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#help-38
short raft
ohhhh so 4
i dont know how i fumbled that at the end but it should be 4 not one fourth
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drifting storm
sorry it was an accident
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umbral trail
Tennis balls are sold in a package. Each package holds three balls. The balls are stacked in a column. The Volume of one tennis ball is 166.7375 〖cm〗^3
Rank the solids in order according to the amount of material required for one package of 3 tennis balls.
Rectangular prism
Equilateral triangular prism
Cylinder
Regular hexagonal prism
Containers are transported in cuboid shaped boxes. Each box holds 12 packages. Rank the solids in order according to the volume and surface area of the packing box required?
Rank the solids in order according to the amount of wasted space inside each container of 3 tennis balls.
Which shaped package is the most efficient?
Consider other sizes of spherical balls.
Assumptions
3 balls per container
Balls are arranged in a column.
Where the balls touch the edge of the container there is no gap.
The packaging has no tabs.
You do not need to give consideration to the balls being pressurized.
The hexagonal cross section of a hexagonal prism can be made of 6 equilateral triangles of the same size.
The height of the equilateral triangle cross section of an equilateral triangular prism is 3 times the radius of the ball.
umbral trail
uhh basically idrk how to do any of it
unborn creek
So u gotta find the volume for each shape?
umbral trail
uhh surface area
so like basically i gotta find the surface area of a rectangular prism, triangular prism, cylinder and hexagonal prism that fits the volume of three tennis balls
umbral trail
So u gotta find the volume for each shape?
each tennis ball has a volume of 166.7375cm^3
daring forum
each tennis ball has a volume of 166.7375cm^3
they're stacked on top of each other
umbral trail
yes
daring forum
you can find the radius and thus diameter of 1 tennis ball
then 3x that
to get the min height required
for a cylinder which is probably the correct answer the rest of the math is easy
umbral trail
yeah cylinder would be correct
but i have to like
calculate all of it anyway sigh
daring forum
do you not know the formulas or is there a different problem
umbral trail
do you not know the formulas or is there a different problem
i dont know anything
formulas ig?
umbral trail
i only have the vol of the tennis ball
daring forum
okay how do you get the volume of a sphere
unborn creek
And is the volume of that the same for the rest of the shapes
daring forum
And is the volume of that the same for the rest of the shapes
reread the problem
unborn creek
Yes
daring forum
okay so
work it out
to find the radius
and then the diameter of the tennis ball
daring forum
how much is pi
umbral trail
3 x 166.7375 divided by 4 x pi
then square root with the three thingy
because radius^3 = 3V/4pi
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wraith hinge
-a-b = -(a+b)
marble wharf
what is 6-2-3 and 6-(2+3) and 6-(2-3) ?
obtuse lantern
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obtuse lantern
What do these weird lines mean
dusky thunder
floor function
olive verge
is that greatest interger function?
obtuse lantern
for instance, floor(1.3829) and floor(1.99) are both 1
Ohk
dusky thunder
yes
obtuse lantern
So floor of pi is 3
olive verge
its same just diff names
obtuse lantern
?
dusky thunder
yes
obtuse lantern
Ic
trim lichen
$\lim_{x \to 0} \floor{\frac{2025\sin(x)}{x}}$
solid kilnBOT
Ann
trim lichen
this?
trim lichen
So floor and greatest integer are same
yes, but "floor" is a better name for it.
obtuse lantern
yes, but "floor" is a _better_ name for it.
Can I put the limit inside the floor
olive verge
0/0
trim lichen
you should not be trying to guess it
olive verge
yes its 2024.
obtuse lantern
yes its 2024.
Booyah
trim lichen
ok, so you cannot just drag the floor function to the outside of the limit, but it will help to actually think about how the function 2025sin(x)/x behaves.
obtuse lantern
ok, so you cannot just drag the floor function to the outside of the limit, but ...
Why is it 2024
olive verge
sinx/x lim x tends to zero is 1.
nova pewter
How does floor even change anything
It's sandwiched between $\frac{2025 \sin{x}}{x}-1$ and $\frac{2025 \sin{x}}{x}$
trim lichen
Why is it 2024
as x goes to 0, sin(x)/x approaches 1 from below.
solid kilnBOT
Bagchi234
trim lichen
which is key.
olive verge
so we have [2025] just and Since the function inside approaches 2025, but never exactly equals 2025
trim lichen
because for x close enough to 0, 2025sin(x)/x will be strictly between 2024 and 2025.
(but it won't ever go above 2025)
olive verge
so its 2024
trim lichen
so we have [2025] just and Since the function inside approaches 2025, but never ...
this is not good wording
obtuse lantern
because for x close enough to 0, **2025sin(x)/x** will be strictly between 2024 ...
And if we floor it we get 2024
trim lichen
yes.
the key is we get 2024 on an entire interval surrounding x=0 (even though it is quite tiny)
thus the limit is also going to be 2024
obtuse lantern
What if it was just $\lim{x \to 0} \floor{\frac{sinx}{x}}}$
solid kilnBOT
Azo
Compile Error! Click the 
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dull pilot
trim lichen
$\lim_{x \to 0} \floor{\frac{\sin(x)}{x}}$
dull pilot
use \lim_{
solid kilnBOT
Ann
trim lichen
anyway
as i said above
sin(x)/x approaches 1 from below
so in some neighborhood of 0, sin(x)/x will be between 0 and 1
but it will never go above 1
dull pilot
this is basically just squeeze but fancier
obtuse lantern
but it will never go above 1
So is the answer 0
trim lichen
yes.
obtuse lantern
yes.
The key here is that limit to zero of sinx/x approaches 1 from left?
Correct?
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obtuse lantern
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nimble stone
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vocal hazel
I’m a bit confused on how they are applying FTC here. How is log x differentiable for all of x> 0? Does it not require for us to have a closed interval to take the integral?
dull pilot
so i cant read this
becaue holy shit
but uh
wdym by closed interval for integral and allat
vocal hazel
wdym by closed interval for integral and allat
Like you see in the theorem (second pic) it says it needs to be [a,b]
But here we are using [1, infinity)
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vocal hazel
so i cant read this
These are my teachers notes 😭
steep yew
How is the handwriting so bad
dusky thunder
I’m a bit confused on how they are applying FTC here. How is log x differentiab...
is this the integral from 1 to infinity of 1/t dt? (it is from 1 to x i see)
worldly wing
that's definitely readable idk what you lot are talking about
dull pilot
hey i cant read it
vocal hazel
<@796760495196864512> what is your *exact* question
My exact question is why we can apply FTC here if our interval we integrate on is not closed
Or like how they are integrating from [1, infinity)
vocal hazel
is this the integral from 1 to infinity of 1/t dt? (it is from 1 to x i see)
I think so
wraith hinge
The interval is [1,x]
vocal hazel
Yeah sorry the interval is [1,x] but I assume they are taking x to be infinity?
dusky thunder
they integrate it from [1,x]
idk where you are getting [1, inf) from
but even if it were [1, inf) and the integrand was like 1/t^2 instead of 1/t
you can define it using limits, if the integral then converges then we call it the area under the curve from [1, inf)
wraith hinge
Nope. Integration of 1/t over [1,\infty) does not even converge
vocal hazel
they integrate it from [1,x]
idk where you are getting [1, inf) from
but even i...
Ah ok
wraith hinge
Point is, log(x) is defined as a function of x for all x>0 using the integral. x is not necessarily infinity here
vocal hazel
I’m a bit confused on how they are applying FTC here. How is log x differentiab...
Ig am confused on what they are doing here in this “proof”
wraith hinge
And over [1,x] for all x>0, 1/t is integrable
vocal hazel
Point is, log(x) is defined as a function of x for all x>0 using the integral. x...
Ah okay, but then doesn’t the FTC require if we want to show log(x) is differentiable over (0, infinity) that 1/t is intervals over (0, infinity)?
vocal hazel
Becuase I think they are taking F(x) = log (x) here
vocal hazel
we require 1/t to be continuous from [1, x]
And also integrable on 1 to inf right
Becuase we didn’t really cover “infinity”
In class yet
dusky thunder
we are covering the interval of 1 to a finite x
why are you bringing up 0 in the first place
vocal hazel
why are you bringing up 0 in the first place
Ah sorry, I mean 1
vocal hazel
we are covering the interval of 1 to a finite x
Wait finite x?
dusky thunder
if we take x to infinity, the integral diverges
vocal hazel
Because I think I want to show log(x) is differentiable on all of x > 0
vocal hazel
if we take x to infinity, the integral diverges
Oh
But I’m not really sure what “interval” they are taking here
dusky thunder
[1, x] for x>0
wraith hinge
1/t is integrable on [1,b] for b>0
Let 0<x≤b
Then F(x) = int((1/t)dt) is continuous on [1,b] by FTC
Moreover, f(t) = 1/t is continuous for all t in [1,b]
Hence F'(x) = f(x) = 1/x by FTC
b can be any arbitrary Real here greater than 0, so it's valid for all x in (0,\infty)
vocal hazel
1/t is integrable on [1,b] for b>0
Let 0<x≤b
Then F(x) = int((1/t)dt) is conti...
OHHH, ohh wait so you are saying they are choosing the interval just large enough that it contains x for every real x?
wraith hinge
Yea
vocal hazel
Hmm I see, but ig why does this work? Because it seems if we do not choose a large enough interval this fails
Oh wait…. I think I kind of see. It’s crucial that 1/t is integrable from [1, to b] where b is any finite real number
wraith hinge
Because you cannot include \infinity as a number in R, and 1/t is discontinuous at b=x=0 so you cannot argue there as well
vocal hazel
Yeah ok
vocal hazel
Oh wait…. I think I kind of see. It’s crucial that 1/t is integrable from [1, to...
Would this understanding be correct?
wraith hinge
Oh wait…. I think I kind of see. It’s crucial that 1/t is integrable from [1, to...
finite real number greater than 0
vocal hazel
finite real number greater than 0
Yeah sorry finite number greater than 0
wraith hinge
Yeah it works
vocal hazel
I see this makes alot more sense then
Thanks
I thought they were doing some random infinit type stuff
wraith hinge
No problem. Have a nice day.
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viscid flower
you were able to do the others?
you can kind of play it like a game of make the pieces fit
youll probably need some linear transform on t to make it make sense with x
lets say it instead
what have you tried
the formula?
that will only work if t goes from 0 to 1
yea
you can do the same thing here
you just also need to translate
yea, exactly
because the length of the interval is 4, and not 1
you divide by 4
here the length is 3
so we'll divide by 3
we also need to add 1
to make it start at 1
well 
lets call that another way
t goes from 1 to 4
so, length 3
yea
and, we need to make sure that its 0 at the start
no
length is end minus beginning
so thats all there is to it
we have to divide by the length
and we have to make sure its 0 at the start
we want to make sure its zero at the start
so instead of $x_1 + (x_2 - x_1) t$
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jan Niku
viscid flower
we use $x_1 + (x_2 - x_1) \qty( \frac{t-1}{3} )$
solid kilnBOT
jan Niku
viscid flower
subtract
idk why i said add
its been a long day
subtract by 2
because at the beginning, when t=2
you want that piece to be 0
we can work out a new formula
or i can type it out, if you want
but i think you get the idea
lets look at this, as t goes from 1 to 4
at the beginning, when t is 1
you have 1-1
that makes everything go away except for x_1, which is what we want
$x_1 + (x_2 - x_1) \qty( \frac{1-1}{3} ) = x_1$
solid kilnBOT
jan Niku
viscid flower
because we want x to start at x_1, when t is equal to whatever it is at the start
viscid flower
this is, for the x
you still have another piece for the y
maybe shouldnt have just typed out part of the answer
but maybe seeing it is helpful
$t$ goes from $t_1$ to $t_2$, so we use $x_1 + (x_2 - x_1) \qty( \frac{t-t_1}{t_2-t_1} )$
solid kilnBOT
jan Niku
viscid flower
yea, basically
wraith hinge
**jan Niku**
To see this:
t in [a,b]
So (t-a) in [0,b-a]
So (t-a)/(b-a) in [0,1]
viscid flower
maybe its helpful to memorize now but you can work it out kinda quickly if you remember the idea, too
viscid flower
you can kind of play it like a game of make the pieces fit
thats what i meant here
theres nothing to do but use the formula now
why would it be the first one?
wraith hinge
Not sure how the answer key took y values 9,-16 instead of 9,-7
It's wrong for both
No wait
They used the same formula, it's just simplified
4 + (-2-4)(t-0)/(3-0) = 4 - 2t
9 + (-7-9)(t-0)/(3-0) = 9 - 16t/3
Then translate t by 1 (basically t -> t-1)
With the formula we derived here, we directly merge these two steps:
4 + (-2-4)(t-1)/(3-0) = 4-2(t-1)
9 + (-7-9)(t-1)/(3-0) = 9-16(t-1)/3
They're the same expression
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short raft
Arc AB = 1/12 of a circle
OA = 12cm
Whats the length of height M (dropped to OA?)
AM = MB btw
main sigil
Arc AB = 1/12 of a circle
OA = 12cm
Whats the length of height M (dropped to OA?...
do you mean AM = MB?
short raft
Oh yeah sorry
main sigil
I'll have to go soon but here's a hint at least:
||The height from M will be exactly half of that from B. (Think about why)|| Why hint: ||similar triangles|||
short raft
Ohhhhhhh i managed to find the answer (6cm), but i just need to think of why it would be exactly half of the same but from B
brazen wyvern
Ohhhhhhh i managed to find the answer (6cm), but i just need to think of why it ...
3cm
short raft
oh yeah oops but point still stands
Nvm found out how to completely solve it, thanks!
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winged breach
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winged breach
Can anyone pls help me with sentence 6 proof
😭😭
I am dying
<@&286206848099549185>
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winged breach
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winged breach
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silent canyon
Which sentence is 6
silent canyon
It's a given statement https://en.m.wikipedia.org/wiki/Arctangent_series
Which part of the proof do you have issue?
winged breach
Are the numbers of the equations
so we just take them and remove the buttom?
And i should not write anything about it to my proof or?
winged breach
From (9) means : from equation (9) we get (10)
i see they are saying *t^2 on the left side, do they do the same on the right side?
quiet notch
And i should not write anything about it to my proof or?
when you want to prove this u have to write like ; f(t) = 1 - t^2 .... and from this we get t^2 * f(t) ) = t^2 ...
quiet notch
i see they are saying *t^2 on the left side, do they do the same on the right si...
yes exactly
quiet notch
on equation 9 try to multiply each side with t^2
quiet notch
how does he get number
quiet notch
and i am getting something weird
Show me what you did
winged breach
quiet notch
Muliply on the right side 1 *t^2 -t^2 * t^2 etc..
quiet notch
winged breach
Niceee
How 🥲
The calculator
😭
U are doing it right
Thank u so muchhhh
I was stressing 😭
quiet notch
Ur welcome
quiet notch
I was stressing 😭
Dont stree take it easy
quiet notch
I got another question
Ofc
winged breach
Let me find it
@quiet notch So how do they find t_96? And how do they get 3 1/7?
I found r/t_96
website if u want to translate it from ur self
for better quality
quiet notch
Ok
winged breach
winged breach
winged breach
I calculated my own way, i just did not do the last step
did i do something wrong in my calculation that i didnt got the same answer?
winged breach
what is r/t_96? here? Mine is something like 30.54683998694405080567402296033919256341434851688519699089760616330856
055925615572827317115267673533
dont look at the p_96 calculation
quiet notch
No you didn not make a mistake
winged breach
what should i do now? How should i calculate it by this methos?
winged breach
what is r/t_96? here? Mine is something like 30.54683998694405080567402296033919...
I got that
quiet notch
what should i do now? How should i calculate it by this methos?
U just compute 96 * 153 / 4673.5 u will get pi < 22/7 and thats ur uppr bound foo pi
If thst your question
winged breach
where does 153 / 4673.5 come from?
I got 30.54683998694405080567402296033919256341434851688519699089760616330856
055925615572827317115267673533
as r/t_96
quiet notch
where does 153 / 4673.5 come from?
bc of the flip
winged breach
i mean from my numbers?
quiet notch
I got 30.54683998694405080567402296033919256341434851688519699089760616330856\
...
That help us to estimate pi
So pi is almost = 96/ ur number
quiet notch
Yeah we just flip it
winged breach
we can just do it? xD
quiet notch
r/ t96 becomes t96/r
quiet notch
https://www.youtube.com/watch?v=BAFvNCrCYHU
this video help to understand what is all about
winged breach
quiet notch
quiet notch
is it legal to just turn them 😄 it feels illegal
Its legal haha
winged breach
really lol
is it because
wait
ahhh yeah u are right
I am just tired hjahahha
i also got another question now
quick
winged breach
or no i know the answer for this question now. but wait i got a last one
i promise
😄
quiet notch
dw
winged breach
https://www.matematiksider.dk/pi_archimedes.html
Or the pictures
quiet notch
𝑎6
is the full side length of a hexagon
t6 half the side length
the defintion
t6 = a6/2
quiet notch
t6 half the side length
think of it like this
a = 100 and t is half of it t = 50
then a = 2 * t
so a6 = 2 * t6
winged breach
ahhh yeah i get it
2*2=4
I am so fucking stupid
right now
i need some sleep
hahahahaha
quiet notch
Nah, thanks! Appreciate it
winged breach
Thank u man u saved my week
quiet notch
Thank u man u saved my week
ur welcome 😁
winged breach
Can i add u? Last time no one could answer my questions arround pi
quiet notch
Can i add u? Last time no one could answer my questions arround pi
sure
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quick knoll
Huhu, I have a question about a notation. Theoretically, if you write that 123.40 is the same as 123.4 but if 12340 cents are to be converted into euros then it is 123.40€ why is 123.4€ wrong? Is there a notation agreement?
hallow spruce
it's not numerically wrong as much as bad practice
".40" directly translates to 40 cents (or whatever the fractional currency is)
sharp heart
Huhu, I have a question about a notation. Theoretically, if you write that 123.4...
Yes, there's a standard way of writing euros with cents.
quick knoll
So it is also important to pay attention to the context?
hallow spruce
that's pretty universally true ye
quick knoll
Yes, there's a standard way of writing euros with cents.
Do u have a link or something
sharp heart
You can either do 123€ if it's a whole number or 123.04€ when cents are included.
Let me see if I can find one.
quick knoll
A father complained to Facebook because it was the same, but I told him that there is a usual quotation (two decimal places). But mathematically, it should be the same
vagrant marsh
i guess it comes down to something similar to significant figures
sharp heart
Do u have a link or something
Sorry, couldn't find anything.
quick knoll
Ok NP.
sharp heart
I do know that some countries switch out the .s with the ,s.
quick knoll
Ty for helping
sharp heart
For example 1,000.00 might be 1.000,00.
Depending on how that country writes its numbers.
quick knoll
Yeah in Germany we use Normaly ,
Jup and the dot mean 1.000.000 that u can better read it
But thx
sharp heart
No problem.
quick knoll
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warm sedge
Help me with this question
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Help me with this question
warm sedge
This is where I’m at and I’m just confused
maiden zinc
What do you need help with
warm sedge
What do you need help with
finding x and y intercepts
maiden zinc
Ye ur y intercept is correct
Bad notation tho
when you plugged in x=0
You said it was equal to 0
warm sedge
okay
warm sedge
That’s better
what about finding x intercepts, the cos3 is confusing me
maiden zinc
what’s the first x intercept of cosx
actually nvm
Don’t go that direction
What is the period
Of this function
remember 2pi/b
@warm sedge
Man
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warm sedge
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wraith hinge
Hello, I got this question on a surprise test asked by my teacher, can anyone help. I am not even able to understand which concept gonna be used here.
If 6⁸³ + 8⁸³ is divided by 49, then the remainder is?
trim lichen
Hello, I got this question on a surprise test asked by my teacher, can anyone he...
did you miss a "not"?
wraith hinge
did you miss a "not"?
Yep sorry
trim lichen
the concept you're looking for is perhaps next called modular arithmetic
wraith hinge
Modular arithmetic?
trim lichen
yes
wraith hinge
Can you explain about it? How can I apply it?
night patio
its possible that its intended to be binomial expansion
wraith hinge
I don't think it's in our curriculum.
night patio
if you haven't learnt modular
night patio
I don't think it's in our curriculum.
hmm, if you haven't learnt binomial or modular arithematic but this is gonna be kinda bad
trim lichen
oh, binomial theorem is also out?
night patio
huh what im confused
wraith hinge
hmm, if you haven't learnt binomial or modular arithematic but this is gonna be ...
I know about binomial, the polynomials with 2 terms are called binomials?
trim lichen
binomial expansion like (a+b)^n
trim lichen
$(a+b)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k$
solid kilnBOT
Ann
night patio
hmm
wraith hinge
And the summation function
night patio
no binomial or modular (🗿)
trim lichen
that's gonna be tough to climb out of...
night patio
what have u learnt
wraith hinge
what have u learnt
Exponents of Real Numbers , Irrational Number , Polynomials , Quadratic Equations , Sequences ( Basics ) , Arithmetic Progression
In polynomials we learn basically about quadratic polynomials and their graphs
Learnt*
night patio
there wouldn't be analytical way for you to solve this i think
maybe the series a_n = 6^n + 8^n has some nice patterns when divided by 49 idk
thats the only reasonable way for you to do it given what you have learnt
wraith hinge
there wouldn't be analytical way for you to solve this i think
This is the only question whole class is finding the solution, I don't think so he should give that, I am in secondary school. And binomial theorem isn't even in curriculum
night patio
This is the only question whole class is finding the solution, I don't think so ...
you might just have to try some patterns to be honest
wraith hinge
you might just have to try some patterns to be honest
Oh
Thanks I will inquire about it to him bc many students were also complaining about it.
wraith hinge
you might just have to try some patterns to be honest
Also I got a question could you help about it?
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hollow wedge
im so stuck rn
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grave relic
okay
first
what is the equation of the straight line that passes through points A and D?
hollow wedge
huh
grave relic
I recommend fractions if possible so it's more accurate
hollow wedge
we dont know values of p and q
hollow wedge
but you know the values of p and q
thats the whole point of the qn🫠
grave relic
my bad sometimes my brain turns off :P
indigo pawn
Hm I haven't done this kinda question in a while so I'm not sure. Unless I'm missing something in the question like equilateral parallelogram or smthn there should be infinitely many solutions to (p,q)
hollow wedge
huh
grave relic
thats the whole point of the qn🫠
do you have the answers to the question
indigo pawn
huh
The points a and d don't have a y intercept restriction so the parallelogram can be however vertically long and it would still satisfy the question
The question itself might be missing some information
grave relic
The question itself might be missing some information
yeah I was thinking that too
hollow wedge
wait ahh my solution booklet is buried deep down
nvm ig its in sch
ig i go ask my teacher
grave relic
okay
indigo pawn
Wait isn't there another from for the linear equation
Lemme Google rq
Hmm
I think ik how to solve this question
Lemme grab some paper rq
hollow wedge
ok
faint stream
Imma take a peek.
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safe spire
HELP , Form the product from the solutions of the quadratic equation. x^2-11=0
trim lichen
safe spire
Resolving for X = Root 11 / -Root 11 , but how do you even form the product , if there is a Root as X1 and X2
marble wharf
what about the root is stopping you from multiplying $\sqrt{11}\cdot (-\sqrt{11})$ ?
solid kilnBOT
Denascite
wraith hinge
Intresting
wraith hinge
Resolving for X = Root 11 / -Root 11 , but how do you even form the product , if...
-11
(-√11) ( √11 ) = (-1) (√11) (√11 ) = -11
its a math joke
It's a help channel
safe spire
What you mean by that , is this not solvable ?
wraith hinge
What you mean by that , is this not solvable ?
No
(-√11) ( √11 ) = (-1) (√11) (√11 ) = -11
The question is x²-11 = 0
safe spire
Ok Thanks a lot 🙂 , This Math Task is part of a Business School in Germany Frankfurt , on of the TOP 3 Actually
wraith hinge
Ok Thanks a lot 🙂 , This Math Task is part of a Business School in Germany Fran...
👀👀👀
I thought you were in high school
void gyro
Ok Thanks a lot 🙂 , This Math Task is part of a Business School in Germany Fran...
srsly
this question was very ez
safe spire
YES
void gyro
i js wanted to knw what kinda math u did
wraith hinge
@safe spire you can close the channel using .close
safe spire
Well as i said thanks a lot , so i guess this Task is more like a Joke rather than a serious Task.
thanks i will do that
wraith hinge
thanks i will do that
You can ask help anytime regarding quadratic equations
wraith hinge
thanks i will do that
If your problem is resolved use .close
safe spire
.close
void gyro
A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm
void gyro
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void gyro
<@&286206848099549185>
obtuse glade
Need my solution?
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Available help channel!
frail edge
Hey guys I’m having some trouble with limits of fourier series
frail edge
So I have a function defined in the closed integral [0, π]
And these Fourier series are given
I need to find the limit as x goes to 0+
I can tell it is zero from the first series
However I don’t now how to justify computing limit inside of series
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frail edge
<@&286206848099549185>
lament reef
well if we just look at the series ignoring the cos (since it goes to 1) and expand the series, we get
2/2^2 + 2/4^2 + 2/6^2 + ...
= 2(1/2^2 + 1/4^2 + 1/6^2 + ...)
= (2/2^2)(1 + 1/2^2 + 1/3^2 + ...)
and it is known that $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$
solid kilnBOT
doaby
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frail edge
and it is known that $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$
Thanks for the help
However I can’t use the known sum
That’s beacause the excercise asks me to show it using the cosine sum later
atomic seal
2 circles intersect one another at points (1,-2) and (3,-4). both of them are tangent to y axis at points A and B. find the length of the segment AB
red mountain
chilly bobcat
you indirectly know the radii
atomic seal
i can find the equation of line joining both the intersection points
but i dont see how thats helpful
atomic seal
you indirectly know the radii
not sure how
red mountain
is this your drawing?
red mountain
make a drawing yourself
atomic seal
i did
red mountain
!show
trim joltBOT
Show your work, and if possible, explain where you are stuck.
atomic seal
ya wait
this is what ive made
ok i feel that the line joining their centers would be perpendiculat to x+y=-1
and it would pass thru mid point of both intersection points
dapper swift
yes it would be the perpendicular bisector of the line segment
red mountain
i have taken radii as a and b
then what can you say about the x-coordinate of the circles?
placid radish
your drawing is a little bit off, (3,-4) is lower than (1,-2)
atomic seal
your drawing is a little bit off, (3,-4) is lower than (1,-2)
*not to scale 🙏
red mountain
the equations are still correct though
placid radish
*not to scale 🙏
it probably better to get the general positioning correct still
atomic seal
i dont remember properites of points of radical axis either
maybe something through that cuz the yt vid was about radical axis
atomic seal
it probably better to get the general positioning correct still<:blobsweat:58450...
i am not giving a drawing exam 😞 im positive that such diagrams work (i dont need to show work either 😛 )
red mountain
i am not giving a drawing exam 😞 im positive that such diagrams work (i dont ne...
the drawing is for yourself to understand it better
red mountain
can i say (0,-1) is the mid point of AB?
probably not
atomic seal
it lies on the intersection of radical axis and common tangent
i feel like i can
the given answer is 2sqrt6
but idk 😭
dapper swift
but idk 😭
understand my working first, for instace, r^2 is the squared distance from (1, -2) to (t, t - 5)
then the distance from (t, t - 5) to the y-axis is the x-coordinate, t
which must also equal the radius
so equating squared radiuses, you have $t^2 = (t - 1)^2 + (t - 3)^2$
solid kilnBOT
south
atomic seal
understood
dapper swift
I mean you could do x = t + 5 and x = t also
dapper swift
then the distance from (t, t - 5) to the y-axis is the x-coordinate, t
but x = t is easier to do cause of this
placid radish
so equating squared radiuses, you have $t^2 = (t - 1)^2 + (t - 3)^2$
t^2=(t-1)^2+(t+2)^2?
atomic seal
yes yes i get it
dapper swift
t^2=(t-1)^2+(t+2)^2?
nope I have it on Desmos so it's correct
dapper swift
why do we equate squared radii?
same as $t = \sqrt{(t - 1)^2 + (t-3)^2}$ but now we square both sides
placid radish
nope I have it on Desmos so it's correct
oh wait nvm i forgot the -5
solid kilnBOT
south
dapper swift
also note that the difference in y-coordinates, $(\alpha - 5) - (\beta - 5) = \alpha - \beta$
solid kilnBOT
south
dapper swift
and $(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4 \alpha \beta$
solid kilnBOT
south
atomic seal
understand my working first, for instace, r^2 is the squared distance from (1, -...
i forgot to read this smh
$t^2-8t+10=0$
solid kilnBOT
∮Ē.dĀ = Qₑₙ꜀/ε₀
dapper swift
perfect you're so close
atomic seal
and i need to find difference of roots
ohhh
i got 2sqrt6
thank you so much!!!
also one more thing
the comments on the video say they used pa.pb=pt^2 but i have no idea how that would work
maybe through locus?
dapper swift
the comments on the video say they used pa.pb=pt^2 but i have no idea how that w...
hmm that is smart
atomic seal
do you know how that would work out?
dapper swift
and then you can use the same secant line
but then if P is that point, use PA instead of PB
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atomic seal
yeah 😅
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Available help channel!
storm quail
!help
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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
trim lichen
If (x,2p+q)=(y,p+2q) then p-q=_______
are these brackets meant to be just ordered pairs
storm quail
idk
storm quail
are these brackets meant to be just ordered pairs
i think so because then x=y ?
storm quail
ok
trim lichen
this will let you eliminate any doubt we have about what the question really says
atomic seal
im getting 0 is it correct??
yes
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Available help channel!
tall star
This is a graph theory question... I need help understanding how to do part f
tall star
According to the question I must select the optimal edges for the wire layout
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@tall star Has your question been resolved?
ivory seal
HELLLPP
uneven rover
Did I do this chain/product rule problem correctly?
trim joltBOT
Did I do this chain/product rule problem correctly?
grim sparrow
Did I do this chain/product rule problem correctly?
looks perfect to me 
pallid lake
👍
uneven rover
?
pallid lake
it's correct
uneven rover
pallid lake
Looks great!
uneven rover
How do I solve this problem?
nova spire
How do I solve this problem?
have you thought about how to compute dy/dx if it weren't given?
dull island
How could I do that for this type of problem?
can you apply the chain rule in a way that doesn't need you to know what dy/dx is?
uneven rover
can you apply the chain rule in a way that doesn't need you to know what dy/dx i...
How can I do that?
dull island
what's your chain rule
uneven rover
what's your chain rule
I have no clue where to perform the chain rule
dull island
y=
if you have an expression inside something you know how to differentiate
you can differentiate as you would normally
then multiply by the derivative of the expression
for example
$\frac{d}{dx} (x^2+1)^3 = 3(x^2+1)^2 * 2x$
solid kilnBOT
Xetrov
uneven rover
Yes, although how will that allow me to solve the problem that I wrote down?
dull island
Yes, although how will that allow me to solve the problem that I wrote down?
replace x^2+1 with f(x)
uneven rover
I rewrote it
How do I solve this problem and get to the answer?
I don’t know how to find f(1)
dull island
X^2 + 1 isn’t even on the main problem
well I'm not going to spoonfeed you the answer am I
uneven rover
well I'm not going to spoonfeed you the answer am I
It’s not spoonfeeding
It’s just some extra help
I’m very confuzzled
Come on, help me
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@uneven rover Has your question been resolved?
empty tulip
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fleet bear
im not sure wat to do for it
I think you labelled angle ACB wrongly
empty tulip
I think you labelled angle ACB wrongly
so its not 101.9
fleet bear
look at part a
fleet bear
so its not 101.9
the angle you found is ACB
empty tulip
the angle you found is ACB
ok
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@empty tulip Has your question been resolved?
fathom flax
I've just been having trouble with this specific problem.
The main part I need help with is trying to get them at the same base, which is what I assume I need to do before being able to make them into a single logarithm, though I might be wrong and it could require a different method.
fathom flax
Here's where I've gotten so far, not sure if I'm going in the right direction with this.
The =1 was just so I could compare if it's still equivalent on desmos.
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@fathom flax Has your question been resolved?
fathom flax
1/log2(6) is a constant that is multiplying log2(y³)
Just out of clarification, is the 1/log_2(6) from the = 1 at the end of the equation?
I'm still pretty confused on where I should go next
fathom flax
The =1 was just so I could compare if it's still equivalent on desmos.
And I feel like I should clarify more on this but the =1 from the image showing my progress isn't apart of the actual problem, I just added it in so I could double check in desmos if what I was doing is still equivalent to the original equation.
<@&286206848099549185> I still need help on what I should do now on how to rewrite the expression so it only contains one logarithm
austere cedar
Just out of clarification, is the **1**/log_2(6) from the **= 1** at the end of ...
No.
log2(y³)/x = (1/x)log2(y³)
fathom flax
Okay, I'm in the middle of trying to understand the whole thing right now
fathom flax
.close
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Available help channel!
tawny moat
can someone explain this whole concept to me, the way i am understanding this at least is theres 2 seperate x's bc of the sub 1 and 2 and i have no idea how theyre graphing this
dusky thunder
can someone explain this whole concept to me, the way i am understanding this at...
think of x_1 and x_2 as x and y instead
so we have x-2y = -1
which yields the familiar form
(-1-x)/(-2) = y
so
1/2 + x/2 = y
tawny moat
when i get to matrix notation should i worry about thinking about it as x and y or does it not matter im just kinda starting on it
dusky thunder
in matrix notation, u only need the coefficients
the x_1 and x_2 are just variables
you can think of them as anything
even x and y
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Available help channel!
neat wren
If yall are super bored please solve this
trim joltBOT
If yall are super bored please solve this
@neat wren Has your question been resolved?
cunning cliff
no
cunning cliff
<@&268886789983436800>
cunning cliff
Please lol
this server isnt for people to do homework for others
neat wren
this server isnt for people to do homework for others
It's called help channel afterall
ivory vault
you can solve the first 5 for everything except for A
neat wren
you can solve the first 5 for everything except for A
Why not
ivory vault
Why not
i mean it as a good thing ig
A only appears in the last equation
so first solve for B to F
then the final equation will become easy, and you can solve that one for A
neat wren
then the final equation will become easy, and you can solve that one for A
So this is just nothing but a long equation afterall
Nothing complicated
ivory vault
So this is just nothing but a long equation afterall
it def looks harder than it turns out to be, i think, yeah
there is a bit of trickiness in solving the first ones
but it's still basic stuff
after using this strategy ig
ivory vault
there is a bit of trickiness in solving the first ones
there is trickiness in this part actually, but i think there is just no way around it either
the solutions for C and F are just complicated
@neat wren
neat wren
there is trickiness in this part actually, but i think there is just no way arou...
Did you try solving it?
ivory vault
Did you try solving it?
yeah
neat wren
the solutions for C and F are just complicated
Can't you try with B first then you could do C or F does it really matter who starts first from them? I think you could just do C first then F something like that
ivory vault
so i start with E = 1000 and D = 100 ofc. and then B = 1/2(D + E) = 550
so we know E, D, and B
then the other 2 equations on top are
$C = 550 - F$ and $F = 2^{550 + 100 + 1000 + C}$
solid kilnBOT
Ginger
ivory vault
these are annoying to solve tho
neat wren
I think it's better to do F first because we cannot really solve C without it but F can solve even forgetting the C
ivory vault
i think either way might turn out tricky
neat wren
these are annoying to solve tho
I'm more curios what would happen in the left lol
ivory vault
we could plug the left eq for C into the right, and we'd get
$$F = 2^{2200 - F}$$
solid kilnBOT
Ginger
neat wren
Yeah this is very tricky
Imagine if some very smartass mathematician just suddenly humble us
ivory vault
idkk if there is any nice closed form at all for the solution
this is what happens with wolfram
,w c = 550 - f, f = 2^(550 + c + 100 + 1000), solve for f, c
solid kilnBOT
ivory vault
ok it gives a bunch of digits lol, those are probably the digits of 2^2200 or something
neat wren
If yall are super bored please solve this
Wait maybe we could simplify or derive this first to make it less complicated? I just don't know how
ivory vault
but it uses that $W_n$ function, which makes it seem like there is no closed form solution (in terms of things like square roots, exponentials, etc)
solid kilnBOT
Ginger
ivory vault
these are the actual solutions tho
even if we simplify, these will still be the solutions
here is a cleaner form
,w c = 550 - f, f = 2^(x + c), solve for f, c
solid kilnBOT
ivory vault
(x represents 2200)
neat wren
Then this must be impossible to solve?
ivory vault
i think impossible to get a closed form solution
vagrant prism
Then this must be impossible to solve?
only using lambert W
it's a transcendental equation
ivory vault
using W_n is like using a "sin" or "cos" kinda, it stands for something
ivory vault
it's a transcendental equation
solid kilnBOT
Ginger
neat wren
using W_n is like using a "sin" or "cos" kinda, it stands for something
Well still how do we solve the paradox on C and F
ivory vault
Well still how do we solve the paradox on C and F
we did just get a solution for F
then C = 550 - F easily gives us C
ivory vault
**Ginger**
these two
so we started the one on the left, solved for C (it already is) in terms of F
then plugged C into the one on the right
that eliminated C
so then we solved for F
it just turned out to be a tricky form
but yeah, it was the "substitution" method of solving a system of 2 equations for 2 unknowns
neat wren
but yeah, it was the "substitution" method of solving a system of 2 equations fo...
What you got in the end I'm really curious
ivory vault
$D = 100$
$E = 1000$
$B = 550$
$F = W_n(2^{2200} \ln 2) / \ln 2
$C = 550 - W_n(2^{2200} \ln 2) / \ln 2$
and A will take a loong time to write out
i don't want to actually find and write out A lol
but at least you can see, if everything in the last equation is just some number, except for A, then it is solvable
neat wren
but at least you can see, if everything in the last equation is just some number...
Why not
neat wren
it would take a long time lol
But it is possible to solve right?
ivory vault
and ideally you should be able to find A too (with enough time)
steep knot
If yall are super bored please solve this
D = 100
E = 1000
B = (100+1000)/2 = 550
C = 550-F
F = 2^(550+C+100+1000)
F = 2^(C+1650)
F = 2^((550-F)+1650)
F = 2^(2200-F)
F = 2²²⁰⁰ / 2^F
F * 2^F = 2²²⁰⁰
ivory vault
But it is possible to solve right?
yes 👍 (as long as we're allowed to use the W_n thing, for the first steps to get B, C, D, E, F)
ivory vault
D = 100
E = 1000
B = (100+1000)/2 = 550
C = 550-F
F = 2^(550+C+100+1000)
F = 2^(...
🎉
i had an extra 550 i think
solid kilnBOT
Ginger
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
ivory vault
fixed ^
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@neat wren Has your question been resolved?