum R
rocky ether
cuz there's like this
but then if i use this theorem, i'm not sure what to put for z or a
because it doesn't say where it's centered at
floral apex
its centered at 0
floral apex
cuz there's like this
because a is 0 in the series
see the $(x-0)^{2n+1}$ in the series
grand pondBOT
jan Niku
floral apex
z is the value of x which creates the bound
its some value of x between the center and your chosen value that maximizes the error
rocky ether
so center = 0, chosen value is 1, so z would be 1?
floral apex
interestingly the theorem goes further and says that there is an x in this range which also makes the approximation actually equal to the real error
floral apex
so center = 0, chosen value is 1, so z would be 1?
not necessarily, but it may be
it is whatever makes the approximation the largest
so, its a classic calculus problem
take the derivative
set it 0
find the critical points
you also need to check the boundaries
unless you can intuit that a critical point must be the max
rocky ether
take the derivative
derivative of a_n?
floral apex
derivative of a_n?
the next term in the series has some derivative of f
the theorem says, truncate at term n
you can use the n+1th derivative of f (and the other stuff pictured there) to bound the error
so, you need to figure out what n is in the problem
and find the n+1th derivative of f
then, maximize it between 0 and 1
rocky ether
so set the next term's derivative of f = 0, so in this case it'd be cos(x) = 0
floral apex
although, its sort of baked into the sum they give you, really
what you could do here is just maximize $(x-0)^{2n+1}$ on [0,1]
grand pondBOT
jan Niku
rocky ether
aren't the values of x and n already set?
z is the variable rigth
or whatever's unkonwn at this point
floral apex
kind of, its more clear if you read the statement of the theorem
in this uhh
maximization problem, its the variable, yes
maybe better thought of as a parameter but whatever
rocky ether
so since the overall series = sin(x), the (3+1) derivative would be sin(x) again
floral apex
lemme grab it
rocky ether
and then you'd have to set sin(x) = 0 between 0 and 1?
floral apex
and then you'd have to set sin(x) = 0 between 0 and 1?
no
sinx is the function we want to maximize on [0,1]
can you intuit where the max will be?
rocky ether
it'd be at 1 right
floral apex
if we want to maximize sinx on [0,1]
we can take sinx' = cosx
set cosx = 0
find that x = pi/2 seems like a candidate
but
,calc pi/2
rocky ether
that's outside the bounds right
grand pondBOT
Result:
1.5707963267949
ok so to fill everything in
grand pondBOT
Result:
0.035061291033662
rocky ether
so then with that R
floral apex
,calc |sin(1) - 101/120|*10
rocky ether
|S-101/120| <= sin(1)/24
grand pondBOT
The following error occured while calculating:
Error: Value expected (char 1)
floral apex
,calc |sin(1) - 101/120|*10
grand pondBOT
The following error occured while calculating:
Error: Value expected (char 1)
floral apex
and then it'd be -101/120 - sin(1)/24 < S < 101/120 + sin(1)/24
youu could go further here
since S = sin(1)
if you wanted
well
maybe thats dumb
rocky ether
wdym go further
grand pondBOT
Result:
-179.1749692793
what is that
floral apex
,calc (sin(1)/24) / ( sin(1) - 101/120 )
grand pondBOT
Result:
-179.1749692793
the ratio between our approximation and the actual error
rocky ether
that seems kinda off
floral apex
this says its 180 times larger? which seems big
rocky ether
lol yeah
floral apex
,w sin(1)/24
grand pondBOT
rocky ether
is there something it's usually closer to?
floral apex
,w sin(1) - 101/120
grand pondBOT
floral apex
is there something it's usually closer to?
it really just depends on the function and the term
i mean, our bound is already pretty small, right?
its nearly 3% of the actual value
,calc 101/120
grand pondBOT
Result:
0.84166666666667
Result:
0.8414709848079
we just underestimate how good the approximation is
which is alright, we were just trying to bound the error
rocky ether
so that works
rocky ether
what
rocky ether
what does that mean
floral apex
the next term is n=5
oh
its already captured in the way its written
so the 4th term is
i mean, our bound is
$\sin(1) \cdot \frac{ 1^9 }{ (9)! }$
grand pondBOT
jan Niku
rocky ether
WAIT THAT'S WHAT IHAD BEFORE
floral apex
,calc sin(1) / 9!
rocky ether
or kind of
grand pondBOT
Result:
2.3188684546073e-6
it was just 1/9!
floral apex
rocky ether
floral apex
,calc sin(1) - 101/120
grand pondBOT
Result:
-1.9568185877017e-4
but now its too small 
rocky ether
how is it too small
floral apex
our bound is smaller than the actual error
although i guess
what n=5 now
so were really working with cos
not sine
then its just 1/9!
,calc 1/9!
grand pondBOT
Result:
2.7557319223986e-6
i mean if we use this
it'd just be (-1)^4 * 1^(9) / (9!)
so it says error would be just 1/9! as well
rocky ether
how come
floral apex
because our bound cant be smaller than the actual error
grand pondBOT
Result:
1.9843759069257e-4
and that's positive
floral apex
and that's positive
the actual error is negative
rocky ether
oh 101/120 < sin(1)
i mean isn't that what the interval is for
101/120 + 1/9! > sin(1)
floral apex
i mean isn't that what the interval is for
the number we are trying to find is a number thats bigger than the actual error
so R should be bigger than sin1 - 101/120
ooo
rocky ether
what's up
floral apex
according to this the calculator here is wrong
which is very suspicious
but it would appear that our bound is actually good
but, it also says that 101/120 is wrong
floral apex
,calc 7003/7!
grand pondBOT
Result:
1.3894841269841
ugh
floral apex
idk this problem should have been so easy just not a great brain day
youll have to forgive me
what im suspicious of
rocky ether
nah allg
floral apex
is their value
because they have 120 in the denominator
which is 5!
oh
the third term
n=2
floral apex
nah allg
so, S3 is taking the sum out to n=2
then we want to use n=3 to calculate the error
when n=2, you get 5! in the denominator
,calc 5!
grand pondBOT
Result:
120
floral apex
,w third derivative of sin(x)
grand pondBOT
floral apex
igotta think more clearly before i just start babbling
rocky ether
we're setting -cos(x) = 0 right
rocky ether
sin(x) = 0 still?
floral apex
rocky ether
is it absolutge value?
floral apex
yes
rocky ether
so then R <= 1*1^4 / 3!
floral apex
,calc 1/(2*3+1)!
grand pondBOT
Result:
1.984126984127e-4
,calc sin(1)-101/120
grand pondBOT
Result:
-1.9568185877017e-4
floral apex
its unfortunate for you that every other term in sin(x) taylor series is 0
its usual to rewrite it without these terms
its implied that when bounding the truncation error you use the next non-zero term
rocky ether
wouldn't it just be n+2)! then
if that's the next term
os is the next term just 7!
1/7!
floral apex
your next non-zero term has 2*3+1 factorial in the denominator
rocky ether
oh
floral apex
because the one you stopped at has 2*2+1 factorial there
floral apex
https://www.desmos.com/calculator/ttpfsfkope
purple line is our evaluation point
rocky ether
there exists a term with 3! tho
floral apex
there exists a term with 3! tho
yes, its present in the 101/120
because its the 2*1 + 1 term
where n=1
rocky ether
ok so that makes sense
so th en
R_3 <=1/7!
|S-101/120| <=1/7!
101/120 - 1/7! < S < 101/120 + 1/7!
is the interval?
these problems always suck
rocky ether
<:blobsweat:584506239661113371> these problems always suck
nah fr
floral apex
sorry i didnt mean to come in here and screw up everything
ive actually done quite a few of these
youd figure they would get easier 
rocky ether
i mean i kinda understood stuff better through the process
so yknow
mayube it wasnt all bad
floral apex
it takes a lot of these
i guess thats not truue
they always suck is more true
maybe you will have better results with practice than me
good luck
did you have any lingering questions
midnight plankBOT
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Available help channel!
viral dagger
find the next term in the pattern
1,4,12,41,170,?
midnight plankBOT
find the next term in the pattern
1,4,12,41,170,?
viral dagger
i genuenly cant think of anything help 😭
viral dagger
wtf
hard shard
context?
viral dagger
nothing
literally like "according to the pattern below, find the next thing in the sequence" question
hard shard
pic?
manic bison
find the next term in the pattern
1,4,12,41,170,?
The first digit is alternating between 1 and 4
So the next number is 4__ probably
viral dagger
grand pondBOT
hard shard
mm not quite
midnight plankBOT
olive matrix
what does the equation look like for a line that is parallel to the x-axis, in 2 dimensions?
right
when it's a line parallel to the x-axis, it involves every variable except x
yea
olive matrix
hmm well it should be an entire plane. is there another equation? such as z = 0?
check the extend to 3d box
right. you start with 3 dimensions. if you constrain it with one equation you'll get a plane. if you constrain it with two equations, you'll get a line. if you constrain it with 3 equations, you'll get a point
so an example of a line would be {y = 1, z = 0}
welcome to linear algebra u have now been initiated
in your screenshot desmos is kind of helping you because planes are big and can make other things hard to see
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twilit field
in 2.1.1 c, what exactly do I do , paramtize the solutions after reducing it to it's RREF/ REF form ?
midnight plankBOT
in 2.1.1 c, what exactly do I do , paramtize the solutions after reducing it to ...
modern sapphire
you got 4 vars and 4eqns
modern sapphire
why do you need parametrization
modern sapphire
I mis-read the b as an a
close, I misread c as a
modern sapphire
lol no worries
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twin crow
Is there any way to rearrange RHS into 3tan(alpha - beta)
midnight plankBOT
Is there any way to rearrange RHS into 3tan(alpha - beta)
twin crow
The question was if
tan(beta) = sin(2alpha)/(5 + cos(2alpha))
Then prove that 2tan(alpha) = 3tan(alpha - beta)
flat veldt
What is beta
mortal pier
Is there any way to rearrange RHS into 3tan(alpha - beta)
Honestly, it's a little bit complicated, but i remember some formula
Still don't get how to rearrange coefficients, but maybe it will help you
twin crow
Still don't get how to rearrange coefficients, but maybe it will help you
Yes i do know this formula, but i dont know how to get there
twin crow
What is beta
Wdym
balmy vapor
do you know the double angle formulas for cos2a and sin2a?
twin crow
do you know the double angle formulas for cos2a and sin2a?
Yes
twin crow
Is there any way to rearrange RHS into 3tan(alpha - beta)
Suppose alpha = a
beta = b
if this is true, then,
3tan(a - b) must be equal to (tan(a) - 3tan(b))/tan(a)tan(b)
And so there should be a way to rearrange this into 3(tan(a) - tan(b))/(1+tan(a)tan(b)
robust forge
The question was if
tan(beta) = sin(2alpha)/(5 + cos(2alpha))
Then prove that ...
Expand sin2alpha as 2tanalpha/1+tan²aplha
And expand cos2alpha as 1-tan²alpha /1+tan²alpha
U should get a relation between alpha and beta
twin crow
Expand sin2alpha as 2tanalpha/1+tan²aplha
And expand cos2alpha as 1-tan²alpha /...
That is how i got here,let me send you my proscess of how i got here,
robust forge
That is how i got here,let me send you my proscess of how i got here,
Got where?
twin crow
U should get a relation between alpha and beta
I need to prove this
robust forge
What exactly have u done in the second last step
Where did that extra tanalpha come from
twin crow
Where did that extra tanalpha come from
On the LHS?
robust forge
forgot it was square
twin crow
Yah
balmy vapor
alright you need to show that 3tan(α-β) = [tan(α)-3tan(β)]/tan(α)tan(β)
twin crow
alright you need to show that 3tan(α-β) = [tan(α)-3tan(β)]/tan(α)tan(β)
Yes yes
balmy vapor
you can use teh inital tanβ equastion to setup a relationship between tanb and tana with the double angle formulas
robust forge
Here
I subtracted 3tanalpha from both sides
Then took 2tan²alphatanbeta to the other side and then took 2tanlpha common then divided both sides by -1-tanalphatanbeta
balmy vapor
arent we trying to prove that 3tan(a-b) = 2tan(a)
balmy vapor
why are we starting from 3(tan-tanb)
robust forge
arent we trying to prove that 3tan(a-b) = 2tan(a)
Yea so go check out the formula for tan(alpha-beta) I'm sure what I have written is the same
twin crow
Here
Aah, i understand what you did there.
But my actual question was since i proved that,
2tan(alpha) = [tan(alpha) - 3tan(beta)]/tan(alpha)tan(beta)
And they told me to prove that,
2tan(alpha) = 3tan(alpha - beta)
Then i can say that,
3tan(alpha - beta) = [tan(alpha) - 3tan(beta)]/tan(alpha)tan(beta)
How do i rearrange this:
[tan(alpha) - 3tan(beta)]/tan(alpha)tan(beta)
Into this:
3tan(alpha -beta)
robust forge
why are we starting from 3(tan-tanb)
huh? Wdym
We started from the given conditions
balmy vapor
its not the same dude you cant use that identity for trig numbers unless im tripping hard
robust forge
its not the same dude you cant use that identity for trig numbers unless im trip...
Which identity?
balmy vapor
o nvm yo did the cross multiplication mb
midnight plankBOT
@twin crow Has your question been resolved?
robust forge
Aah, i understand what you did there.
But my actual question was since i proved ...
Hmmm
Can't think of a way rn
I mean since they are supposed to be equal equate them and arrive at a statement which is true or proven and then just read it backwards
balmy vapor
I proved it with a really messy way but it holds
unfortunately I dont know bot commands so this will have to do
@twin crow
robust forge
damn that's long
balmy vapor
well yeah I think to solve this you need to equate exrpession with the equation you are trying to prove
and show that its always true
so probably there is a shorter way to do it
last slate
is sample variance = population variance if the sample sizes are equal?
midnight plankBOT
is sample variance = population variance if the sample sizes are equal?
modern sapphire
ofc not, sample variance depends on what samples you pick
last slate
a sample is just a subset of the population right?
I mean yes i chose no but the answer was yes lmao
last slate
okay anyway so like
in the formula
the sample mean would be equal to population mean in this specific case right?
but in general the formula distinguishes itself there too?
@modern sapphire right..?
last slate
yall crying for help rn i would be very very gratefull all the ais gave up on me <@&286206848099549185>
last slate
if sample size and population size is same
okay so sample var >= pop var
correct?
in this special case
last slate
yall crying for help rn i would be very very gratefull all the ais gave up on me...
u know it's trivial to do this wiith a computer right?
even if not it's still trivial because L is the inverse of all the elimination matrix
but wait this is my channel so u should prolly ask elsewhere
last slate
u know it's trivial to do this wiith a computer right?
its not allowing me man its giving me wrong answers even idk
modern sapphire
okay so sample var >= pop var
yes, coz sample has that n-1 in denominator unlike population
!occupied @last slate
midnight plankBOT
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).
last slate
but wait this is my channel so u should prolly ask elsewhere
ik its ur channel im askinf u for help
last slate
OH LMAO I JUST RELAISED
modern sapphire
ik its ur channel im askinf u for help
bruh you are spamming every help channel
last slate
wait so how do i do that
last slate
bruh you are spamming every help channel
im new here ok
modern sapphire
Someone else is already using this help channel. If you need help with a questio...
.
latent bear
wait so how do i do that
go to one of th ehelp channels and then just type in your question and enter
last slate
go to one of th ehelp channels and then just type in your question and enter
isnt that what i did ??
onyx plover
isnt that what i did ??
The NON occupied channels
last slate
isnt that what i did ??
look just repost your question
here
@modern sapphire thanks
.close
midnight plankBOT
modern sapphire
npnp
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twilit field
midnight plankBOT