because I don't know if I have to do it set by set
#help-0
flat saddle
as in if I should do for all x in A x1 is in B and x2 is in B therefore A is a subset of B
potent garnet
The only x that satisfy the quadratic equation are x=1, and x=3, so A = {1,3}. Since A = B = {1,3}, they are identitical.
wide bay
lone heartBOT
wide bay
I need help with both of these problems please
potent garnet
So for the first problem, I would find the area of the whole rectangle (pool+deck) and subtract the area of the inner rectangle (pool).
wide bay
thats what i first assumed but why does it say the widwth if it is 2 meters
should I add the 2 to the 12?
potent garnet
First of all, the deck is going around the whole pool, so you don't just add something to the width of the pool. Second of all, you need to add 4, since you are adding 2 on each side.
Does that make sense?
wide bay
only slightly, why would i add 4 if i only need the one side of width
cause rectangles are lw=a
flat saddle
yeah and the length and width will be increased by 2 on each side
wide bay
mhm i do
flat saddle
look at the picture I sent
flat saddle
if the pool is 20m long and the deck is 2m longer at each end then the decks length is?
wide bay
24m
flat saddle
repeat the same for the width
wide bay
so the width would be 16
so my final answer is 144
tyvm
do you know how to do #20 by any chance
.close
lone heartBOT
lean lily
y is just a random variable like x, you decide what it equals, and by convention people in a lot of exercices set f(x)=y
yes
this is wrong btw
f(y) = |2y|^3 = 8|y|^3
he cubed the 2 and kept in inside
ye
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
vale wigeon
@alpine sable what are those strange black spots over the y's at the end?
right...
and i presume that the L shape with a number inside it means factorial?
ok then y = e^x
hybrid rune
hi can someone help me with this question please thank you
lone heartBOT
hi can someone help me with this question please thank you
real gazelle
hi can someone help me with this question please thank you
how many days is 2 weeks
hybrid rune
14 days
real gazelle
yup
so if 3 carpenters do one wardrobe in 14 days
how much does 1 carpenter do in 14 days
(assuming they work independently)
real gazelle
not quite
dividing by 3 is right though
but which number do you want to divide by 3
real gazelle
no 14 is the # of days that stays the same
what changes is how much wardrobe they make
so if 3 carpenters make 1 wardrobe in 14 days
how much does 1 carpenter make in 14 days?
hybrid rune
0
real gazelle
how did you get 0
hybrid rune
i have no idea actually, i don’t understand
real gazelle
lemme ask you a different question
hybrid rune
3/1?
real gazelle
if three people can eat a cake in one day, how much can one person eat in a day?
hybrid rune
1
real gazelle
no if the three of them together eat 1
then one of them can't eat 1
right?
how much of the cake can one of them eat
hybrid rune
oh yeah 1/3
real gazelle
yup 1/3
so going back to the original question, if 3 carpenters make 1 wardrobe then how much does 1 carpenter make
hybrid rune
1/3
real gazelle
yup
so then if 1 carpenter makes 1/3 wardrobe in 14 days
how much does 1 carpenter make in 1 day
hybrid rune
is it 1/3 divided by 14?
hybrid rune
okay 1/42
real gazelle
yup
so then if it's 1 carpenter does 1/42 wardrobe in 1 day
then how much do they do in 6 days
hybrid rune
multiply by 6
hybrid rune
which is 1/7
real gazelle
yup!
real gazelle
no prob! but that's not the final answer
hybrid rune
oh
hybrid rune
7
real gazelle
yep! that's the answer
lone heartBOT
lone heartBOT
Available help channel!
pliant flume
Hi people, could anyone tell me what the big line in the middle means?
lone heartBOT
Hi people, could anyone tell me what the big line in the middle means?
@pliant flume Has your question been resolved?
empty plover
where does this come from?
lone heartBOT
where does this come from?
keen bear
are you asking how the identity holds?
trig functions mantra: when in doubt, draw a triangle
$n^2+n+1=\frac{n^3-1}{n-1}$
ocean sealBOT
GoldenPhoenix
empty plover
$n^2+n+1=\frac{n^3-1}{n-1}$
And?
empty plover
trig functions mantra: when in doubt, draw a triangle
I am not sure how that would go
empty plover
arctan is the inverse of tan so it takes arguments from -inf to +inf
keen bear
not what is its domain, what type of argument does it take? an angle measure, a fraction, an integer?
keen bear
tan(theta)=opp/adj
gotta be careful to include the argument here
empty plover
Deal
keen bear
because we can rewrite this as theta=arctan(opp/adj)
do we have a fraction in the argument of arctan here?
empty plover
yes
keen bear
so do we know the opposite and adjacent sides for our triangle?
empty plover
so the opp side is length 1 and the adj side is length n^2+n+1?
keen bear
yes
empty plover
but how do i draw the n^2+n+1 side ?
keen bear
draw a triangle and label one side with that polynomial
empty plover
and how does this help
keen bear
well, it turns into a difference of two other arctans, right?
empty plover
well, it turns into a difference of two other arctans, right?
when? :/ i now just have a triangle
keen bear
(I'll be honest I'm mostly spitballing here to stumble through it, but this is the basic process for how to demonstrate that a trig identity holds)
keen bear
when? :/ i now just have a triangle
you have a triangle representing the left side, but we have a right side as well
coral prairie
Is anyone able to help me with my math problems
keen bear
so our goal is to try and get from the triangle we have to get to the right side
empty plover
okay but isnt the other side angle just arctan (n^2+n+1)?
coral prairie
so our goal is to try and get from the triangle we have to get to the right side
can anyone help me please
keen bear
it looks like you already have someone helping you in your channel
coral prairie
it looks like you already have someone helping you in your channel
I would really appreciate it
empty plover
go and help him @keen bear its fine ill try to walk through it again with what you told me
lone heartBOT
@empty plover Has your question been resolved?
empty plover
where does this come from?
any clue?
languid bolt
<@831267103293964299> Has your question been resolved?
btw click the X if you're not finished so it doesnt autoclose
empty plover
what x
empty plover
its not really important its just bothering me that its put in my notes as an example with no justification for it whatsoever as if its obvious
languid bolt
nvm gtg eat, i dont understand
empty plover
Deal
fervent grail
#help
fervent grail
The number of real solution of x^2-2x+2+|x-1|=0 is ?
empty plover
none
fervent grail
Any other way ?
fervent grail
And the laziest way
But it can't be done without a graphing calculator
Any other way ?
fervent grail
Ikt but I want to do it with evaluation and all
iron mulch
Okay well use the quadratic equation to factor the first 3 terms of the equation and see if it gives you any real answer, and then see if there are real answers plug it into the absolute value function and see if it gives you a 0
Otherwise if the roots of the quadratic don’t work then there is no real solution
iron mulch
What
tacit arch
I am not able to remove the mod
do you know the definition of absolute value
fresh parcel
well you could do casework for x<1 and x>1
and solve both of those quadratics
to see if it gives you a solution
lone heartBOT
@fervent grail Has your question been resolved?
azure trout
lone heartBOT
azure trout
How would I start with this?
languid bolt
multiplying both sides
ocean sealBOT
MarveI
azure trout
so its the first one
azure trout
languid bolt
$(5\sqrt{3} - 2)\sqrt{2} \neq 5\sqrt{3} - 2\sqrt{2}$
ocean sealBOT
MarveI
azure trout
ive legit tried everything
languid bolt
$\sqrt{2}(5\sqrt{3} - 2)$
ocean sealBOT
MarveI
languid bolt
do you know how to distribute the square root of 2?
languid bolt
ye
azure trout
lone heartBOT
azure trout
i tried solving for x but it didnt make sense
nvm im dumvb
forgot to make it =0
.close
lone heartBOT
languid bolt
ok?
lone heartBOT
Available help channel!
orchid heron
what is the difference between the line and vector
lone heartBOT
what is the difference between the line and vector
abstract fractal
Ones a line, the others a vector
orchid heron
vector is the direction ?
azure trout
lone heartBOT
azure trout
.close
lone heartBOT
lone heartBOT
✅
azure trout
Is this correct?
frigid rune
Yes that's correct
ancient moss
yes
ember grotto
I want to get target's relative angle to my plane's heading vector
The compass is my heading angle and theta is its standardized value (I had to do some computations to transform game's output to standard mathematics)
x and y are my plane's coordinates and x2 and y2 are target's coordinates
Another important note is that the y axis is reversed in game's output so deltaY is actually -deltaY so in some of the calculations I used -deltaY to neutralize the reversed axis' effect
distance variable is calculated easily based on deltaX and deltaY
From now on please correct me if i'm wrong
Now let's assume I am at the center of coordinates (0, 0)
Let's calculate line equation of my plane's heading vector
It will be: y = tan(theta).x
So tan(theta).x - y = 0
Now based on the formula of distance between a dot and a line which is:
Ax + By + C = 0 => distance = (|A.x0 B.y0 + C|) / sqrt(X0^2 + Y0^2)
A = tan(theta); x0 = deltaX; B = -1; y0 = -deltaY; C = 0;
lineDistance variable is calculated:
(|tan(theta).deltaX + deltaY|) / distance
Now the thing is if I did all the calculations correctly, distance always would have been greater than line distance. But most of the times distance is less than lineDistance which is odd
By the way all the distances (x, y, x2, y2) are between -1 and +1
tacit arch
show your work?
ember grotto
show your work?
What work? On paper?
tacit arch
if I did all the calculations correctly
ember grotto
Ah this
Ok
I mean most of the work is code
Here it is:
deltaX = x2 - x;
deltaY = y2 - y;
theta = -compass + 90;
nomalizedTheta = degreeNormalize(theta);
distance = sqrt(deltaX * deltaX + deltaY * deltaY);
lineDistance = (tan(radians(nomalizedTheta )) * deltaX + deltaY).abs() / distance; // .abs() is |-1| ==> +1
alpha = degrees(math.asin(lineDistance / distance));
Let me simplify it
I hope it's clear
I have some stuff written on paper but those aren't very clear 😅
Compass is my plane's heading angle
Hopefully it's fine to ping helpers now
<@&286206848099549185> 👋 😅
Cheers!
iron mulch
ember grotto
Oh well I can write it somewhere on paper or something
tame willow
I just mean like
What’s the problem you want to solve
If it’s within code I cannot really read it
ember grotto
I want to get target's relative angle to my plane's heading vector
The compass i...
Have you checked this? 😄
iron mulch
Sorry I only know basic python :)
ember grotto
Have you checked this? 😄
@tame willow
Making sure you haven't missed this message 😄
lone heartBOT
@ember grotto Has your question been resolved?
lone heartBOT
@ember grotto Has your question been resolved?
lone heartBOT
@ember grotto Has your question been resolved?
warm moth
lone heartBOT
warm moth
hey guys I am kinda noob at English
can anyone confirms that this one means the origin is at (0,5) ?
not the height of the pillar
placid zinc
The origin is always at (0,0)
warm moth
hmm
placid zinc
That's what an origin is haha
warm moth
lowest point of the cable intersecting the vertical axis
placid zinc
Lowest point of the cable is at (0,5)
warm moth
placid zinc
It says "the resultant force W(x)"
The resultant force of what?
Eh, well they're getting into what shape the wire is, I suppose.
warm moth
if I want to show sth to be first linear ode
how can I approach this qs
I got my dy/dx = W(t)/H
oh sike
gtg
someone pls give me some guidance if possible
lone heartBOT
@warm moth Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wooden owl
lone heartBOT
wooden owl
this unit is permutations and combinations
not sure how to begin solving this question
formula sheet
lone heartBOT
@wooden owl Has your question been resolved?
lone heartBOT
@wooden owl Has your question been resolved?
fossil gate
Is there any more context for the question? Or is that it? @wooden owl
lone heartBOT
lone heartBOT
Available help channel!
stable night
lone heartBOT
stable night
Hi, can someone help me with part ii?
lone heartBOT
@stable night Has your question been resolved?
distant estuary
algebra
lone heartBOT
@stable night Has your question been resolved?
lone heartBOT
@stable night Has your question been resolved?
lone heartBOT
Available help channel!
unborn meteor
lone heartBOT
unborn meteor
Question b iv
What does it mean by find the endurance limit?
‘When repeatedly subjected to force F’
And the ‘endurance limit is the force below which the steel will not break even if subjected to an infinite number of application of that force’
Meaning it can be hit by 70 Newton’s of force infinitely and not be affected at all
But if it’s hit by 71 Newton’s of force repeatedly
There will be some damage
It should be a constant value
So then how do I do this
lone heartBOT
@unborn meteor Has your question been resolved?
lone heartBOT
@unborn meteor Has your question been resolved?
placid zinc
It's not being "hit by"
It's being "stressed with"
You're trying to pull that metal bar apart by pulling on it many times
If your math is correct, then 70N of force, no matter how many times it is applied, will never break the bar.
Worth saying that 70N is very small
What did you do to get 70N?
lone heartBOT
@unborn meteor Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
vital dagger
2^* X 5* = 8000
lone heartBOT
2^* X 5* = 8000
vital dagger
2^* X 5* = 8000
sorry the asterisk is supposed to be the variable x
noble sinew
$2^x \cdot 5^x=8000$?
ocean sealBOT
ScapeProf
pliant wave
these are private help channels. if you want to have one of your own, read the channel instructions first
silent sapphire
these are private help channels. if you want to have one of your own, read the c...
oh ok thanks
vital dagger
Now it is readable
yea how do i solve this
actually the base number 2 is raised to the power of 2x not x
mb
noble sinew
Prime factor 8000
kindred anchor
Why not use logarithm?
noble sinew
Its the same
vital dagger
Why not use logarithm?
this is supposed to be mainly indices only
vital dagger
Its the same
what am i supposed to do
noble sinew
Can you use a calculator? Can you prime factor?
solid imp
lone heartBOT
solid imp
hi so the question was what are the asymptotes
and give their function
SA is diagonal asymptote
but id understand that ''In x'' means
in minus inf and in positive inf
like dont both asymptotes exists in both + & - infinity
vale wigeon
sure, the asymptotes themselves are straight lines that extend infinitely in both directions
but your graph only approaches the slanted asymptote as you go left
and only approaches the horizontal asymptote as you go right
solid imp
so the In +inf and In -inf talks about the direction of the x-axis
alright thankyou
.close
sick venture
I have this spectral curve plotted as a function of wavelength. However as you can see, it bottoms out at around 600nm. I would like to extend the characteristic of the slope so that it continues at the same rate it was declining before bottoming out (regardless if that decline is exponential). I want to essentially remove the bottoming out and instead extend it's decline down to 0. How would I go about this?
lone heartBOT
I have this spectral curve plotted as a function of wavelength. However as you c...
@sick venture Has your question been resolved?
noble sinew
Remove the points from 600 to 610 or whatever
And then just fit the points until 640 or whatever
Now you have a regression line you can continue
sick venture
And then just fit the points until 640 or whatever
Is there a way to make the extension mathematically relevant to the change that was taking place from the point of when the slop started?
noble sinew
Wdym
sick venture
Meaning factor in the trajectory of the slope. So that the values which extend it are relevant to the path it was taking
With the bottoming out values removed
I tried by finding the medium of relative change between each point. Then deducting that value from each previous point down to 0.
But I don't think it was very elegant. Visually it made the extension look like I all of a sudden just added a straight line past the point
Meaning, it didn't seem to follow the overall trajectory of the slope in a smooth way
example
that definitely AIN't it
I need a way to know the trajectory it is moving, so I can generate relevant values to continue the slope down to 0
sick venture
Wdym
This is tabulated data. In csv form. It's not just a graphic.
I'm working from the actual values
sick venture
exactly my issue
How to generate values to continue the slope, when it's not linear
sick venture
And you are trying to make it linear
Not my goal, only the outcome of not knowing how to continue it's none linear slope
sick venture
How
noble sinew
Any program
sick venture
Let's say I took the range of values between 610nm to 650nm. How can I find out what the none linear change is. So that I can generate relevant values to extend the slope to 0.
?
noble sinew
y=a * b^x
If its perfect exponential its just picking two points and solve for a,b
Otherwise you need regression
If that is the case use any program to do that for you
sick venture
I don't believe it's exponential. It seems to hit a straight line portion after the toe
noble sinew
After what?
sick venture
I'm really don't know jack about math HAHA. What's a regression
noble sinew
,w linear regression
noble sinew
Is an example (linear regression)
sick venture
toe
noble sinew
You have points which aren’t perfectly linear so you make a least squared fit for it
sick venture
What's a least squared fit?
noble sinew
Google is a thing and I don’t see how its relevant to what you are asking
sick venture
Google is a thing and I don’t see how its relevant to what you are asking
I'm just following that you said I need to make a least squared fit. Again I need help with the math. I don't understand any of these concepts
noble sinew
And like I said any program can do it
sick venture
Okay, how do I do it in google sheets
sick venture
If I wanted help through google I wouldn't have asked here
I thought you'd actually give me the answer. I don't study math. I'm just trying to solve a problem
noble sinew
And I don’t want to google how to do it for you
sick venture
Don't get me wrong I appreciate the source of concepts. But can we just cut to the chase
sick venture
Save me the hassle of trying to understand it for like 2 hours
noble sinew
There is nothing to understand
sick venture
This is tech support
What's the difference?
noble sinew
You just need to click whatever buttons
Your program needs
Which google tells you
How is this math
sick venture
So your response to me not understanding the concepts is that I should use google or figure out how my program can do the math. I'm trying to understand the math so I can apply it. If you understand how to solve this problem why are you redirecting me to figure the rest out
sick venture
Okay great, this is math help. Teach me
noble sinew
So I said go google how to do it in your fav program
You refused and wanted me to google it for you
For me to type what google said?
sick venture
So the program was written by AI, the math that the program operates on is not mathematically producible by humans?
noble sinew
What?
sick venture
You're saying the math to solve this problem is not doable by hand
Who wrote the script
noble sinew
I’m saying the calculations aren’t feasible to do by hand
sick venture
So AI discovered this mathematical concept, and the only way to execute it, is to use the program the AI wrote. Or maybe just maybe, people who understood the math wrote the program. To complete the task. Of which they understand the math and can reproduce it. Because how else would they write the program.
noble sinew
And your program is just a calculator
sick venture
So google sheets is nothing but a calculator
noble sinew
All I said was google and figure out how your fav program calculates line of best thing for you
Yes?
Like what
I don’t understand why you are getting mad
sick venture
That's different to using a calculator. That's finding an operation. Preset calculations. Of which was written by a human. Let's skip the part where I hope and pray I can find this very specific operation available in google sheets. And just tell me the formula. Is it really that difficult?
tell me the secret formula crabs
noble sinew
$$\hat\alpha=\bar{y}-(\hat\beta \bar{x})$$ and $$\hat\beta=\frac{\sum_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^n (x_i-\bar{x})^2}$$
sick venture
Thank you. Can you define the variables please
noble sinew
y_i=alpha+beta x_i+eps_i
ocean sealBOT
ScapeProf
sick venture
?
noble sinew
?
noble sinew
I did
sick venture
I only symbols I understand in there is sum
noble sinew
Seems like just using your fav program is faster doesn’t it?
y=alpha+beta x is linear relation
sick venture
Not if you want to understand what you're doing
sick venture
I'm surprised how many absolute symbols there is in math
I was under the impression, most were just definable variables per equation. Like programming
Thanks for your help
So for this specific curve, it would require a linear regression right?
Not a nonlinear regression?
dark hull
so for this question
lone heartBOT
so for this question
weary wyvern
This is not a sequence
dark hull
$\frac{n^n}{n!} \geq \frac{n^n}{(n+1)!}$
ocean sealBOT
Kekistan
dark hull
This is not a sequence
series*
weary wyvern
Wdym by a decreasing series
dark hull
next term less than the first
weary wyvern
Hmm well that's not true here
ocean sealBOT
Kekistan
weary wyvern
Each term alternates between being positive and negative
It keeps going above and below 0
Because of (-1)^(n+1)
So it's neither increasing nor decreasing
ocean sealBOT
Kekistan
weary wyvern
Well the numerator grows a lot quicker than the denominator
So the sequence tends to infinity
So it can't be decreasing
weary wyvern
dark hull
weary wyvern
It might be a good idea to plot the sequence on desmos btw, if you want to see how it behaves
rancid trail
find all the zeroes of the polynomial $f(x)=2x^4-9x^3+5x^2+3x-1$, given $\alpha=2+\sqrt{3}$, $\beta=2-\sqrt{3}$
ocean sealBOT
ThickduckPlayz
rancid trail
i feel like i need to divide $f(x)$ by $x-\alpha$
ocean sealBOT
ThickduckPlayz
gray isle
there's a nicer way to approach it
as alpha and beta are conjugates,
it would be less tedious to expand (x-a)(x-b) before doing division
alternatively since you're given 2/4 of the roots, it would also be relatively simple to consider sum and product of roots
ocean sealBOT
ThickduckPlayz
rancid trail
should i divide it with the polynomial?
gray isle
if you're using this approach yeh
rancid trail
also one doubt.
why does it make sense to divide this with the polynomial?
my teacher said it is common sense to divide the factors with the polynomial because the remainder is zero
but it doesn't make any sense to me, what am i going to do with the quotient and how is it related to the other zeroes?
gray isle
are you familiar with factor theorem
rancid trail
yeah
if a is an zero of f(x), (x-a) is a factor of f(x)
also when i divide, i get remainder to be 32x-8
gray isle
consider the factored form of a quartic polynomial (can be applied to pretty much any degree)
k(x-a)(x-b)(x-c)(x-d)
rancid trail
ok
gray isle
if you know that (x-a) is a factor,
dividing by (x-a) gives leaves you with a polynomial 1 degree lower: which makes it easier to find the remaining zeroes/roots
lone heartBOT
@rancid trail Has your question been resolved?
grave lance
lone heartBOT
grave lance
Hey I was given both of these and told I am supposed to search for the area Integral of those shown
but Im a bit confused... what exactly am I supposed to do?
I mean I'm guessing I have f_1(x,y)=x and f_2(x,y)=y²+3L²
And then integrate them over the area shown in the diagramm
but how exactly do I tackle the circle?
lone heartBOT
@grave lance Has your question been resolved?
versed crater
What does a represent
lone heartBOT
@grave lance Has your question been resolved?
grave lance
What does a represent
it's a double integral
wet pagoda
grave lance
What do you mean exactly intersect?
They way I understood is, is that I need 2 curves or lines or whatever shape to build the boundaries of one of the Integrals but I am looking at a linear function and a circle
I mean doing the double integral of the linear line would be easy
but the circle kind of gives me big???
slender marten
Just split the region up into three regions.
For the circular region at the top, it's a circle of radius L centered at (2L,2L).
Thus (x - 2L)^2 + (y - 2L)^2 = L^2.
grave lance
so one with boundaries for the dy Integral with 0 -> 2x
one with with the boundaries from 1L < x < 3L
And one with the circle as the boundaries?
But for me I'm still a bit confused how to incorporate the circle
slender marten
0 to 2x?
I'd probably solve (x - 2L)^2 + (y - 2L)^2 = L^2 for y and use the fact that the third region will be one with the positive square root. Then we clearly have L <= L <= 3L.
grave lance
well isnt the Integral for the straight with a gradient of 2 for the dy Integral 0 to 2x?
because it's not just a straight line
so it's 0 <= y <= 2x
slender marten
You're looking at the subregion labelled 1?
grave lance
yea
slender marten
Yes.
grave lance
because it's just a square region
so it's a bit easier for the circle can't I do a coordinate transform?
let x~ = x + 2L
and the same for y to put those at the center of the circle
slender marten
You could but I wouldn't if you're keeping it in cartesian anyway.
Well for setting it up anyway. For evaluating then it makes sense.
I'd imagine both are fine when I think of it.
grave lance
I'm still looking at the circle and idk how to incorporate it into the integral
slender marten
View it like this.
Since we have a circle of radius L centered on (2L, 2L) then we know it's equation is
(x - 2L)^2 + (y - 2L)^2 = L^2.
grave lance
yea
slender marten
Solve it for y.
We obtain that (y - 2L)^2 = L^2 - (x - 2L)^2. And the desired curve is
y = 2L + sqrt(L^2 - (x - 2L)^2)
R3: L <= x <= 3L, 2L <= y <= 2L + sqrt(L^2 - (x - 2L)^2)
grave lance
ok yea sure that makes sense
slender marten
Just write your integral as the sum of the three double integrals over the three regions and you should be done.
grave lance
yea I understood that part aswell
but I'm already looking at the integration of a sqrt boy is this gonna be fun again
slender marten
Have you used polar coordinates before?
If so could be worth using x = 2L + r cos(theta), y = 2: + r sin(theta). dA = r dr dtheta still.
Or just use a integral calculator.
grave lance
hm yeah this isnt just for fun in my freetime
so I gotta actually learn how to do these Integrals by hand for the test
which is gonna be annoying
slender marten
Well you have to integrate with respect to y first anyway so you end up with a y^4 so it might not be too bad.
grave lance
well if I first just do the f(x,y)=x
slender marten
Oh right.
Well in that case.
Instead of isolating for y. Insolate for x instead.
grave lance
if I get rid of the first integral for the circle I'm left with the Integral of L -> 3L of x*sqrt(x²+4Lx-3L²)
slender marten
R3: 2L <= y <= 3L, 2L - sqrt(L^2 - (y - 2L)^2) <= x <= 2L + sqrt(L^2 - (y - 2L)^2)
grave lance
y twice?
slender marten
slender marten
In the x direction you are bounding by two curves. In contrast the the other where you was bounded below by the flat line y = 2L up to the curve.
grave lance
but wouldnt those boundaries up there that you wrote be true for the entire circle area
not just half of it
slender marten
It is but the y bound ensures we have only the top part we require.
2L <= y <= 3L.
grave lance
oh right yea
I mean if in the integration I dont have to integrate a sqrt term
and just simplify it
that would already help a lot
bcs I'm pretty sure we cant even solve quadratic terms under a sqrt
I can solve something with a²-x² under a sqrt
slender marten
That's what I thought since if we integrate x we get a x^2 term to simplify things.
I got the integrand to be 4Lsqrt(L^2 - (y- 2L)^2) between y = 2L and y = 3L.
grave lance
lemme slap it into an integral calculator
slender marten
$\iint_{R_3} x \dd{A} = 4L\int_{y = 2L}^{3L} \sqrt{L^2 - (y - 2L^2)} \dd{y}$.
ocean sealBOT
stabulo
grave lance
Hm but you still have to do the ax²+bx+c term under the sqrt
which I am unable to solve
unless you can rewrite it but I cant see how
slender marten
**stabulo**
I think the integral is simply the area of a particular circle.
grave lance
is there not a way to somehow define the boundaries in a way that you get the sqrt term wheen you have to integrate by a variable that isnt inside the sqrt
I mean to me all roads kind of point towards a polar double integral
which I think simplifies the integral for the circle
slender marten
I think there's a simple way to get the answer. One second.
The integral is the area of the quarter circle of radius L.
Therefore the integral is 4L( 1/4 pi L^2) = pi L^3.
$4L\int_{y = 2L}^{3L} \sqrt{L^2 - (y - 2L^2)} \dd{y} = 4L \left(\frac{\pi L^2}{4} \right) = \pi L^3$.
ocean sealBOT
stabulo
grave lance
ok yea makes sense
but that's like just looking at the circle and knowing what the area function is and then multiplying that by the distance towards the plane
but what about when you have the term y² + 3L²
slender marten
Maybe there's a similar trick. I've not looked.
grave lance
yea bcs then it's not just a cylinder but one with one side being the 2d plane of the function f(x,y)
lone heartBOT
@grave lance Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
unreal crow
So I am solving a non linear equation of motion problem, I am told to first use the first two terms of the taylor series to change the equation of motion to one which has cubic nonlinearity, what does this mean? The equation of motion should have ^3?
lone heartBOT
So I am solving a non linear equation of motion problem, I am told to first use ...
@unreal crow Has your question been resolved?
lone heartBOT
@unreal crow Has your question been resolved?
thick star
So I am solving a non linear equation of motion problem, I am told to first use ...
yes
tacit arch
So I am solving a non linear equation of motion problem, I am told to first use ...
Show the full original question
unreal crow
Hopefully you can see that.
tacit arch
Nah just screenshot and upload
unreal crow
Nah just screenshot and upload
Okay here you go.
lone heartBOT
@unreal crow Has your question been resolved?
last ether
Show the full original question
Oh hell naw Riemann without the green role
lone heartBOT
@unreal crow Has your question been resolved?
tacit arch
Okay here you go.
it means to put $\sin(\theta) \approx \theta - \theta^3 / 3!$
ocean sealBOT
riemann
molten pivot
Am I the only one who thinks that this is phrased ambiguously
tacit arch
Am I the only one who thinks that this is phrased ambiguously
yea it is. that's why i asked for the full question. but got ignored, so /shrug
iron mulch
.close
tropic oasis
lone heartBOT
tropic oasis
could i get some help on starting out on this problem?
iron mulch
First draw or look at the graph of that function
tropic oasis
where did the 3 come from?
tropic oasis
ohh i see
okay
so its basically telling me to only go from
-2 -1 0 1
on the x axis?
for finding the area?
iron mulch
Uhhhhh wha
iron mulch
I’m just saying you need to put 6 rectangle with the rivht most ending at 1,3 and then fit them evenly spaced within thay region
I hate Riemann sums and suck at them so @tacit arch can you give help
tropic oasis
yeah i'm kind of confused 😭
tacit arch
I hate Riemann sums and suck at them so <@261933205387477002> can you give help
just pretend they're called caden sums
tropic oasis
LOL
iron mulch
tropic oasis
like i get the drawing the rectangle part
tropic oasis
is this part basically telling me my limits for my x axis for where i find my area?
iron mulch
Riemann you got this 👍🏻
tacit arch
make a table
that's the hardest part. the rest is multiplying length times width repeatedly to get areas of rectangles and adding them up
tacit arch
.
tacit arch
you only gave 3 subintervals
[-2, -1], [-1, 0], and [0, 1]
can you find a way to divide [-2, 1] into six sub-intervals, preferably each of equal length?
tropic oasis
hmm
i could divide 4 by 6?
it's basically telling me to find 6 points of those limits?
meaning theyre going to be some sort of fraction if im understanding it correctly
tacit arch
hint: length of [-2, 1] is 1 - (-2) = 3
tacit arch
looks right
tropic oasis
(1 - (-2))/6 = 3/6 = 1/2
which answer is 1/2
so my graph should have
-2, -3/2, -1, -1/2, 0, 1/2, 1?
tacit arch
-2, -3/2, -1, -1/2, 0, 1/2, 1?
your table should use 6 of these points. which 6 depends on if you're using the left or right endpoints
tropic oasis
right end points
so it would be 6 starting from the right?
which basically excludes the -2?
tacit arch
yup
tacit arch
tacit arch
https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-2/v/riem...
a rectangle's area is given by length * width. find out what the width is. if you're stuck, i recommend watching this video.
tacit arch
,w integral -2 to 1 of x^2 + 2
ocean sealBOT
tacit arch
,calc 59/8
ocean sealBOT
Result:
7.375
hm
tacit arch
,calc ((-3/2)^2 + (-1)^2 + (-1/2)^2 + 0^2 + (1/2)^2 + 1^2 + 6*2) * 1/2
ocean sealBOT
Result:
8.375
Result:
67
oh...
i see what i did wrong
i was doing x^(2)+1
in my calculator 😄
instead of x^(2)+2
tacit arch
ha
tropic oasis
Result:
```
8.375
```
i got this as my answer
tacit arch
i got this as my answer
okay maybe i lied. the hardest part is getting the right function in your calculator
flat mortar
<@&286206848099549185> is 10/31, 10/32, 10/33 answers for the question
"List 3 Intergers between 1/2 and 1/3"
thank you for helping 🙂
lilac nest
!15m
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
iron mulch
You complete fuck
pliant sun
LMAO
iron mulch
You absolute fuck WHY CAN NO ONE READ
pliant sun
feel caden's wrath
flat mortar
sorry lol
pliant sun
are we not gonna talk about the question though
iron mulch
<@&286206848099549185> is 10/31, 10/32, 10/33 answers for the question
"List 3...
There are no integers between that they are fractions
pliant sun
3 integers between 1/3 and 1/2 LMFAO
iron mulch
flat mortar
.close
lone heartBOT
iron mulch
I don’t
flat mortar
thanks
iron mulch
lone heartBOT
Available help channel!
knotty wren
good resources to learn these two units?
lone heartBOT
good resources to learn these two units?
pliant sun
good resources to learn these two units?
is this for the probability exam?
wait its probably not
I got excited for a bit
languid bolt
good resources to learn these two units?
do you want a book reccomendation or a website reccomendation
lone heartBOT
@knotty wren Has your question been resolved?
sharp moth
Am I understanding phase shift correctly?
lone heartBOT
Am I understanding phase shift correctly?
sharp moth
You have to put the periodic function in the form of Asin(B(x-C))+D
And that yields the horizontal movement of the graph (which is C)
north glacier
Basically, for all f(x+a) where a is a positive real no., the graph is shifted a units to the left. Hope this helps
lone heartBOT
knotty wren
do you want a book reccomendation or a website reccomendation
video or website
knotty wren
is this for the probability exam?
yes
knotty wren
whats that?
pliant sun
its expensive but it helped me pass it first try
its software to help study for the exam
pliant sun
best bet is probably youtube then
knotty wren
i cant find videos on youtube
pliant sun
uhhh
idrk then these concepts are pretty niche
how have you studied for the exam thus far
lone heartBOT
Available help channel!
lone heartBOT
how have you studied for the exam thus far
knotty wren
how have you studied for the exam thus far
youtube
but these topics are so specific I cant find any videos
pliant sun
how long have you been studying for the exam
I'm not sure where you could find any videos
maybe in a manual somewhere but
you might have to pay
knotty wren
rip
lone heartBOT
@pliant sun Has your question been resolved?
kind eagle
Hi, can I have help with b & c?
lone heartBOT
Hi, can I have help with b & c?
pliant sun
pa means per annum here?
kind eagle
yes
pliant sun
you can do this by just brute force
there's probably a formula that makes it faster but I can't think of it off the top of my head
kind eagle
for b, I know how to solve it, but wondering why the arithmetic series is
( 40000 * (1.04^n - 1) ) / (1.04 - 1)
and not
( 40000 * 1.04 * (1.04^n - 1) ) / (1.04 - 1)
pliant sun
ah right arithmetic series
so the increase happens
the 2nd year right
so your initial term is 40,000
not 40,000 x 1.04
kind eagle
oh right ok yep that makes sense
and for c, the equation would be arithmetic series for eleanor = geometric series for henry, but not sure how to solve it
( 40000 * (1.04^n - 1) ) / (1.04 - 1) = (10/2) * ( 2 * 40000 + 2000(n-1) )
pliant sun
you may have to use natural logs
to pull the n down from being an exponent
or again you could brute force it but that's not the most efficent way to solvve
kind eagle
the answer suggests "the start of the 13th year", but for some reason I'm getting n = 9 instead, by trying to simplify and brute force that equation
is the equation set up correctly?
oh wait that 10 should be an n
which apparenlty gives
oh wait that's over the integers
i think i'm just answering my own question here, i'll work on it more :)
.close
alpine sable
I wanted to know what's factor theorem and remainder theorem
gray isle
those are easily searchable
read up and come back if there are any parts you don't understand
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
read up and come back if there are any parts you don't understand
Mhm, i wished to be explained here ... I tried on yt before but still didn't got it
gray isle
what were you watching and which parts don't you understand
we're more or less going to be saying the same thing
be more specific and we may be able to clarify certain parts for you
alpine sable
I just want it to be explained about it slowly.. and like in simple words... I don't have anything to specify.. wanna know from start
gray isle
when a polynomial P(x) is divided by (x-a),
P(a) will give the remainder (which is the remainder theorem)
if a is a root/zero, (x-a) will be a factor. and the remainder when dividing by P(x) by (x-a) will be 0 (which is the factor theorem which is a special case of the remainder theorem)
vale sapphire
To write it all out, the key is that you can perform euclidean division on polynomials. Hence, you can write P = (X-a)*Q + R, for R of degree 0 (strictly less than 1, the degree of X-a) i.e a constant. If you evaluate this at a, you get R + (a-a)Q = P(a), i.e R = P(a).
So P = (X-a)*Q + P(a)
vague mirage
@alpine sable
In very simple Words
Factor theorem is used for taking out the factor like How you factorise and it's just factor theorem and reminder Theorem are same but has a little bit of difference
And the Reminder theorem
Is just a replacement for long division method is used when you just want to calculate the reminder
alpine sable
Thanks a lot for your help! I'll try solving sums based on this and will ask any more doubts if i have 
@vague mirage @vale sapphire @gray isle
vague mirage
Wlcm
keen python
the leibnitz kriteria doesnt say that it converges absolut right ?
marsh rapids
the one for alternating series ?
if so then no
because (-1)^n / n converges as an alternating series, but doesn't converge absolutely
marsh rapids
why should it ?
the alternating convergence test works because the series is alternating
because you go back and forth, it suffices that each step is smaller than the last for your back and forth to converge
if you always went in the same direction, you'd need your steps to get smaller and smaller at a sufficient pace
keen python
a series converges absolut when you put it in absolut
so |-1^n|/n = |-1|^n / n = 1 / n
ah an
Sum of 1/n is an harmonic series
which does not converge
bc there is a sentence
a series converges if the sequence is a zero sequence.... but I see its not that way around
I'm not sure on how to write an answer here
ive a potenz series
and calculated the convergenzradius
is the potenz series absolut converget in (1/2 ; 3/2) AND !!! convergent in the edge point x = 1 / 2
and divergent for x < 1/2 AND!!! x >= 3/2 ?
i think this would be correct answer
karmic rapids
are you german
lone heartBOT
@keen python Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
cinder condor
does this have an expansion?
lone heartBOT
does this have an expansion?
marsh rapids
this is just a geometric series
alpine sable
Lol
thick lynx
lone heartBOT