i get that
#help-17
drowsy widget
but holy moly
that was a lot of math
but i see the correlation now
thanks for all ur help appreciate it š
ik u hv to sleep but can u really quickly tell me what im supposed to look for the oither part of this question
really quickly
Express Tn for n ā„ 3 using some number from the previous questions
do u know from the top of ur head which number its referring to?
or no
its fine if u dont its pre vague imo
is this for finding closed form?
hybrid flicker
You preshot it somehow, it's kinda like fibonacci sequence
Now that you got Tn+2 = 2Tn + 2Tn-1
You solve the characteristic equation
rĀ² = 2r + 2
drowsy widget
is that golden ratio * 2?
hybrid flicker
It's not twice the golden ratio I'm afraid
At least I think
No the roots are $1 \pm\sqrt{3}$
twin meteorBOT
rafilou2003
hybrid flicker
Name them $r_1,r_2$
twin meteorBOT
rafilou2003
hybrid flicker
The general solution will look like $T_n = Kr_1^n + Lr_2^n$
twin meteorBOT
rafilou2003
hybrid flicker
Find K and L using the values you got of T1, T2
drowsy widget
mhhm
ok
where did u get this again:
rĀ² = 2r + 2
because ik roots of 2rĀ² = 2r + 2
are the same as the ones u mentioned abpve
so did u mean 2rĀ² = 2r + 2
hybrid flicker
When you have recurrence $T_{n+2} = aT_{n+1} + bT_n$, the characteristic equation is $r^2 = ar + b$
twin meteorBOT
rafilou2003
hybrid flicker
So for fibonacci, a=b=1 and you get rĀ² = r + 1
In this case, a=b=2, so different roots
drowsy widget
oh ok
but i believe 2rĀ² = 2r + 2
works too
but anyways
u gotta sleep
ill let you go lool
hybrid flicker
but i believe 2rĀ² = 2r + 2
You mean what?
drowsy widget
dont wanna take too much of ur time
drowsy widget
You mean what?
im pre sure 2rĀ² = 2r + 2 works instaed rĀ² = 2r + 2
hybrid flicker
im pre sure 2rĀ² = 2r + 2 works instaed rĀ² = 2r + 2
"Works" as in "the roots are golden ratio and inverse"?
Idk what "works" mean for you
drowsy widget
as in we get same roots
hybrid flicker
as in we get same roots
2rĀ² = 2r + 2 has the same roots as rĀ² = r + 1
It's called "multiplying by 2"
Ya know the thing we did here
hybrid flicker
?
drowsy widget
**rafilou2003**
u said rĀ² = 2r + 2 has these roots
hybrid flicker
Yep
drowsy widget
2rĀ² = 2r + 2 has same ones
hybrid flicker
No
drowsy widget
ik cuz i did it in a question before the one we did
hybrid flicker
2rĀ² = 2r + 2 has same ones
2rĀ² = 2r + 2 has golden ratio as root
$2r^2= 2r + 2$ has for roots $\frac{1\pm\sqrt{5}}{2}$
twin meteorBOT
rafilou2003
hybrid flicker
If rĀ² = 2r + 2
Twice that quantity will NOT be 2r + 2
It will be 4r + 4
Double of that
drowsy widget
ohh im trolling i did have x^2 = 2x + 2
hybrid flicker
Bruv
hybrid flicker
Alr gtg
compact sluice
vocal sleetBOT
compact sluice
How would you solve for this problem?
vocal sleetBOT
How would you solve for this problem?
@compact sluice Has your question been resolved?
vast shale
idk where to begin
vocal sleetBOT
idk where to begin
vast shale
i dont understand the problem
deep zenith
Use similar triangles
Look at the triangle with the pole. You know the ratio of pole height : pole shadow height.
That's the same ratio as tower height : tower shadow height
deep zenith
There are two triangles, a big triangle with the tower, and a small triangle with the pole.
The two triangles are similar because one of the angles is a right angle, and another angle is shared between the two triangles.
In similar triangles, the ratio of corresponding sides are the same.
vast shale
im not understanding the question i reread it like 5 times
ik its simple like you find the ratio then mutiply
deep zenith
What part of the question do you not understand?
deep zenith
The question says 4.75 but yes.
vocal sleetBOT
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frank plover
vocal sleetBOT
frank plover
how could I set this up to find the answer by hand using u substitution
novel osprey
hmm like normal u sub? the first thing that comes up to mind is trig sub
frank plover
hmm like normal u sub? the first thing that comes up to mind is trig sub
like i tried this and got stuck
novel osprey
How I would approach this, you can find out sec3 theta bydoing integration by parts
vocal sleetBOT
@frank plover Has your question been resolved?
frank plover
How I would approach this, you can find out sec3 theta bydoing integration by p...
oh my
ty
i bout to watch a video on trig sub
novel osprey
oh did you not learn it.... i feel like its best not to use it if you have never seen it
frank plover
oh did you not learn it.... i feel like its best not to use it if you have never...
possibly but if I did I forgot since my integration chapter
frank plover
oh did you not learn it.... i feel like its best not to use it if you have never...
why are you able to set x to tan theta?
vocal sleetBOT
frank plover
.reopen
vocal sleetBOT
ā
novel osprey
i never knew too much in detail why its like that, in general if the integral involves sqrt(a^2+x^2) you use x as: atan(theta)
vocal sleetBOT
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sage dew
$\int \frac{x^2}{1-ax}dx$ need help figuring out if im doing this correctly
twin meteorBOT
Triaxyz
sage dew
I used poly long division and got $\frac{x^2}{1-ax}=\frac{1}{a^2(1-ax)}-\frac{x}{a}-\frac{1}{a^2}$
twin meteorBOT
Triaxyz
sage dew
which could then be integrated normally
pale perch
,w [1/(a^2(1-ax)-x/a-1/(a^2)]
twin meteorBOT
sage dew
plotted both on desmos with a as slider and showed the same thing with different a values
but it's the integration part that gets a different answer from wolfram
hexed needle
an easier way would be to let u = 1 - ax
pale perch
different how
hexed needle
could try that if you're not confident with this method
sage dew
let me write it 1s
pale perch
might just be a constant thing
vast shale
Couldn't partial fractions be used?
pale perch
not quite no
sage dew
**Triaxyz**
integrating this gave $\int \frac{x^2}{1-ax}=a^2 (\frac{1}{a}\ln(1-ax))-\frac{x^2}{2a}-\frac{x}{a^2}$
twin meteorBOT
Triaxyz
sage dew
Couldn't partial fractions be used?
degree of numerator is higher than denominator
nope
vast shale
Oh, i see
sage dew
$\int \frac{x^2}{1-ax}=a^2 (\frac{-1}{a}\ln(1-ax))-\frac{x^2}{2a}-\frac{x}{a^2}$
twin meteorBOT
Triaxyz
sage dew
missed negative sign
pale perch
should be -1/a^3 no?
hexed needle
^
crisp zenith
I was wondering if someone could walk me through this problem, Iām not even sure where to start
A spherical rain drop of radius R and mass M falls vertically through a cloud layer. The drop enters the cloud layer at a height H from the ground and exits the cloud at a height h. While inside the cloud the drop accumulates water molecules so that its mass and size grow with time. The mass of the rain drop at time t when inside the cloud is given as follows: m(t) = M + Ī±t with t = 0 at the time the drop enters the cloud, and Ī± the rate at which water molecules accumulate.
a) Write an expression for the acceleration in the vertical direction of the raindrop, as a function of time and the velocity v. Choose a coordinate system in which downwards is positive.
vocal sleetBOT
I was wondering if someone could walk me through this problem, Iām not even sure...
summer lichen
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
There was a hint that said you should think of this problem as a rocket with a constant external force but instead of losing mass it is gaining mass. So maybe itās something like
acceleration = aln(M/(at+M))
but it says it wants it as a function of velocity and time
vocal sleetBOT
@crisp zenith Has your question been resolved?
vocal sleetBOT
@crisp zenith Has your question been resolved?
mild jasper
Let the "force" be F and the acceleration be A, then:
v=(MA)/(M+at)
MA= v(M+at)
MA= vM+vat
A=v+[(vat)/M]
restive ermine
So, you know by Newton's second Law that $ F_ext = \frac{dp}{dt}$
$$ F_{ext} = \frac{dp}{dt}$$
twin meteorBOT
The Mad Pirate
restive ermine
where p(t) = M(t)*v(t) , therefore :
$$ F_{ext} = \frac{dM}{dt} \cdot v(t) + M(t) \cdot \frac{dv}{dt}$$
twin meteorBOT
The Mad Pirate
twin meteorBOT
The Mad Pirate
restive ermine
being g the acceleration due to gravity
so
$$ a(t) = g - \frac{\frac{dM}{dt}}{M(t)} \cdot v(t) $$
twin meteorBOT
The Mad Pirate
restive ermine
@crisp zenith There , I corrected the sign
@crisp zenith Now it makes sense, if the mass increases, then the drop will decelerate.
@crisp zenith when a(t) becomes zero, the drop will reach terminal velocity and move with constant terminal velocity v_tm from there
vocal sleetBOT
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long pagoda
vocal sleetBOT
long pagoda
How would i express #4
safe wharf
Do you know the definition of definite integral
long pagoda
Do you know the definition of definite integral
The area under the curve is defined
vocal sleetBOT
@long pagoda Has your question been resolved?
vocal sleetBOT
@long pagoda Has your question been resolved?
tulip spear
how do I quickly find what function fits a table the best?
vocal sleetBOT
how do I quickly find what function fits a table the best?
@tulip spear Has your question been resolved?
vocal sleetBOT
@tulip spear Has your question been resolved?
tawdry wedge
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vital wave
vocal sleetBOT
vital wave
Do I need to convert the radians to cos/sin coordinates? Like for a) theta = pi/4.
should I do X = 5cos(sqrt(2)/2)? Or X = 5cos(pi/4)
quaint mist
well, if you do so, you'll have the coordinates of P, yeah?
civic drift
Do I need to convert the radians to cos/sin coordinates? Like for a) theta = pi/...
How does $x = 5\cos(\frac{1}{\sqrt{2}})$ make sense
twin meteorBOT
ColdTee
civic drift
How is that different
vital wave
Oh Iām thinking of a unit circle
civic drift
Even tho l = 5?
civic drift
$r\cos(\theta) = x$
twin meteorBOT
ColdTee
civic drift
$r\sin(\theta) = y$
twin meteorBOT
ColdTee
civic drift
,w 5\sqrt{2}/2
twin meteorBOT
vital wave
I guess it makes sense tho cause a^2 plus b^2 = c^2?
vital wave
,w 5\sqrt{2}/2
Wait thatās different then mine
If you do 5cos(pi/4) you get 4.999
I did it in demos
civic drift
,w 5cos(pi/4)
twin meteorBOT
civic drift
,w 3.5^2 + 3.5^2
twin meteorBOT
civic drift
,w 5^2
twin meteorBOT
vital wave
Wait Iām still kinda lost on how i can get that with a calculator
Bc even on my calc i got 4.998
vital wave
That would make sense wut am I doing wrong
civic drift
Change it to radian
civic drift
Click stuff till you see rad
vital wave
Legit did all of them
vital wave
lol
civic drift
Perhaps
vital wave
We havenāt done grade yet idk wut that is
civic drift
I have no idea
vocal sleetBOT
vital wave
.reopen
vocal sleetBOT
ā
vital wave
@civic drift wait I donāt think Iām allowed to use a calc
Is it possible to do this without a calculator
zenith viper
how do you define an overflow?
Does the question need to specify the number of bits in the adder?
Because if that's the case I can solve it, but this without anything idk
full nova
Does the question need to specify the number of bits in the adder?
yes overflow usually occurs when resulting bits are more than the bits that register can handle
so i believe according to definitions you are correct
zenith viper
so i believe according to definitions you are correct
All three, yea?
full nova
yea since no size is given and definitions fits correctly it seems correct
zenith viper
Ok and for b and c, since they're unsigned, there's always no overflow?
Overflow happens when there's a problem with the signs according to what my professor said
Since we have no signs in unsigned then in this case (no size) always no overflow
.close
vocal sleetBOT
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Available help channel!
agile onyx
I need help with this question
vocal sleetBOT
I need help with this question
left lichen
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
vocal sleetBOT
@agile onyx Has your question been resolved?
ashen olive
I have a question
vocal sleetBOT
I have a question
ashen olive
What is this chapter called in english so I can search it up on youtube? I tried searching for "rotation around an axis" but i found very little
pale escarp
hi
ashen olive
hey
pale escarp
i need help on math im not good
full nova
make separate channel
ashen olive
u gotta go to an unoccupied help channel
ashen olive
i need help on math im not good
pale escarp
where
full nova
https://discord.com/channels/268882317391429632/488120190538743810
go here @pale escarp
pale escarp
ty
ashen olive
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vocal sleetBOT
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nocturne shale
$f(x) = (x - 1)^2(x + 1)$
vocal sleetBOT
$f(x) = (x - 1)^2(x + 1)$
twin meteorBOT
GMDennis
nocturne shale
i have absolutely no clue as to how i'm supposed to do this
i think that it can theoretically become
$(x - 1)(x - 1)(x + 1)$
twin meteorBOT
GMDennis
hard atlas
nocturne shale
i need to sketch it
im trying to find all the correct x ints
so that it can be easy to graph
nocturne shale
ofc
cobalt ocean
ie. (x+1)(x-1)^2 = 0
but ab = 0 only if a = 0 or b = 0
so (x+1) = 0 or (x-1)^2 = 0
does that help
nocturne shale
uhh
i figured out that if there's two x ints that are the same then it's basically just 1 one of them, i.e. it doesn't go throught x-axis at that point, it just touches it
dusty umbra
im trying to find all the correct x ints
$0=(x-1)(x-1)(x+1) therefore (x-1)=0 or (x+1)=0$
twin meteorBOT
marcus
nocturne shale
i figured out that if there's two x ints that are the same then it's basically j...
is this right?
dusty umbra
Sry first time using the bot
nocturne shale
dude i got it alright
all right*
im getting the hang of this
im so excited
.close
urban laurel
are divergence and curl defined for scalar valued functions ?
vocal sleetBOT
are divergence and curl defined for scalar valued functions ?
heavy yoke
no
heavy yoke
the multivariable chain rule is used in computing derivatives, which may be useful for computing a differential operator like divergence and curl
is there a specific problem or context for this?
urban laurel
is there a specific problem or context for this?
last question is unrelated to divergence and curl
i just want to know if the multivariable chain rule is defined for vector valued fcts
heavy yoke
what is the derivative of a vector function?
twin meteorBOT
Adam Chebil
heavy yoke
then if x, y are functions of some variable t, then the total derivative with respect to could be calculated with the multivariable chain rule in each component
vocal sleetBOT
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Available help channel!
pliant wolf
I wanna know if I did it right
vocal sleetBOT
I wanna know if I did it right
true cliff
looks good
but just for next time
dont make it so messy
you can write $\frac{1}{x-1} as (x-1)^-1$
twin meteorBOT
sin
twin meteorBOT
sin
pliant wolf
aigh fsfs
true cliff
u good w calculus or-?
yeah
true cliff
$y = [(x-1)^-1]-[9(x-5)^-1]$
twin meteorBOT
sin
vocal sleetBOT
pliant wolf
Np
true cliff
can I dm you?
sure if i can help
vocal sleetBOT
Available help channel!
terse granite
Does anyone know how to take the inverse of a matrix using elementary row operation?
vocal sleetBOT
Does anyone know how to take the inverse of a matrix using elementary row operat...
terse granite
icy spear
Start with the identity matrix on the left side and row reduce until you get the identity matrix on the right
terse granite
Wait what I thought the identity matrix went on the right of the original matrix
icy spear
Doesn't really matter
modest dirge
Wait what I thought the identity matrix went on the right of the original matrix
If you thought that then clearly you know this method already
ripe nova
When in doubt, write it in form of a system of linear equations
vocal sleetBOT
@terse granite Has your question been resolved?
terse granite
I forgot how to row reduce by hand -_- um do you swap r1 with r2
ripe nova
Lol, still, when in doubt, come back to the associated system of linear equations. The "operations" are simply the way you manipulate and solve the systems, put more rigorously
I'm sure if I ask you to solve
0x + 2y + 3z = a
1x - 1y - 2z = b
2x + 2y + 3z = c
then you'll have no issue
then you can translate how you solve that system to appropriate operations
terse granite
Thank you!
graceful matrix
curious if im doing something wrong
vocal sleetBOT
curious if im doing something wrong
plain walrus
curious if im doing something wrong
This is a quadratic function word problem correct?
graceful matrix
This is a quadratic function word problem correct?
thats what im thinking, the assignment is called "Solving Real Life Exponential & Logarithm Problems"
flat whale
curious if im doing something wrong
their "time" is continuous and not in units of years
So you need to use continuous compounding formula or something
N * exp(rt)
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Available help channel!
thin vale
vocal sleetBOT
thin vale
I'm wondering what I missed here about it being surjective. I can't see why this is "not quite"
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vocal sleetBOT
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ionic dagger
vocal sleetBOT
safe wharf
recall the formula for area of trapezium
ionic dagger
1/2(sum of lengths of the parallel sides)
x height
what does GR equal
ohh
nvm
i got it
its 168
.close
vocal sleetBOT
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night pasture
night pasture
<@&286206848099549185>
austere goblet
could you translate to english?
vocal sleetBOT
@night pasture Has your question been resolved?
night pasture
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vocal sleetBOT
night pasture
could you translate to english?
Sorry
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Available help channel!
mild fog
serene viper
I need some guidance in figuring the length and width of the rectangle in order to find the area of the complete square
vocal sleetBOT
I need some guidance in figuring the length and width of the rectangle in order ...
serene viper
Iām confused as to how I can used the given information that the area is 18 of the rectangle cause I know the length and width wonāt be the same as a square š
waxen hawk
Why no one willing to save him. heās in urgent situation, that he might lost his home, composed by ice, if we do not take any action towards the deteriorating weather pattern.
vocal sleetBOT
@serene viper Has your question been resolved?
waxen hawk
I will help you then
serene viper
Thanks I appreciate it, cause Iām confused how to approach in finding the sides of the rectangle
waxen hawk
Thanks I appreciate it, cause Iām confused how to approach in finding the sides ...
Does the final answer include ālā and āomegaā?
Ohh
serene viper
Does the final answer include ālā and āomegaā?
Nope according to my friend is 324 but he couldnāt explain it cause he had to go to sleep
serene viper
Yea since its a square finding one side of the inner rectangle would be enough to find the whole area of the room
waxen hawk
I thought it is solved?
Let me ran on that poor system of equations
I found omega = 6 and l =3
Which, after we plotting them into the lengths of the square room, gives us 324 aka 18^2 as the area of the room
waxen hawk
The top equation is derived from the property of square (the wide and height are the same in such a shape)
serene viper
Ah I see now makes sense
waxen hawk
While the bottom is derived from the given information that the rectangle tile has an area of 18
serene viper
Damn did not think of system equation lol
waxen hawk
Damn did not think of system equation lol
Remember that once youāre given to variables
Let me think how to phrase my words
if there are ārā variables in a situation, then you would need ārā of equations to solve them
And r is numbers
For instance, given you have l and omega, that is, two variables
Then you need to find 2 equations in order to solve them
And, noted that, it is 2 ādifferentā equations involved these 2 variables ālā and āomegaā
serene viper
Makes sense for sure now, at first I had in mind creating 15 + s and 12 + w but wasnāt sure how to use it because the chapter the book is based on polynomials lol
And forgot system equations were a thing to help solve situations like these where you have 2 missing variables
Thank you so much for the explanation, I can definitely sleep well tonight in my igloo š
waxen hawk
No problem, now you can sleep well in your ice home.
serene viper
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vocal sleetBOT
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daring topaz
heya, can anyone help explain this one
vocal sleetBOT
heya, can anyone help explain this one
daring topaz
vocal sleetBOT
daring topaz
been here for a solid hour
so i know the first step is to take the partial derivatives
and i get
$f_x1=2_x1-4_x2=0$
twin meteorBOT
The Lean Monster
pale perch
$f_{x_1}=2x_1-4x_2=0$
twin meteorBOT
Aā¤Ć
pale perch
okay, sure
daring topaz
ye mb i was tryin to figure out the latex notation
so i have the partial derivatives for x_1 and x_2
as far as i'm aware, we set these equal to 0 and solve
pale perch
indeed
daring topaz
i just get x_1=0 and x_2=0 so i'm assuming i did something wrong
pale perch
$f_{x_2}=-4x_1+4x_2=0$
$$x_2=x_1$
$$2x_2=x_1$$
$$x_2=2x_2\implies x_2=0 \implies x_1=0$$
twin meteorBOT
Aā¤Ć
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pale perch
seems fine
pale perch
there is such a thing, i just need to go find it, been a while
daring topaz
ye
this is totally new to me lol
prof dropped this on my class without explaining
probably assumed we knew it
anyway here's what i get
$f_{x1x1}=2$
$$f_{x2x2}=4$$
twin meteorBOT
The Lean Monster
pale perch
daring topaz
yeeee
both my second partial derivatives are above 0
so looks like we have a minimum?
oh wait
i didn't read lmfao
pale perch
looks like a saddle
daring topaz
so 2*4-some term i don't know how to calculate
is that last term basically a partial derivative but i take the derivative of both variables
pale perch
the last term is just the x partial derivative of the y partial derivative
pale perch
for your purposes its $f_{x_2 x_1}$
twin meteorBOT
Aā¤Ć
pale perch
(-4)^2 yeah
daring topaz
ye so we get 4*2*(-4)^2
alright epic
so does that mean i'm done lol
the goal here is to find the optimum but i can't think of any other place where the tangent will equal 0
vocal sleetBOT
@daring topaz Has your question been resolved?
shrewd elbow
vocal sleetBOT
safe wharf
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Show
shrewd elbow
so I differentiated it
to get 2mx x>=1
and 6x + k/2(x+1) when 0 < x < 1
but after putting 8 and 1/8 it doesn't cancel to a value
near tartan
as simple as it gets
just do the continuity and differentiability tests, you will get 2 equations in m and k to solve them
then u can simply find both of those derivatives to get the value
shrewd elbow
can you gimme a sample or solve one of em?
vocal sleetBOT
@shrewd elbow Has your question been resolved?
shrewd elbow
<@&286206848099549185>
vast shale
kya hua
jaha f(8) lena hain , waha x >= 1 ki function ki value lagao
aur f(1/8) lena hain waha woh 0<x<1 ki value lagao
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shrewd elbow
jaha f(8) lena hain , waha x >= 1 ki function ki value lagao
aur f(1/8) lena hai...
so I differentiate it then put the values?
I've done something wrong ig
shrewd elbow
jaha f(8) lena hain , waha x >= 1 ki function ki value lagao
aur f(1/8) lena hai...
I differentiated and put the values in but it's wrong.
shrewd elbow
<@&286206848099549185> can someone check this solution?
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ionic marlin
what test can I use here?
ionic marlin
to find if it converges absolutey/conditionally
i thought if we take absolute value then it becomes 1/log(n)^n
and then i thought we oculd use some kind of comparision test
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Please stick to your channel.
sly sierra
and then i thought we oculd use some kind of comparision test
sounds promising, any thoughts on what to compare it with?
ionic marlin
sounds promising, any thoughts on what to compare it with?
i thought we could do it with 1/log n
but then we need to prove 1/log n converges for which we can use ratio test
sly sierra
but does the sum(1/log n) converge?
ionic marlin
but does the sum(1/log n) converge?
yeaaa i dont know how to prove if it does or not
i am stuck there
ionic marlin
do you agree with that?
oh so you want to compare it with 1/n??
sly sierra
oh so you want to compare it with 1/n??
well sum(1/n) doesn't converge either (it's the harmonic series)
sum((-1)^n / n) converges, but not absolutely, so the comparison test can't be used with it
but since sum(1/n) doesn't converge, sum(1/log(n)) can't converge, so i wouldn't use either one for the comparison
what about sum(1/n^2)?
ionic marlin
what about sum(1/n^2)?
yeaa that converges
so
something like:
1/log(n)^n < 1/log n < 1/n^2 and since 1/n^2 converges 1/logn^n also?
sly sierra
the 1/log n in the middle isn't correct, try just directly comparing
1/log(n)^n < 1/n^2
ionic marlin
the 1/log n in the middle isn't correct, try just directly comparing
1/log(n)^n ...
got it
thankyouu for all the help
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last canopy
Hey
I want to know how and from where does the extra 1 revolution come from ( the answer is 4, i looked yt videos but didnt understand a thing
gritty sage
Hey
I want to know how and from where does the extra 1 revolution come from ( t...
The center of circle A is what travels around circle B.
outer warren
last canopy
https://en.wikipedia.org/wiki/Coin_rotation_paradox
i read the entire thing.
but i still didnt understand how
last canopy
The center of circle A is what travels around circle B.
i don think so
gritty sage
The center of circle A moves, right?
last canopy
nope
gritty sage
OK, get two coins.
last canopy
it travels like the coins in the above link ( gif)
last canopy
OK, get two coins.
i did
last canopy
i want to know, how does the extra 1 come from ( in mathematical sense
gritty sage
Yes, and I'm telling you that.
last canopy
Then, move the other one around the stationary one.
i already did that,
it came out to 2 rotations
gritty sage
I don't care what it came out to.
gritty sage
Did the center of the circle that you moved move?
last canopy
umm yes ig
gritty sage
How far?
last canopy
i dont get what u are trying to tell.
last canopy
the centre moved in the respect to the 2nd plane ( table) i put it on
but it didnt move if i take the respect of the coin itself
gritty sage
So what?
last canopy
werent u going somewhere with it?
gritty sage
Obviously one circle moved regardless of your frame of reference.
gritty sage
Pick one of them and tell me how far the center went.
last canopy
By tracing the center's movement.
^^ why is this neccesary
gritty sage
How am I supposed to lead you to the answer without taking the steps to lead you to the answer?
Do you want me to lead you to the answer before I can continue leading you to the answer?
last canopy
gritty sage
Right, now trace the center of the moving circle.
gritty sage
I know that.
Since you know how it moves, trace the movement of the center of the moving circle.
last canopy
like this
gritty sage
OK, what's the radius of the traced circle?
hoary cypress
last canopy
OK, what's the radius of the traced circle?
3x+ x = 4x
last canopy
https://www.youtube.com/watch?v=FUHkTs-Ipfg&vl=en
i alr said i watched the vid and didnt understand.
gritty sage
OK, so what's the circumference of the circle?
last canopy
3x+ x = 4x
wait no that's wrong
hoary cypress
i alr said i watched the vid and didnt understand.
mb
last canopy
3x+ x = 4x
no i am right
gritty sage
Yes, if x is the radius of the small circle.
last canopy
OK, so what's the circumference of the circle?
2 pi 4x
gritty sage
OK, what's the circumference of the moving circle?
gritty sage
OK, so you have a circle with a circumference of 2 pi x and you need to travel 8 pi x along its edge.
That will be 4 rotations.
gritty sage
You're welcome.
last canopy
this applies to circles with any measures right? ( even equal
oh yeah
it does
thanks so much fr
gritty sage
Yes, it will always need 1 extra rotation.
You can see that by doing the same exercise with 3 replaced by m.
The radius of the traced circle will be mx + x = (m + 1)x.
And then you can continue from there.
last canopy
alright
gritty sage
The idea behind it is that you can take your traced circle, cut it at one place and then lay it out in a straight line.
Then you have the circle rotate to get it to move along that straight line.
last canopy
if i take the circle ( with 3x as radius)
and lay it out in a straight line the answer comes to 3
last canopy
oh the one traced by the centre
gritty sage
Right.
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gritty sage
No problem.
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hexed ivy
How do u write an equation using this
vocal sleetBOT
How do u write an equation using this
hexed ivy
Does the half life matter?
scenic ravine
Hint:- It;s a first order reaction
$\frac{d\left[R\right]}{dt}=k\left[R\right]$
twin meteorBOT
Why am. I here
scenic ravine
!original
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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.
hexed ivy
Idk what that is
How do u find the initial value
That is the whole question
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rugged orchid
bit of a terminology question here
vocal sleetBOT
bit of a terminology question here
rugged orchid
what does "complementary" mean here?
ancient knoll
dropped a word maybe? probably meant to be complementary cumulative distribution function
so 1 - P( X <= k) = P( X > k) which looks like the form you have
rugged orchid
the Pr{} is acting like a CDF right?
and also then what's a complementary cumulative distribution function
oh
the cdf goes from -inf to some k
complementary cdf as in going from k to infinity
is that right?
ancient knoll
yes
vast shale
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spiral turtle
,rccw
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spiral turtle
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@vast shale
vast shale
1
spiral turtle
So there are 12 months in a year, right?
spiral turtle
So let's call the original function, f(x) = 1000(1.08)^x
vast shale
alright
spiral turtle
And we want to find g(x), such that g(12x) = f(x)
vast shale
yes
vast shale
g(x) = f(x/12)?
spiral turtle
What is f(2)?
vast shale
dont we divide the whole equation by 12?
f2 is 200
oh wait
nvm
f(2)= 1000(1.08)^2
spiral turtle
exactly
spiral turtle
so f(x) = 1000(1.08)^x
f(2) = 1000(1.08)^2
f(12928) = 1000(1.08)^12928
f(30/19) = 1000(1.08)^(30/19)
what is f(x/12)?
vast shale
f(x)=1000(1.08)^1/12X?
vast shale
yes
vast shale
yes
spiral turtle
well, sorry,
vast shale
oh ok
spiral turtle
I don't understand why you put x in the denominator
vast shale
so what can i put as the final equation?
spiral turtle
If you're asking me this, then it doesn't sound like you understood any of the work.
so
here is what I'm going to ask from you
please start here #help-17 message , and go back through the work, and if you get the a point where you don't understand something that I did or the reason why I did something, link me it and ask me about it.
vast shale
alright thank you
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hexed shore
Can someone help explain this limit? I'm confused on why 3 when pulled out from the square root is just 3. I understand, that since the limit is to negative inf, the absolute value of x is -x. But why is 3 just 3, and not sqrt(3). Wouldnt the answer be 2/-sqrt(3) ?
vocal sleetBOT
Can someone help explain this limit? I'm confused on why 3 when pulled out from ...
lucid crypt
when you pull constants out of roots they dont need an absolute value
frozen bobcat
it should still be in a square root
lucid crypt
that too
frozen bobcat
looks like a mistake.
hexed shore
Okay so it's just wrong lol. I see
Yeah, the fact the 3 wasnt in the square root was my only question. I understand the absolute value stuff
I started thinking Im insane and that you only need to root the x if it's multiplied together
daring marsh
@frozen bobcat sir please help me in 37
dark void
what is 37
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frozen badge
Help.
f(x) =(a + b)Ā² -1
vocal sleetBOT
Help.
f(x) =(a + b)Ā² -1
echo fiber
Help.
f(x) =(a + b)Ā² -1
whats the question
dawn kestrel
maybe take a screenshot or smn?
frozen badge
Can you explain how I solve it Iām asking for a friend
Is it like a graph or something
echo fiber
we cant solve it without the question
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hollow prism
is Z5 x Z5 x Z5 -> Z25 x Z5 isomorphic?
vocal sleetBOT
is Z5 x Z5 x Z5 -> Z25 x Z5 isomorphic?
empty frigate
is Z5 x Z5 x Z5 -> Z25 x Z5 isomorphic?
no, one of them has an element of order 25 (namely (1,0)) and the other doesn't (anything multiplied by 5 is (0,0,0))
hollow prism
no, one of them has an element of order 25 (namely (1,0)) and the other doesn't ...
f((a,b,c))=(5a+b, c)
f(mod 5, mod 5, mod 5) = (mod 25, mod 5)
empty frigate
well that's a bijection, but you said "isomorphic" so i assumed you were talking about some sort of structure
they are isomorphic as sets because they both have cardinality 125, but no isomorphism preserves + or *, assuming that the structure on Zn is modular arithmetic
hollow prism
Oh sorry maybe its a different question then,. the original q was Prove or disprove: Z5 x Z5 x Z5 is isomorphic to Z25 x Z5
Zn is addition mod n
empty frigate
f((a,b,c))=(5a+b, c)
f((0,2,0)+(0,3,0)) = f((0,0,0)) = (0,0)
f((0,2,0))+f((0,3,0)) = (2,0) + (3,0) = (5,0)
so that's not a homomorphism
the issue is that Z25 x Z5 has elements like (1,0) in it, that are still not zero when you multiply by 5, and Z5 x Z5 x Z5 doesn't
so they're not isomorphic
hollow prism
no, one of them has an element of order 25 (namely (1,0)) and the other doesn't ...
is this a theorem? I want to disprove it then since you convinced me
how to write a formal disproof*
empty frigate
that's pretty much a proof, you might just want some extra details
namely that isomorphisms preserve order, if you haven't already proven that
hollow prism
i might know that isomorphisms need to have the same orderfrequency to be isomorphic but idk if it is the same thing ur talkin about
empty frigate
namely that isomorphisms preserve order, if you haven't already proven that
and then just like
every element of Z5 x Z5 x Z5, if you multiply it by 5 you end up with (5a,5b,5c) = (0,0,0)
and then if you assume something gets mapped onto (1,0) in Z25 x Z5 you get a contradiction
empty frigate
i might know that isomorphisms need to have the same orderfrequency to be isomor...
"order" as in the number of times you have to add the element to itself to get 0
hollow prism
yep
empty frigate
in Z5 x Z5 x Z5, everything is order 5 (except (0,0,0) which is already 0 and therefore has order 1)
in Z25 x Z5, (1,0) is order 25
empty frigate
i don't think it really has a specific name? it's kind of just an instance of the general principle where isomorphisms tend to preserve basically everything
but it should be fairly simple to just like
you can prove by induction that f(nx) = nf(x), for a natural number n and an element x and f any homomorphism
and then you can just take the definition of order and apply that to it
nx = 0 iff f(nx) = 0 iff nf(x) = 0
empty frigate
you can prove by induction that f(nx) = nf(x), for a natural number n and an ele...
the first one because f is an isomorphism, the second one because this
empty frigate
nx = 0 iff f(nx) = 0 iff nf(x) = 0
and then from that you get that the order of x and the order of f(x) are the same
hollow prism
and then from that you get that the order of x and the order of f(x) are the sam...
Thoughts ? Sorry Im simple minded I do not want to remind myself of induction haha
Z5 x Z5 x Z5:
ord((0,0,0))=1
anything else is ord 5
Z25 x Z5:
ord((0,0))=1
ord((1,0))=25, which is not in Z5 x Z5 x Z5
Since isomorphisms must preserve order, they are not isomorphic.
empty frigate
yep that works
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viscid zealot
Linear Algebra Question: If I get the kernel of a matrix to be the zero vector, what is its dimension?
vocal sleetBOT
Linear Algebra Question: If I get the kernel of a matrix to be the zero vector, ...
sly sierra
do you know how dimension is defined?
sly sierra
number of independent column vectors
but yea
maybe think about it geometrically
say we're in 3 dimensional space
what does a 2-dimensional subspace look like?
sly sierra
nope, that's one dimensional
viscid zealot
so a plane
sly sierra
yep
viscid zealot
so a point would be zero dimensional
sly sierra
now you have a vector space which is just the origin basically
yep zero dimensional is correct
sly sierra
sure, cheers
viscid zealot
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tawny vessel
can someone explain me this pls š
vocal sleetBOT
can someone explain me this pls š
tawny vessel
<@&286206848099549185>
vast shale
.
tawny vessel
just do what it says
yea i dont know how to do it, its really confusing i need someone to explain it to me
lavish river
when you expand it out you get that. when n=0 or 1 it's obvious. from there just inductively multiply by a+b and you'll get the next one thus it holds for all n. you can look at the binomial expansion, each term is the sum of the two above it
halcyon shore
yea i dont know how to do it, its really confusing i need someone to explain it ...
basically
do u know the pascal triangle
tawny vessel
yes i did expand it and apparently we have to take "n" value as K and multiplying both sides with (a+b)^1 we i get (a+b)^k+1
tawny vessel
do u know the pascal triangle
yea
halcyon shore
can someone explain me this pls š
well c is each position for the pascal triangle
so if (a+b) is adding then every part of the equation is positivo
POSITIVE
tawny vessel
well c is each position for the pascal triangle
halcyon shore
and then for the left side of the equation (a) u start from n and every time u substract 1 to the exponent until u reach b^n
halcyon shore
in here ur gonna take for C n+1 rows
so if n = 2
ur gonna take the 3rd row
1 2 1
those are the values of C
and then if u got (x+y)^3 for instance
u would use the 4th row 1 3 3 1
followed by the eeuqations
halcyon shore
can someone explain me this pls š
this shi
halcyon shore
ALRIGHT WHAT AM I WATCHING
halcyon shore
ITS WHAT IM TELLING U THERE IS NO OTHER WAY
tawny vessel
the first pic, look under (a+b)^k (a+b)
this is so fucking confusing, ive been breaking my head over this for so long š
halcyon shore
and then if u got (x+y)^3 for instance
here u do x^3
then u do 3x^2 * y
u substract the exponent of one variable and add it to the other one
tawny vessel
ahhhh i see
halcyon shore
ahhhh i see
follow
what would be the rest of the equation
i gave u 2 components
give me the rest
tawny vessel
but is it necessary to write so fucking much like in the pic ive shown you or can i shorten it
halcyon shore
Man thatās theory
it depends on the number of n
until the second component (in ur case b) reaches b^n
halcyon shore
and then if u got (x+y)^3 for instance
do this one
tawny vessel
until the second component (in ur case b) reaches b^n
so can i write it as KC0a^k+1+KC1a^k+KC2a^k-2.......+KCkb^k+1
tribal moss
first of all, you should have said at the beginning that you were talking about the inductive proof of the binomial theorem, this is clear from your pictures that you pasted here. You will find a lot of exactly such proofs written on the Internet, I don't think anyone here would spend two hours writing such a proof, which is not difficult, but it is time-consuming.
tawny vessel
add and substract from the god damn exponents
aight got it
halcyon shore
tawny vessel
first of all, you should have said at the beginning that you were talking about ...
well sorry i didnt mention it clearly, mb
tawny vessel
DO (a+b)^3
alr wait
halcyon shore
u donāt need to add the 3 dots
halcyon shore
also when u reach a^0 ur done donāt continue
and donāt wirte the a because anything ^0 is 1 so donāt matter
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topaz swift
wouldnt the first equation be on top?
vocal sleetBOT
wouldnt the first equation be on top?