new to this
#help-19
sullen ferry
8^1/6 × (-1)^1/6
this is also a way to think about it
mortal trench
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sour basin
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odd edgeBOT
mortal trench
this is also a way to think about it
Where were you going
I don't see how writing the polynomial helps
sullen ferry
.you end up with z^6=-8 and you can divide both sides by 8, bring it into the 6th power by taking sixth root of it, and then you got a root of unity
.so its just adding extra steps to what you did i guess
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plucky palm
hey shouldn't the summation sign be the other way around?
plucky palm
because the way u solve it would be from inside summation to outside summations
dawn tiger
no this is the only order that makes sense
both i and t change values, only T is a fixed number. if you switched the summations, you’d have an outer sum that has i range from 1 to t, but you wouldn’t know the value of t for the outer sum since t would be indexed by the inner sum
echo ginkgo
the way you compute the sum yourself doesn't magically change the meanings of the sum symbols
that first sum will still define a scope in which t makes sense
same for the second one
@plucky palm
plucky palm
that first sum will still define a scope in which t makes sense
ye I see it now thanks, t is a variable and it's value is assigned from the outer summation so therefore this is correct order right?
echo ginkgo
yea
plucky palm
if u switch the i = 1 to t summation can't even be defined
since u don't know the value of t
odd edgeBOT
@plucky palm Has your question been resolved?
plucky palm
yea
hey can I also ask about linear, I have a hard understand of when it's linear when it's not.
so y = ax+b is linear I know if u do smth like y = x^2 is not linear but say u have multiple variables for example y = x_1 * x_2 is also not linear why?
I assume it's not a striaght line but I can't realy plot it
odd edgeBOT
@plucky palm Has your question been resolved?
odd edgeBOT
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tulip elm
I was wondering if there is a method to confirm the result within revolution of solids. This is the type of problems I have:
odd edgeBOT
I was wondering if there is a method to confirm the result within revolution of ...
@tulip elm Has your question been resolved?
odd edgeBOT
@tulip elm Has your question been resolved?
tulip elm
<@&286206848099549185>
torpid owl
<@&268886789983436800>
odd edgeBOT
@tulip elm Has your question been resolved?
willow root
in circle A, line BE is perpendicular to line DC, and line BE is congruent to line DC. angle BFC is 90 degrees and angle DCE is 23 degrees. what is the measure of angle EDC and what is the measure of arc DBC?
willow root
i got 46 degrees for angle EDC and 222 for arc DBC, and im not sure if its correct.
odd edgeBOT
@willow root Has your question been resolved?
odd edgeBOT
@willow root Has your question been resolved?
odd edgeBOT
@willow root Has your question been resolved?
steady tide
The following reaction is a nuclear fission reaction of Uranium-235 [
^{235}{92}U + ^1_0n \rightarrow ^{95}{42}Mo + ^{139}{57} La + 2^1_0n + 7e^-
]
Given the nuclear masses $m_U=234.99u, m{Mo}=94.88u, m_{La}=138.87u, m_n=1.0087u$. The heating value of gasoline is $46\times10^6J/kg$. Calculate the amount of gasoline (kg) needed to release an amount of energy equivalent to that of 1 gram of uranium undergoing nuclear fission?
clever fjordBOT
steady tide
how do i calculate the energy of 1g uranium fissioning? i can calculate its bond energy to be 1973.8mev
mystic saffron
can you translate your question into something purely mathematical in nature? I doubt people know much about chemistry fission reactions here for one
azure turtle
how do i calculate the energy of 1g uranium fissioning? i can calculate its bond...
Hey
steady tide
can you translate your question into something purely mathematical in nature? I ...
hm, the formula itself is what im struggling with. computation-wise, i can handle that i believe
steady tide
And subtract them
hm, e = mc^2?
azure turtle
hm, e = mc^2?
Yes
steady tide
but thats mass, not sure about energy
azure turtle
And 1u=931 million ev
steady tide
oh wait
azure turtle
And 1u=931 million ev
Lemme just check it
steady tide
instead of calculating the energy both side, i think i can calculate the mass of both sides
find their mass discrepancy and use mc^2
steady tide
And 1u=931 million ev
1u=931,5mev/c^2
azure turtle
find their mass discrepancy and use mc^2
Same method but yeah
azure turtle
1u=931,5mev/c^2
Hey u were the one who posted the question right?
steady tide
yes
steady tide
Same method but yeah
uh, whats the mass of electron in u?
one of the reaction products is 7e-
azure turtle
uh, whats the mass of electron in u?
I think mass of electron is u/1008
odd edgeBOT
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severe gull
When adding and subtracting larger surds like √54 + √2400 - √294, how do I find the common factor when simplifying them that will make them all go together? Do I use prime factorisation for each surd? Like I think it's 6, but I don't know how to show my working for getting there.
severe gull
I made a factorisation graph to find the common number. So I divided 54 by 2 to get 27, then 27 by 3 to get 9, then 9 by 3 to get 3 then 3 by 3 to get 1 to get 2, 3, 3, 3 as the prime factors. Then likewise with 2400 I discovered I got 2, 2, 2 , 3, 2, 2, 5, 5 and with 294 I got 2, 3, 7, 7.
So I ended up thinking 3 was originally the highest common factor, but it turns out it's 6. So what way is it that I'm thinking about this that's getting me the wrong answer? How would I end up discovering that 6 is the factor that allows me to multiply numbers to obtain each of these surds that can be simplified further.
So for instance: √6 x 9 + √6x400 - √6x49 = 3√6 + 20√6 - 7√6 = 16√6
I hope I have not butchered my wording in trying to describe my thought process 😅
low locust
look at all the factors they have in common
they all have 2 and 3 in common
so 2*3=6 is a factor of all of them
ashen juniper
I know that this is just simaltaneous equations
odd edgeBOT
I know that this is just simaltaneous equations
ashen juniper
but do we do 15-T =2a for the top block and (8 X 9.8) -T = 8a for the second?
when is T (tension) subtracted and when is it added?
brittle notch
when is T (tension) subtracted and when is it added?
u can subtract both for a
ashen juniper
u can subtract both for a
but in the setup for the equations is it correct to put T as negative for both?
or is it 15 + T = 2A for the first one
as opposed to 15 + T = 2A
brittle notch
as opposed to 15 + T = 2A
this is right
ashen juniper
this is right
and then for the second equation
brittle notch
that is right
ashen juniper
(8 X 9.8) -T = 8A?
brittle notch
yes
ashen juniper
When is T positive
brittle notch
ok so
ashen juniper
I remember our teacher doing + T sometimes
brittle notch
when a force is acting along the acceleration it is +ve
else -ve
for top one tension is the one making it move and friction is opposing
so T positive and f negative
for second one weight is draggin but tension is opposing
ashen juniper
so T positive and f negative
so T- 15 = 2A
brittle notch
so mg is +ve and T is -ve
brittle notch
so T- 15 = 2A
yep
ashen juniper
for second one weight is draggin but tension is opposing
so 78.4-T = 8A
brittle notch
yes
odd edgeBOT
brittle notch
np
ashen juniper
.reopen
odd edgeBOT
✅
brittle notch
u consider one direction of acceleration
and solve the equations
if u get a is +ve then ur direction is right
else the acceleration is opposite to direction u considered
ashen juniper
im doing this and getting a -ve acceleration
and then T = 30.06
Is that right?
cause I dont have the markscheme
brittle notch
how did u do it?
ashen juniper
36cos30 = 31.18
T-31.18 = 5a
3 X 9.8 = 29.4
29.4-T = 3a
29.4 - (5a +31.18) = 3a
a = -0.0225
T = 5(-0.0225)+31.18
T = 30.06
thats all for 4.3
nvm I got it
ty
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odd edgeBOT
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mystic saffron
odd edgeBOT
mystic saffron
How would you do b
warped glacier
How would you do b
What is the maximum possible y value of the circle?
given the centre and radius
sullen ferry
you did part a) so you know these
warped glacier
(it's the maximum one cause the minimum one would make k negative)
mystic saffron
What is the maximum possible y value of the circle?
Uh
I can work it out
I think
Maybe
I don’t think I can
Thing is
Anywhere there
I don’t see “P”
Point P
warped glacier
I don’t think I can
Okay, so to reach the maximum y-value, which direction from the centre do you need to go?
mystic saffron
Okay, so to reach the maximum y-value, which direction from the centre do you ne...
Up
mystic saffron
You can label it on your circle
Hmm
warped glacier
Add the radius
mhm
clever fjordBOT
Result:
2.8102496759067
cause of this
mystic saffron
That’s P
warped glacier
k is a positive constant
clever fjordBOT
warped glacier
therefore it requires a minimum
No, so you take the maximum y-value
warped glacier
yeah that's completely unrelated nw
mystic saffron
Yeah max y value
warped glacier
But yes local max does mean f''(x) < 0 btw
warped glacier
y = 3?
No
y = 2.81
And x = 6
Given you just moved P directly up from the centre, so the x coordinate doesn't change
mystic saffron
Yes
mystic saffron
Given you just moved P directly up from the centre, so the x coordinate doesn't ...
Yeah
y=2.81
That’s it and then
“Is a tangent to C”
Lmao what
What is this meant to mean
warped glacier
“Is a tangent to C”
Basically the line y = k only intersects the circle at one point
mystic saffron
But is it not also meant to be the tangent to C?
warped glacier
warped glacier
But is it not also meant to be the tangent to C?
C is your circle
warped glacier
So yes the horizontal line touches the circle at only one point
mystic saffron
I forgot
My bad
Okay
Ah
That triangle
That’s a segment
How do you work that out
warped glacier
Part c right?
mystic saffron
Yeah
warped glacier
If so then the origin has x coordinate 0
warped glacier
Your centre has x-coordinate 6
mystic saffron
Into C
mystic saffron
Hmm
warped glacier
But yes plugging y = 0 is valid
mystic saffron
You can’t find y
warped glacier
There's just another way by symmetry, since P is the reflection of O across the vertical line through the centre
sullen ferry
you can find Q
mystic saffron
Why x
sullen ferry
x=0 is the y-axis
warped glacier
OH I misread, you're finding intersections with the y-axis sorry
Then that's x = 0
mystic saffron
🤖
mystic saffron
Bro
But
Plugging in y = 0
Will help you find the x value for Q
Am I wrong or is my RAM running out
Oh you make em equal to each other
Don’t you
But wait
warped glacier
y = 0 is the x-axis
The question wants the y-axis
mystic saffron
No
The question wants the area of the triangle
Whatever method we use doesn’t matter
y = -12.81
I’m tired and confused
22%, gonna die soon
warped glacier
I’m tired and confused
Honestly give yourself a break then
Cause what we're saying clearly isn't being processed in your brain
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
viscid flint
daring pelican
oof
it's an infinite sized one
sec I'll just post a picture, it worked beforehand so idk why the code is breaking
daring pelican
new help channel..
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Available help channel!
mystic saffron
In my class teacher solved a integration problem. Question 22.i copied answer but didnt understand. Why we take f(x) as 1 0 1 2 3 4 instead of directly 0 1 2 3 4 5
mystic saffron
I know integration and how we got units from graph but dont know why f(x) start from 1 not 0
tidal idol
In my class teacher solved a integration problem. Question 22.i copied answer bu...
the list of {1, 0, 1, 2, 3, 4} is the numbers you get after substituting x = {0, 1, 2, 3, 4, 5} into f(x) = |1-x|, we didn't really choose it, it is the only possible list
tidal idol
np
mystic saffron
.close
odd edgeBOT
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gleaming schooner
since im given the endpoints of the diameter, i can calculate the midpoint of those 2 points to get the center of the sphere using
(x1+x2)/2, (y1+y2)/2, (z1+z2)/2
I can also use the distance formula to get the length of the diameter and the radius
and the general equation of a sphere x^2+y^2+z^2=r^2
that should give me the answer right? or am I tripping because the answer im getting is not correct
nimble blaze
show your work
and the general equation of a sphere x^2+y^2+z^2=r^2
and not quite, that would be for a sphere centred at the origin (which your sphere is not)
gleaming schooner
show your work
its all scattered so u wont understand it but:
from the given points, the center of the sphere is (-8, 10, -2) (right?)
and then thats the radius
so
(x+8)^2 +(y-10)^2+(z+2)^2 - 10.3923 = 0
gleaming schooner
i tried that too
gleaming schooner
thats r right there, r^2 is 108 which is what I was entering initially
but i had **+**108 on the left side
instead of -108
-108 is correct
smh 
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odd edgeBOT
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floral onyx
if a 3d vector field has 0 divergence everywhere does that mean it's necessarily the curl of another vector field
odd edgeBOT
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graceful perch
odd edgeBOT
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@graceful perch Has your question been resolved?
frigid canopy
post the entire question
junior ingot
Find x
Assume that lines that appear to be tangent are tangent
@helper
<@&286206848099549185>
Help pls
<@&286206848099549185>
It’s due at 12:36
drowsy moat
Do you know about tangent secant theorem?
junior ingot
No
drowsy moat
no problem!
flint shore
lim x-> -∞ 2-2cos(x) / sin(x²)
odd edgeBOT
lim x-> -∞ 2-2cos(x) / sin(x²)
flint shore
how am I supposed to determine the limit of cos and sin
since it varies between -1 and 1
tight schooner
true garnet
you sure it is infinity and not 0 ?
flint shore
Analyze the function f for the existence of non-vertical asymptotes to its graph. If any exist, write their equation(s).
actually I just noticed -inf is not even in domain so idk how to proceed
true garnet
what happens to f as x -> infinity?
true garnet
ah ok
but we are only looking for horizontal asymptotes
those occur when x approach +- infinity
true garnet
what happens to f as x -> infinity?
so
flint shore
horizontal asymptote y = 0
but if you use the graph
theres an oblique asymptote
when x -> -inf
thats what I'm not understanding
true garnet
but the domain restricts x to be greater than -pi/2
so we dont consider the negative asymptote
odd edgeBOT
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Available help channel!
delicate agate
odd edgeBOT
delicate agate
Idk even know where to start
mystic saffron
,rcw
clever fjordBOT
mystic saffron
,rcw
delicate agate
I’m not gonna lie I have no idea how to do trig
clever fjordBOT
raw herald
solve x first. you have a triangle that have 19° angle and a given hypotenuse.
What trig function can we use if we are looking for the opposite side and an angle and hypotenuse is given?
raw herald
ok. great. now solve for x
delicate agate
I don’t even know how to do that
I started this math course last week
I didn’t do 10 level
And we didn’t learn trig in year 9
raw herald
why are you even answering this?
delicate agate
Bc this course is a course for both 10 level and 20 level
I get both credits for this
For completing one course
raw herald
ok. lets start with sine function
sin(theta) = opposite/hypotenuse
delicate agate
Okay
raw herald
since we are looking for the opposite side,
opposite=hypotenuse*sin(theta)
delicate agate
Okay copy
raw herald
you try it. solve for x
delicate agate
Kk
One sec
I will be back with an answer
Okay
So
X = 93mm * sin (theta)
So now I need to solve for sine?
raw herald
theta is the angle
delicate agate
Oh okay
raw herald
in trigonometry, we use greek letters to represent angles. Usually it is theta.
raw herald
yes
delicate agate
Okay copy that
So now I plug all of that into my calculator than round up the decimal to one place right?
raw herald
yup
raw herald
Upper limit - 3, lower limit - 2
Function: x^1 dx
Is the answer 5/2?
please use another help chat
solid haven
👍
delicate agate
Okay
One second
I’m just putting this all down on paper now
I was using a scrap piece to do this
raw herald
solve for y. same process but the hypotenuse is unknown
delicate agate
Okay
raw herald
sin(theta) = x/hypotenuse
since x=30.3, y=hypotenuse
sin(theta) = 30.3/y
now, try it. solve for y
raw herald
try again
delicate agate
Y = 30.3/ sin (55°)
raw herald
correct. now solve for y
delicate agate
Kk
How would I even plug that into my calculator?
Cause the second I press sin it gives me the decimal
raw herald
do you press equal sign after pressing sine then the angle?
delicate agate
Nope
raw herald
can i see your calculator when you press sine
delicate agate
It’s my phone calculator that might be why
Imma go get a real calculator
Gimme one second
raw herald
ok. take your time
delicate agate
Idek if I can get one right now, its lunch and all my teachers are on break
delicate agate
Okay thank you
Okay so it would be the same as X
But instead I would have to divide instead of multiply
raw herald
yes
delicate agate
Okay thank you very much for your time
raw herald
also you can download scientific calculators app
delicate agate
Oh thank you im gonna download it right now
Thank you for your time you have a wonderful day
raw herald
🆗
delicate agate
.close
odd edgeBOT
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oak pebble
what is the cofactor of the matrix from type 1x1?
odd edgeBOT
what is the cofactor of the matrix from type 1x1?
forest sky
it doesn't have an obvious definition. one way could be to define it as 1 (since the determinant of a 1x1 matrix is its entry)
odd edgeBOT
@oak pebble Has your question been resolved?
oak pebble
the adjoint of all square matrices from type 1x1 are equal to identity so
adj(A) = (cof)^T
I = (cof)^T
I^T = cof
cofactor = I
so the cofactor of all matrices from type 1x1 is equal to identity?
edgy mica
odd edgeBOT
edgy mica
how do i do this exactly
ivory dock
Hint : polynomials like these can be rewritten in term of (x-x_1) * (x-x_2) * ... where each x_i is one of the functions zeroes
So if (x-2) and (x+3) are factors then these numbers refer tooo.....
edgy mica
So if (x-2) and (x+3) are factors then these numbers refer tooo.....
where its touching the x axis
ivory dock
ye
edgy mica
but how do i know what it looks like
like
the curves and stuff
hmm
let me just give it a try lmao
mb
ivory dock
do you know how to divide polynomials?
ivory dock
well divide the initial polynomial by the two solutions you're given
and solve the quadratic you get
for the other two zeroes
a 4th degree polynomial has 4 (complex number) zeroes
they can be real too
ivory dock
well if they're complex then they don't
basically it touches the x at every real root
edgy mica
well if they're complex then they don't
yeah
right every real root
so i just find the roots and connect them
but
idk where they start or like
how a polynomial like that looks
ivory dock
note that 5 is a double root
edgy mica
right
ivory dock
double roots are places where the function goes from one sign to the same sign
so it does a jump
from positive to positive
or negative to negative
on all other roots it's changes sign
edgy mica
how TF am i supposed to know this in the middle of an exam 😭
ivory dock
from positive to negative
or negative from positive
now mark those 3 points on your x axis
edgy mica
double roots are places where the function goes from one sign to the same sign
equal and real
ivory dock
ye
edgy mica
how on earth would i have known in the middle of an exam that the graph would look like this
edgy mica
and then?
ivory dock
then plug in a value less than the lesser point into the function
in this case plug in -4
edgy mica
we wanna find out what's happening to the left of -3
hmmm
edgy mica
then plug in a value less than the lesser point into the function
so the lesser point is the furthest root to the left?
are you just calling it that for this case or for all cases
ivory dock
it's not a root
it's just some value
we wanna see if the function is positive or negative
left of -3
it's positive right?
so the function goes positive -> 0 at -3 -> negative -> 0 at 2 -> positive -> 0 at 5 -> positive again (because of double root)
so now just draw a curve along this path
edgy mica
it's positive right?
right
ivory dock
it's a sketch, not a full drawing
it says to not label stationary points, so maximums and minimums can be ignore
edgy mica
right
edgy mica
note that 5 is a double root
does that mean that when factorising its be (x - 5)^2 or just x-5 once
edgy mica
ah ok
ivory dock
does that mean that when factorising its be (x - 5)^2 or just x-5 once
it'll be (x-5)*(x-5)
correct
odd edgeBOT
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loud plume
Hi. My question is to approximate the x(1) value of x' = t - x, where x(0) = 1, and h = 0.5
therefore, I have t1/2 = t0 + h/2, t1/2 = 1/4
using that, to plug it into the euler method, x(n+1) = xn + h * f(xn,tn)
x(1/2) = x0 + h/2 * (t0 - x0)
x(1/2) = 1 + 0.25 * (0 - 1)
x(1/2) = 0.75
x(1) = x0 + h * (t1/2 - x1/2) (explicit midpoint method)
x(1) = 1 + 0.5 * (0.25 - 0.75)
x(1) = 1 + 0.5 * -0.5
x(1) = 1 - 0.25
x(1) = 0.75
however, the answer in the answer sheet is 0.78125. Where did i go wrong?
odd edgeBOT
@loud plume Has your question been resolved?
loud plume
<@&286206848099549185> please let me know if i've formatted it horribly and need to re-write it
here is the question, i'm doing 2.2
loud plume
if someone could ping me if they have a chance to read over it/lend a hand, that'd be awesome thanks
odd edgeBOT
@loud plume Has your question been resolved?
outer fractal
ok
loud plume
?
odd edgeBOT
@loud plume Has your question been resolved?
odd edgeBOT
@loud plume Has your question been resolved?
odd edgeBOT
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Available help channel!
keen vortex
odd edgeBOT
brittle notch
yes its right
keen vortex
also dont worry this is not a test
brittle notch
pythagoras
keen vortex
how about this?
keen vortex
u just put the formula right but couldnt sub values properly?
damn i guessed it actually...
rotund musk
a^2+b^2=c^2
brittle notch
law of sines
pythagoras theorem?
keen vortex
pythagoras theorem?
i was thinking of that too
brittle notch
mhm
brittle notch
y do u need calc for such small thing ;-;
keen vortex
y do u need calc for such small thing ;-;
sorry ://
brittle notch
yes
brittle notch
use calc ;-;
keen vortex
im sure u cant use phythagorean
keen vortex
umm like
.766 smth
and in degrees
45 smth
but it's not in the choices
am i doing it wrong
keen vortex
do you know inverse trig ratios
yes
ohh yea
like the arc thingy
hold on
the closest i got is 45
man
rotund musk
what are you inputting
odd edgeBOT
@keen vortex Has your question been resolved?
odd edgeBOT
real trellis
!15m
odd edgeBOT
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.
real trellis
also dont ping mods for math help
odd edgeBOT
@silent belfry Has your question been resolved?
odd edgeBOT
silent belfry
Can anyone solve any of these equations using matrices?
odd edgeBOT
Available help channel!
broken heath
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odd thunder
Is it a simplifying problem?
broken heath
I need this simplified
broken heath
Is it a simplifying problem?
yes
odd thunder
There's a lot of ways to approach this, in general, you should learn exponent identities and it should be pretty easy.
broken heath
There's a lot of ways to approach this, in general, you should learn exponent id...
ik but the thing is im not sure if the answer i got is correct or not
so thats why im asking for help
broken heath
oh thanks
warped wadi
how do you do the half angle formula, I am getting very confused
odd edgeBOT
how do you do the half angle formula, I am getting very confused
@warped wadi Has your question been resolved?
odd edgeBOT
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crisp flume
how to solve for $\lambda$?\
$\frac{y^2}{(2-2\lambda )^2}+\frac{x^2}{(1-4\lambda )^2}-4=0$
clever fjordBOT
Slowaq
ivory dock
What have you tried so far?
crisp flume
What have you tried so far?
i tried putting it into the same fraction and putting 4 to the other side
but dunno what next
ivory dock
have you tried cross multiplying then?
or rather, switching the 4 on the right with the bottom of the fraction on the left
crisp flume
nvm i think i fugured it out finally
it is a system of three equations and i did previous steps wrong
but thanks for help!
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odd edgeBOT
ivory dock
aight, bet
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tired obsidian
$D$ is the domain contained in the first quadrant and delimited by the $x$ axis, the parabola $y = x^2-2$ and the bisector of the first and third quadrants.
clever fjordBOT
alee
tired obsidian
can anyone help me determine this domain
odd edgeBOT
@tired obsidian Has your question been resolved?
tired obsidian
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odd edgeBOT
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fallen venture
Can anyone help me understand integral calculus? In specific I’m stuck in the anti derivatives
copper quarry
i recommend watching a youtube video on it or looking at some other online sources, there are plenty that have great explanations cuz people cant rlly help you if you dont have a specific question
odd thunder
Can anyone help me understand integral calculus? In specific I’m stuck in the an...
I can teach ya
fallen venture
It’s alright I’m watching a video hopefully it will be enough
Thank you tho
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odd edgeBOT
@fallen venture Has your question been resolved?
signal oar
odd edgeBOT
signal oar
For the fifth case, can we find a way?
frigid canopy
sounds like hilbert's hotel imo
this may help
though it practically gives away the solution
signal oar
though it practically gives away the solution
Yeah, though I already did 1, 2, 3, 4
Just wondering if 5 is even doable
Or if we'd need a larger hotel for that
signal oar
Maybe the nth guest moves to room n^2?
frigid canopy
there would still be overlaps
signal oar
ok
frigid canopy
There are $N$ buses with $N$ passengers
clever fjordBOT
ƒ(Why am. I here)=I don't Know
frigid canopy
think in terms of powers
signal oar
nth guest moves to room n^n?
signal oar
You can give the answer
frigid canopy
each current guest, gets room $2^{\text{Their room number}$
clever fjordBOT
ƒ(Why am. I here)=I don't Know
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frigid canopy
remember a prime^n is unique
signal oar
each current guest, gets room $2^{\text{Their room number}$
Ah
signal oar
remember a prime^n is unique
Is this relevant?
with 14^(their room number) each guest would get a unique room too
frigid canopy
Is this relevant?
it is
uneven lodge
with 14^(their room number) each guest would get a unique room too
They mean that $\text{prime}^{n}$ is unique in the sense that you won't have $\text{prime}{1}^{n} = \text{prime}{2}^{m}$
clever fjordBOT
Mikkel Angelo
uneven lodge
For some chosen n and m
signal oar
They mean that $\text{prime}^{n}$ is unique in the sense that you won't have $\t...
Well why'd we have to worry about that?
uneven lodge
This way you can map each bus to a unique prime (except for 2, since it's used for the hotel quests)
signal oar
We map n to somenumber^n anyways
uneven lodge
And each passenger to the power of the prime
So hotels quests gets mapped to 2ⁿ, passengers of the first bus gets mapped to 3ⁿ, passengers of the second bus gets mapped to 5ⁿ and so forth
signal oar
oh
uneven lodge
And you know this mapping is injective to ℕ since there will be no overlaps
That is why the part about no overlaps is important
signal oar
That is why the part about no overlaps is important
I thought moving each nth guest to room 2^n is enough
But that's just for the first bus of N people
Right?
uneven lodge
I thought moving each nth guest to room 2^n is enough
Well, it's enough to "generate" the empty rooms needed
But you still need to map the passengers
And the prime-technique is an example of that
signal oar
Is this what you thought of too @frigid canopy ?
Or did you want to map to the empty rooms
uneven lodge
(The prime number technique does use 2 fundamental assumptions though: 1) there are at least a countable infinite amount of primes, and 2) each natural number is unique in their prime factorization)
signal oar
(The prime number technique does use 2 fundamental assumptions though: 1) there ...
Wait, so we have N busses of N passengers
The first bus drives in
We map each guest to 2^n
Then each guest from the bus to 3^n
uneven lodge
Yes
uneven lodge
signal oar
<:catthumbsup:614540188747563008>
So the passengers of bus i get mapped to rooms p_(i ** + 1**)^n
Right?
uneven lodge
Yes, exactly
signal oar
Yes, exactly
Ok, thanks! Is there a way this hotel will really be full, as in there is not enough space for the people that come?
N times N busses of N guests arrive
What happens then?
uneven lodge
If you have ℝ people coming
uneven lodge
N times N busses of N guests arrive
Finite cartesian products of countable sets are countable
frigid canopy
like the set of rationals
clever fjordBOT
Mikkel Angelo
signal oar
Finite cartesian products of countable sets are countable
Oh, so we need something like R or 2^N to not have enough space
uneven lodge
like the set of rationals
The rationals are not bigger than the naturals in the sense of cardinality
uneven lodge
Oh, so we need something like R or 2^N to not have enough space
Yes
frigid canopy
The rationals are not bigger than the naturals in the sense of cardinality
got it
frigid canopy
Oh, so we need something like R or 2^N to not have enough space
$2^N$?
clever fjordBOT
ƒ(Why am. I here)=I don't Know
frigid canopy
what does that mean?
frigid canopy
or N^2
uneven lodge
what does that mean?
It's notation for the power set of the naturals
frigid canopy
It's notation for the power set of the naturals
ok
clever fjordBOT
Kepe
uneven lodge
In general you can view $A^{B}$ as ${f ; | ; f : B \to A}$
clever fjordBOT
Mikkel Angelo
uneven lodge
For sets A and B
Taking $2 = {0, 1}$, you get the sets of mappings $2^{\mathbb{N}} = {f ; | ; f : \mathbb{N} \to {0, 1}}$ as the power set of $\mathbb{N}$ if you for each mapping view the values 0 and 1 as a natural number not being in and being in a set
clever fjordBOT
Mikkel Angelo
uneven lodge
So basically all of this comes down to "is the number of guests coming countable...
Yes, because the free space you can create with countable rooms (and countable quests already being there) is countable
odd edgeBOT
uneven lodge
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ornate remnant
this is false?
odd edgeBOT
this is false?
amber schooner
it is conditionally convergent
do you know why
do you know what it means for something to be conditionally convergent
amber schooner
conditionally convergent means the absolute value diverges
but not absolute value converges
ornate remnant
@amber schooner how do i do this my final result was x converges for all values not = center
amber schooner
so the radius is infinite
but what about -1
that’s 1/n+1
diverges
oh i didn’t read the question
true garnet
eh
amber schooner
yea it will converge at its center because then it’s just 0
true garnet
question had me so confused
amber schooner
my fault i thought you said you did the ratio test and found it converges everywhere
it doesn’t
the radius should just be 1
amber schooner
<@834774466290253834> how do i do this my final result was x converges for all v...
how’d you get that
ornate remnant
i think my biggest problem is that i dont know how to get R
like i got abs(x+2) < R
now what
wait so i redid it and got
-3<x<-1
then i substituted and found that at -3 its convergent and at -1 its divergent
since itsb etween those ranges it means its convergent at
[-3,1)?
so it is convergent at its center?
odd edgeBOT
@ornate remnant Has your question been resolved?
tired elk
i gotta prove this
odd edgeBOT
i gotta prove this
tired elk
I proved it this way
ember oak
I proved it this way
what language is this?
tired elk
i don't think this can be proved with remainder tables right?
willow root
what language is this?
cursive
tired elk
what language is this?
it's english but i assume you don't understand my caligraphy
willow root
bery hard to read
ember oak
it's english but i assume you don't understand my caligraphy
It's very hard to read
I thought it was Russian at first
tired elk
was taught how to write in cursive but for spanish sadly 😔
ember oak
was taught how to write in cursive but for spanish sadly 😔
que lastima
tired elk
si te lo escribo en español, le echas un ojo?
ember oak
🇲🇽 or 🇪🇸?
tired elk
are you asking for my nationality?
ember oak
yeah. Just curiosity
ember oak
si te lo escribo en español, le echas un ojo?
I prefer English
tired elk
i'm venezuelan
ember oak
ah.
tired elk
anyways, my point is that i already solved the exercise
ember oak
I've never known Mexico to require cursive, so I was surprised. I figured you had to be from somewhere else.
ember oak
anyways, my point is that i already solved the exercise
Okay let me try to read it
tired elk
but my real question is, it can't really be solved with remainder tables right?
ember oak
but my real question is, it can't really be solved with remainder tables right?
I'm not familiar with remainder tables, so I cannot answer that sadly
tired elk
like, some guy solved the same exercise with this table
ember oak
Oh I see what a remainder table is. Okay
tired elk
thing it, i belive it's wrong
ember oak
Yeah you should be able to prove it with a remainder table. $7|a^2+b^2$ is equivalent to $a^2+b^2\equiv 0$ mod $7$.
tired elk
or at least i don't understand why would he separate the remainders of a and b divided by 7
clever fjordBOT
SWR
tired elk
but one would have to write a table for a^2 and b^2 separately? i thought one had to write a remainder table for both a^2 + b^2
which are a bunch of cases
ember oak
but one would have to write a table for a^2 and b^2 separately? i thought one ha...
i thought one had to write a remainder table for both a^2 + b^2
what do you mean by both?
ember oak
like, some guy solved the same exercise with this table
This is the remainder table for a²+b² right here
tired elk
take for example this exercise
ember oak
Red is the remainder table for A, blue is the remainder table for B, and green is the remainder table for a²+b². Note that the remainder of a²+b² is 0 only when both a and b's remainders are 0.
ember oak
take for example this exercise
You can do this with a remainder table as well
ember oak
Yeah this is fine
tired elk
i don't know i'm just confused, i thought one had to make a table for a^2 + b^2 simultaneously
ember oak
Red is the remainder table for A, blue is the remainder table for B, and green i...
The difference is that your example remainder table is one-dimensional because you only have one input variable. But a²+b² has two variables, so you end up making a 2-dimensional table as you see here
tired elk
like a^2 + b^2 = 1 or every possible way to add 1
like 0 + 1 = 1 or 1 + 0 = 1 and so on
ember oak
Red is the remainder table for A, blue is the remainder table for B, and green i...
This is that exact table you are asking for. For example, the first green row is a²+0², the second row is a²+1², the third row is a²+2² and so on.
tired elk
is this method of remainder tables good only for one or two variables?
i mean i understand it for 1, for two i gotta study it more but what if i had a bunch of variables on one side
ember oak
i mean i understand it for 1, for two i gotta study it more but what if i had a ...
You can do any N-dimensional table, it would just be very tedious to write out.
tired elk
right, i think i understood, but, i think the table you made is not right, correct? like, shouldn't the number in purple be 4? for a^2 + b^2 = 4 + 0?
odd edgeBOT
regal apex
no..
brittle notch
Ok so listen
In binomial expansion
(a+b)^n
The general term
Is given as
Tr+1 = nCr*b^r*a^n-r
Use that
regal apex
oh god what is that
long tinsel
[ T_{r + 1} = \binom{n}{r}a^rb^{n-r} ]
clever fjordBOT
Sadie Carnot (η > 1)
regal apex
i’m sorry i have to go for lunch im gonna do some studying up so hopefully the next person has an easier time explaining..
thank you!!
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odd edgeBOT
odd edgeBOT
Available help channel!
zenith tartan
odd edgeBOT
zenith tartan
can i just multiply the matrices first and then take its transpose
is it gonna change anything?
im just kinda lazy to do it with an example
zenith tartan
like one way is just to mulitply the transpose of B and A just how this property states
but what i need to know, if we can first mulitply A and B and then take their transpose
zenith tartan
alr so i can do that right?
warm nacelle
ah how can i explain this
it is like the (a+b)^2
you can add the numbers and then take the squar
which will same is a^2+b^2+2ab
in question you wont get a matrix
but will have to solve them by using properties, so when you will need to simplify you can convert (AB)' to B'A'
zenith tartan
you can add the numbers and then take the squar
yea ok
that's what i wanted to know
ok thanks a lot
🙏
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odd edgeBOT