so like this
#help-13
sacred grail
yeah
limber snow
tysm
sacred grail
you dont have to write it with x and y though
limber snow
you dont have to write it with x and y though
ye my bad i was j doin it as rough work
but could u proofread
and lmk if this makes sense
sacred grail
that makes sense to me
errant mantle
can someone help with physics or is this beyond the sevre
cedar kilnBOT
can someone help with physics or is this beyond the sevre
errant mantle
.close
cedar kilnBOT
vestal bear
can someone help with physics or is this beyond the sevre
we can help
errant mantle
.reopen
cedar kilnBOT
✅
errant mantle
it's quantum physics @vestal bear
vestal bear
bruh
errant mantle
vestal bear
well i cant help
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
exotic verge
<@&286206848099549185>
open nacelle
,w sum from n = 1 to infinity of n!/n^n * sin(pi/2 * (2n + 1))
wraith daggerBOT
ebon juniper
because its a sum of values
exotic verge
So what will the sum of the series be if i want to approx it within 0.01
,w (1!/1) (-1)^1 + (2!/4) (-1)^2 + (3!/27) (-1)^3 + (4!/256) (-1)^4 + (5!/3125) (-1)^5 + (6!/46656) (-1)^6
wraith daggerBOT
exotic verge
Is this the correct sum of the series?
faint breach
Do you have advice for high school? Im going to start high school in a few weeks
muted bear
Have fun, its not that serioues
runic garnet
I think different countries may have different perspectives
Depends on ur situation ig
cedar kilnBOT
@faint breach Has your question been resolved?
jolly sable
cedar kilnBOT
crystal raptor
arctan(0) is 0
untold torrent
technically it can be any multiple of pi
but the arctan function gives 0 yes
forget what I said actually
this isn't an equation
its just straight up arctan value
jolly sable
But arc tan range doesn't take pi?
crystal raptor
what? you're inputting 0 into arctan
cedar kilnBOT
@jolly sable Has your question been resolved?
jolly sable
. reopen
jolly sable
what? you're inputting 0 into arctan
Noo
flint plinth
why are you feeding an angle to arctan
crystal raptor
that just isn't true
flint plinth
tan takes angles, arctan does not
jolly sable
Yes edited
jolly sable
Arctan (0)=pi
When it happens?
crystal raptor
that is also not true
flint plinth
pi is an angle for which tan(theta) = 0, but it's not the arctan of 0
flint plinth
Then why did they write?
they didn't say the answer is pi, they are saying it's any integer multiple of pi
jolly sable
They should have written in the last line
Arctan0=0
jolly sable
they didn't say the answer is pi, they are saying it's any integer multiple of p...
How can it be true?
flint plinth
for multi-valued functions there's a distinction between the principal value (one number, constrained to be within a particular range) versus the set of all possible values
the principal value of arctan is between -pi/2 and pi/2
you get the set of all possible values by taking the principal value plus $n\pi, n \in \mathbb Z$
wraith daggerBOT
Bungo
flint plinth
in this example, 0 is the principal value of arctan(0)
and the set of all values is $n \pi, n \in \mathbb Z$
wraith daggerBOT
Bungo
flint plinth
you can see more details here: https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Principal_values
flint plinth
Suppose we take 3 pi, 4pi
the tan of both of those is zero
jolly sable
If there are options 0 is not available i will pick integers multiple of pi right?
flint plinth
not available in what context?
crystal raptor
that solution is all kinds of wrong
their method will get them 0
because this is undoubtedly 0
they're not checking the hypothesis of this theorem, you need arctan(a) + arctan(b) to be between -pi/2 and pi/2
,w arctan(12/5) + arctan(3/4)
wraith daggerBOT
flint plinth
they got the right answer but their reasoning is wrong
all three terms in the initial question are positive, so they certainly don't sum to zero, but their second to last line does sum to zero
cedar kilnBOT
@jolly sable Has your question been resolved?
jolly sable
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
midnight onyx
Hi, where do I start?
cedar kilnBOT
Hi, where do I start?
vagrant elbow
Probably start by using arctan a + arctan b
Or you could use sin 2x and simplify that
crimson sedge
could I do tan^-1 of 1/x then do 2 * that? then sin of that?
Use sin2x
long arrow
with legs 1 and x (such that tan(theta) = 1/x)
then hypotenuse is sqrt(1+x^2)
use double sin and that's it
midnight onyx
k, i'll work thru it again. thx
cedar kilnBOT
@midnight onyx Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
rotund fox
$\int^1_{-2}\frac{1}{x^2}dx$
cedar kilnBOT
$\int^1_{-2}\frac{1}{x^2}dx$
wraith daggerBOT
shockshwat
rotund fox
please ping me if you know how to do this
slate lintel
please ping me if you know how to do this
if you're in a class that requires this you should know how to do this
vagrant elbow
Isn't this the blackpenredpen thing
rotund fox
Isn't this the blackpenredpen thing
whats that?
vagrant elbow
He goes through this exact integral
rotund fox
if you're in a class that requires this you should know how to do this
pls tell how to do it
gentle flower
pls tell how to do it
what have you learned in class?
slate lintel
hint: $\frac{1}{x^2}$ can be written as $x^{-2}$
wraith daggerBOT
Hayley
rotund fox
**Hayley**
yeah cant be solved with this
rotund fox
i need to show that the integral is diverging
vagrant elbow
...
random rover
hi
crude blaze
Do u know the answer?
crude blaze
I might have a clue
See 3^4=81
So we can multiply the 3 from the r.h.s
As the base is same the powers would add up
Similarly 2^5 =32
Multiply it to the r.h.s
Again the base is 2 so the powers would add up
random rover
hmmm i dont get it tho
random rover
so its 2^5 right
crude blaze
Yes
random rover
5y what does it mean actually?
x+5y
y is another + or its a number starting with 5
crude blaze
No no it's part of the power
crude blaze
Wait
Can I send a pic in this server?
proven thistle
Take ln on both sides
random rover
Wait
Can I send a pic in this server?
yes i think
random rover
Take ln on both sides
ln means?
crude blaze
Natural log
crude blaze
I don't think ln would be applied here tho
vague rapids
You need to compare powers
crude blaze
cedar kilnBOT
@random rover Has your question been resolved?
crude blaze
iwhy is it like that
Ummm I have no idea
crude blaze
You need to compare powers
...
vague rapids
$$\frac{81^{\left(x+5y\right)}}{32}=\frac{3^{\left(4x+20y\right)}}{2^{5}}$$
$$\left(\frac{2}{3}\right)^{x}=\frac{2^{x}}{3^{x}}=\frac{3^{-x}}{2^{-x}}$$
wraith daggerBOT
beard420
random rover
sorry but 💀 what does comparision means
crude blaze
**beard420**
As the base is same we can compare the powers
4x+20y=-x eq 1
5=-x eq 2
From eq 2 we find x
X=-5
Put x in eq 1
4(-5)+20y=-(-5)
Now find y
cedar kilnBOT
@random rover Has your question been resolved?
limber snow
Im honestly confused
cedar kilnBOT
Im honestly confused
limber snow
I dont really know what to do
cold briar
Wait... is this even possible?
So let's split it into 3 matches
Naruto vs Gaara
Gaara vs Sasuke
Sasuke vs Naruto
if the winners are
Naruto vs Gaara
Gaara vs Sasuke
Sasuke vs Naruto
how would you put them in a queue?
where would Gaara be?
cold briar
I was actually also asking a genuine question... not testing you
cuz from figure 2 we can see that
(a) beats (b), (b) beats (c), (c) beats (a)
but if b doesn't beat anyone, or c beats 2 people, how would they be queued?
ohhh
okay nvm i see how it is
limber snow
i dont get it
crystal raptor
yeah the key is that they beat the person right behind them
cold briar
yeah the key is that they beat the person *right behind* them
just realized that
yeah
limber snow
whats if B beats A, C beats A
what would the last fight be
wait how did A beat the person right behind him in the figure
according to the figure the queue was
B , A, C, B ?
wait wtf
the queue in the figure doesnt make sense to me
oh my fucking god nvm
it says behind.
i was doing for in front of them
@cold briar @crystal raptor
would this be valid
crystal raptor
Sure but that's kind of overkill, there's really only two cases:
- one person beats two people
- everyone wins and loses one fight
limber snow
Sure but that's kind of overkill, there's really only two cases:
1) one person ...
ohhhh
true
also
im stuck for the second part of my induction proof for this question
what should I do
ok I think i got it can someone lmk if its correct
<@&286206848099549185>
ancient lodge
I'm pretty sure that's fine, but can't you just use the formula for the sum of an arithmetic series?
limber snow
how so
ancient lodge
$1+2+\cdots+(n-1)$
wraith daggerBOT
civil_service_pigeon
limber snow
eh if my current solution is fine then ill just stick to that
also one more question
what the hell do they want me to do for this question
i did this much so far but idk if im on the right track
like do i do the same thing i did for the one before this
limber snow
wait wym
so for my base case
wait what im confused
so my base case is correct and for the second part u want me to work with k instead of k+1
ancient lodge
Wut
limber snow
im confused sorry
limber snow
Imma guess to consider the original k
what do u mean by this
ancient lodge
Invoke your inductive hypothesis in the inductive step to say that you can arrange k in a queue
Then you just need to figure out how to put the (k+1)th in said queue
warped laurel
Considering the sum of two standard dice, i need to Create a probability question, in the form "What is the probability of _____?", where A and B are mutually exclusive and justify why the events are mutually exclusive.
I can't think of any events that would be mutually exclusive in this scenario
crimson sedge
are you familiar with the definition of mutually exclusive?
warped laurel
yes, events that can not happen at the same time (like right and left hand turns or winning and losing a game)
crimson sedge
yup, thats correct
could you give an example of mutually exclusive events for rolling a single die
warped laurel
even and odd numbers at the same time?
crimson sedge
yeah, that works. We can do something similar here
notice that in any resulting roll, the red die cannot be even and odd at the same time
warped laurel
yeah, but it needs to be an event related to the sum of two standard dice
warped laurel
no
crimson sedge
so these could be your mutually exclusive events
tropic socket
hi
tropic socket
$\sqrt{\floor{x^2}}$
wraith daggerBOT
j0sephthea
tropic socket
how can I take derv of this
crimson delta
cold ibex
I need help with this
cedar kilnBOT
I need help with this
cold ibex
$100kx+200kx=300$
wraith daggerBOT
.differentialequations
cold ibex
Solve for x
cold ibex
$200kx = 300$
wraith daggerBOT
.differentialequations
vagrant elbow
no
livid hound
don't troll
vagrant elbow
you should really care about others time
livid hound
you've been doing calc+ stuff
vagrant elbow
just because you have an hour to kill doesn't mean we do
livid hound
don't abuse helpers
cold ibex
.close
crimson sedge
Can someone help me
cedar kilnBOT
Can someone help me
dire geode
Can someone help me
crimson sedge
The instructions say to find volume, but doesn’t give the side lengths
How would I get a valid answer?
It said to simplify variable expressions
tropic oxide
,rccw
wraith daggerBOT
tropic oxide
It said to simplify variable expressions
well yeah...
the volumes of all these shapes will be expressions in terms of s
your answers will contain the letter s
is that something you're allergic to? @crimson sedge
tropic oxide
you're not sure what what means?
crimson sedge
Because if I try to find the cylinder or cone I can’t simplify the variable
tropic oxide
so... you get SOMETHING, but you feel it is unsimplifiable?
crimson sedge
I plug s in for say the cylinder and I get v = pi (r squared) (s)
crimson sedge
1/2 s
crimson sedge
S/2 ^2
I don’t know how to simplify this
You can’t simplify the variable
Or maybe just s^2 pi
S/2 ^3 π
Bruh
tropic oxide
S/2 ^2
bad notation
ok, let's try this
what does $\pi \cdot \paren{\frac{s}{2}}^2 \cdot s$ simplify to?
wraith daggerBOT
Ann
tropic oxide
incorrect
ok, let's try a simpler one
what if i asked you to simplify only (s/2)^2?
(don't include anything else in here until i tell you to)
crimson sedge
Sxs/2
tropic oxide
don't use the letter x for multiplication.
also, no, (s/2)^2 is not the same as s*s/2.
crimson sedge
I’m on mobile rn
tropic oxide
yeah, it should be possible to turn autocaps off.
in any case.
what does s/2 * s/2 simplify to?
crimson sedge
Do I cross multiply?
tropic oxide
i don't know what you mean by that. could you perhaps show on paper what'd happen if you did that?
crimson sedge
S^3/2 pi?
tropic oxide
why'd the four transmogrify into a two
tropic oxide
that'll do.
might want to put the pi in front, but if you're actually writing this on paper as $\frac{s^3}{4} \cdot \pi$ i reckon it's just fine.
wraith daggerBOT
Ann
tropic oxide
do you have any other questions you'd like to ask at this stage?
crimson sedge
And it states that assume the cube fits perfectly inside the sphere so the diameter of the sphere could be the dotted line extending from the front lower corner to the back upper corner
I’m not sure how to find the diameter
tropic oxide
well, that dotted line is the diameter, yes.
it's also the space diagonal of the cube.
do you know how to find that?
crimson sedge
Not sure
tropic oxide
ok, then let's go a dimension down.
do you know how to find the diagonal of a square?
crimson sedge
Pythagoras theorem?
tropic oxide
geat.
great*
you can apply that to the cube too.
you'll need it twice.
use the diagonal of one of the faces as a stepping stone.
crimson sedge
What do you mean by you’ll need it twice?
tropic oxide
i mean exactly what i said
in order to find the space diagonal from the sides, you will need to apply the pythagorean theorem twice
crimson sedge
in order to find the space diagonal from the sides, you will need to apply the p...
But shouldn’t the two be the exact same?
tropic oxide
idk what "the two" are
no, the diameter isn't 2s^2 + s.
what you did wrong is that you're trying to find the space diagonal blind and thus confusing yourself as to what it is that you're calculating.
crimson sedge
I don’t know how to find the diameter of
Cuz the diameter doesn’t just go from bottom upper vertice to top uppervertice
tropic oxide
ok, let's backtrack.
crimson sedge
It goes bottom to upper
tropic oxide
forget about the sphere and the cube for a moment.
i want you to draw me a square of side length s, draw a diagonal in it, and find the length of the diagonal.
do it on paper, clearly label everything, and send me a picture.
crimson sedge
tropic oxide
,rccw
wraith daggerBOT
tropic oxide
$\sqrt{2s^2} = \sqrt{x^2}$ is correct
wraith daggerBOT
Ann
tropic oxide
$2s = x$ is not
wraith daggerBOT
Ann
tropic oxide
$2s^2 = 2(s^2) \neq (2s)^2$
wraith daggerBOT
Ann
tropic oxide
we're not done here yet.
i pointed out where you went wrong.
i want you to fix it.
tropic oxide
fix this.
crimson sedge
I did
tropic oxide
show the fixed working out of x.
tropic oxide
so then what is x?
crimson sedge
Square root of 2s^2
tropic oxide
this can and should be simplified.
crimson sedge
So 2s?
tropic oxide
no!!!
crimson sedge
Or square root 2•s•s
tropic oxide
what's a?
"square root of 2*s*s" is ambiguous as SHIT.
and at best it is a do-nothing simplification.
no
$\sqrt{2s^2} = \sqrt{2} \cdot \sqrt{s^2} = s \sqrt{2}$
wraith daggerBOT
Ann
crimson sedge
That makes a lot more sense
tropic oxide
sure does...
when finding the diagonal of a cube, you will be faced with a triangle in which one of the legs is s and the other is s*sqrt(2)
tropic oxide
it's the hypotenuse of a right triangle with legs s and s.
but this same side will play the role of a LEG in a SECOND triangle.
crimson sedge
Ok so the first hypotenuse is s sqroot 2
I don’t know what to do once I find both hypotenuses tho
crimson sedge
So the green is the diameter?
tropic oxide
yes
tropic oxide
s sqrt(3)/2, yes
crimson sedge
.close
tulip pecan
Can someone explain how the numerator in the RHS of ds(t)/dt came to be?
short blade
look at the box on the top right
we are calculating the slope between the point at (t, s(t))
and (t + dt, s(t + dt))
tulip pecan
mhm
short blade
use the slope formula on that
tulip pecan
y2-y1/x2-x1?
short blade
yes
clever marsh
dense cobalt
an ellipse in plane is a curve with the equation (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ 2) = 1 here a, b are positive real numbers. Such an ellipse encloses an area Tab. What are positive real numbers a, b such that ellipse contains the point P(1, 2) and a minimum area. chose from bellow
a = 2
b = 4sqrt(3) / 3
a = sqrt(3)
b = sqrt(6)
a = 3
b = 3sqrt(2) / 2
a = sqrt(2)
b = 2sqrt(2)
a = sqrt(5)
b = sqrt(5)
cedar kilnBOT
an ellipse in plane is a curve with the equation (x ^ 2)/(a ^ 2) + (y ^ 2)/(b ^ ...
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
since its multi choce, you can check each option
dense cobalt
yes but i need to see how its solved
kindred storm
yes but i need to see how its solved
Well, what's the area formula for an ellipse?
cedar kilnBOT
@dense cobalt Has your question been resolved?
little thunder
cedar kilnBOT
little thunder
How do i avoid labeling my triangle incorrectly? The first picture is the solution, and the second one is my own work. I always label it wrong and Im not sure what I'm doing wrong
kindred storm
The triangle labels are fine.
little thunder
The triangle labels are fine.
So should I try other variations of the triangle if it doesn't work or would one not working mean there are no solutions at all?
kindred storm
There are no solutions.
I don't know if your numbers are right, but you're correct about that.
little thunder
Yeah I checked my own triangle wasn't solvable cause it's height is greater than side b
kindred storm
8 sin 25⁰ is the smallest b can be, and it's over 2.
Like if it's a right triangle, b will be going straight down toward the bottom side.
That's the shortest distance down to the bottom side.
little thunder
I see I see
little thunder
So if I were to find no solution like in the first Pic, I can just go ahead and say for sure there are no solutions
kindred storm
Yes.
little thunder
OK great
kindred storm
The multiple solutions will be different angles from the arcsine.
But there are no solutions to that arcsine.
little thunder
.close
raven chasm
I don't get how to do this question?
cedar kilnBOT
I don't get how to do this question?
raven chasm
I don't get what it means by the second line.
undone epoch
So one of the points A-G is on the graph, you're going to find the point.
And by observing the points, you find something in common about them.
raven chasm
So one of the points A-G is on the graph, you're going to find the point.
I still don't get it. am I just dumb?
wait i might have a idea of what you talking about
undone epoch
I still don't get it. am I just dumb?
I think you got confused by the gray and red points.
So, a function y = -x^3 + 3x^2 - x, has revealed four of its points, the gray ones.
Now, you're going to determine the fifth point, out of points A-G.
raven chasm
I think you got confused by the gray and red points.
So, a function y = -x^3 +...
now that makes more sense
thank you for help
how do i close :/
undone epoch
.close
raven chasm
.close
wintry roost
idk y this is so confusing to me
cedar kilnBOT
idk y this is so confusing to me
cerulean star
idk y this is so confusing to me
The graph is horizontal position with respect to time, or x(t)
wintry roost
So is it always moving to the right then?
cerulean star
You want to be thinking about the velocity function, dx(t)/dt
cerulean star
So is it always moving to the right then?
No
Recall that that the first derivative changes sign at the critical points (local max and mins) of the function
So when velocity is +, the partical is moving to the right
When it is -, it is moving to the left
An easy way to visualize this with the graph of x(t) is to trace your pencil along it and note when you are increasing over time and when you are decreasing over time
wintry roost
so its increasing from (0,2)U(6,8) and decreasing (2,6)?
cerulean star
Oh, I needed to exclude the endpoints
wintry roost
so it'd be accelerating from (6,8) and have negative acceleration (0,6)
nvm thats wrong
cerulean star
i graphed the derivative and its like a porabola w the centerpoint at (0,6)
Are you sure the vertex of the parabola is at (0,6)?
wintry roost
i thought so now idk
cerulean star
Vertex is at the inflection point
wintry roost
nope its not
cerulean star
Horizontally, anyway
wintry roost
it crosses up the x at 6 idk the vertex
neg accelation 0 to 4
and positive 4 to 8
cerulean star
neg accelation 0 to 4
Yes
cerulean star
and positive 4 to 8
Yes
violet pagoda
stuck on 2a
cedar kilnBOT
stuck on 2a
violet pagoda
Where did I mess up
Oh
I forgot to make y=x^2 so ‘y to the power of half’ becomes just x
Crazy
.close
violet pagoda
2b bro
violet pagoda
slate lintel
uh several issues here
violet pagoda
i figured
slate lintel
a clear algebra error, $\sqrt{2x+1} \neq (2x^{1/2} + 1^{1/2}$
wraith daggerBOT
Hayley
slate lintel
that denotes a serious lack of understanding of algebra
violet pagoda
my bad
slate lintel
but beyond that if you're integrating dy you need it to be an expression involving y
slate lintel
so you would need to solve $y = \sqrt{2x + 1}$ for $x$
wraith daggerBOT
Hayley
slate lintel
and then integrate $\int_1^3 \pi x^2 \dd{y}$, as you wrote
wraith daggerBOT
Hayley
violet pagoda
would x be 'y squared / 2' -1
slate lintel
no, that's not how order of operations works
violet pagoda
aw man
slate lintel
the first step is indeed to square both sides though so you've got that part
you have $y^2 = 2x + 1$
wraith daggerBOT
Hayley
slate lintel
yes, $x = \frac{y^2 - 1}{2}$
wraith daggerBOT
Hayley
wraith daggerBOT
Hayley
slate lintel
✅
violet pagoda
the answer is 124/15 pi tho
ive got to have messed up somewhere
is it the y cubed over 6 - x/2
slate lintel
oh you didn't square it! I didn't notice that
you had $\int_1^3 \pi x^2\dd{y}$ and then you wrote down $\int_1^3 \pi y\dd{y}$ for some reason
wraith daggerBOT
Hayley
violet pagoda
is that not how im m eant to do it
violet pagoda
neither
slate lintel
substitute that in there
violet pagoda
ok
so x=whatever i got, then i square it
do i just square everything in the equation
slate lintel
take $x = \left(\frac{y^2-1}{2}\right)$ and plug it into $\int_1^3 \pi x^2\dd{y}$
wraith daggerBOT
Hayley
slate lintel
the entire thing will get squared yes
pulsar garden
cedar kilnBOT
pulsar garden
Just really need the answer really really quickly please!
royal loom
we can't give answers
cunning loom
Just really need the answer really really quickly please!
Why would you need it so quickly?
cedar kilnBOT
@pulsar garden Has your question been resolved?
pulsar garden
Cause it’s gonna go in anti
pulsar garden
we can't give answers
Who’s stopping u?
cedar kilnBOT
cedar kilnBOT
Available help channel!
agile linden
Hey, I was wondering if someone can tell me what I did wrong
agile linden
2y^2*9=198y^2
2y^2*x^2=-2y^2x^2
2y^2*y^2=2y^4
x*9=9x
Ooh okay I see which
thank you
!
.close
hazy flicker
Why hello
hazy flicker
I am yet again asking for help on simplep roblems becuz I am dum'
I just don't really understand finding the area using washer/disk method in y-interpretation
like idk it's hard to wrap my head around it
<@&286206848099549185>
:( so sad
<@&286206848099549185>
well I thought it was 1, but I got them all wrong
now I'm just depressed like 3pi isn't correct somehow im so confused
I'm not understaind revolving aroudn the y axis nearly as well as I am the x acis
axis** lord
I really assumed I got #1 on my problem correct but it was wrong somehow
wow I am freaking out literally nothing I'm doing is giving me a correct asnwer
let's try washer since that's the one I'm weak on
yeah cause it's y = sqrt(x) which becomes x
x^2/2 ?..
times pi too
so 9/2 pi ??
okay yeah I don't know how I messed that up, BUT NOW IT IS THE VERY HARD part
the Y revolution
so r(x) becomes y^2 right?...
gosh idek where to start
I'm just so lost I keep getting the same integral like
0 to 3, (9 - y^4)
but then you get like NEGATIVE stuff at the end like what
wow
but if there's just one function (aka y = sqrt(x) why is R(x) AND r(x) a function similar
so R(x) stays the same ?.. when you switch to y?
that's intense, okay so let's solve for x in terms of y? which onme do we use for that
I guess conceptually it just makes no sense to me like WHY is R(x) = to y^2 randomly
Thats what I was missing
was the sqrt 3
yeah it makes sense, so with the washer method you shouldn't think of like (top minus bottom)
cause that's what I was doing, when you rotate using the y-axis WHICH function goes first?.. the one farthest away from the axis of rotation?..
so it's 3.11769
wow that's abunch, but thankfully earlier I was the same track I just didn't change the bounds for some reason
it makes perfect sense, you gotta change the y bounds to match up
I also assumed r(x) = y^2, but that makes zer osense\
since r(x) is the distance from the axis of rotation, in this case is zero?
so just a quick thing - the only difference between rotating on the y axis and rotatin on x=3 IS THAT r(x) = 3 and NOT 0?..
why thank you, I'm trying to down this mass gainer shake literally tired as hell at 9:40 but I'm a bit behind in my calc 2 class
well, I really appreciate your help!! You saved me a ton of time :)
yeah I need to start doing it everyday
I'm sure we'll talk again when I'm having the download the weirdest calc 2 information on the planet
thanks! :)
.close
dreamy zenith
what do i do after factoring 6
cedar kilnBOT
what do i do after factoring 6
thin roost
Perhaps instead of factoring open it upon cos²=1-sin², so it becomes quadratic.
dreamy zenith
Perhaps instead of factoring open it upon cos²=1-sin², so it becomes quadratic.
so make the right 4-sin^2
thin roost
4(1-sin²) != 4 - sin²
cedar kilnBOT
@dreamy zenith Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crude gale
Am I suppose to treat sequences as a separate" type of object" from functions since it has different definition of equality
tropic oxide
don't confuse equality with equivalence
crude gale
wouldn't equality just mean equivalence relation so: symmetry,transitivity and reflexive?
Or do you mean we give different names to these different equivalence relation or something else?
earnest socket
not every equivalence relation is the same as the equality relation
sequences are just functions, yes. the definition provided is for equivalence of sequences, not equality.
the function notion of equality (equality at all points in the domain) also applies to sequences, but we don't generally tend to consider equality for sequences
crude gale
okay, would it be right to say that any type of object only has a single well-defined equality relation?
earnest socket
hmm
tropic oxide
yeah
astral bay
"equality" means two things are literally exactly the same
so yeah nothing would have multiple distinct "equality"s
tropic oxide
i mean equality for sequences is just termwise equality
earnest socket
i think you would be free to define equality in other ways
tropic oxide
while your notion of equivalence is morally a ~ b iff lim (a_n - b_n) = 0
earnest socket
lol bad troll
tropic oxide
do you have any more insightful commentary to add?
crude gale
"equality" means two things are literally exactly the same
so yeah nothing would...
but for two objects of same type to be exactly the same, we just have to to have the two objects satisfy an equivalence relation+substitution
crude gale
while your notion of equivalence is morally a ~ b iff lim (a_n - b_n) = 0
Would this mean i could have chosen to use the notion of equivalence as equality and the notion of equality to be an equivalence?
crude gale
but for two objects of same type to be exactly the same, we just have to to have...
i mean from here^ to that
tropic oxide
also i think you're confusing yourself at this point?
crude gale
i am very confused yes.
tropic oxide
like, two sequences are one and the same iff their terms all match up
earnest socket
equivalence of sequences has nothing to do with the corresponding terms being equal
crude gale
Yes I understand theres a difference between equality of sequences(terms match up) and saying that the two sequences are equivalent(for any epsilon,..., there exists N st n>N then |an-bn|<epsilon)
Im asking would it be possible to have equivalence of sequences be instead used to define equality, and have equality of sequenecs be instead just be an equivalence
astral bay
..."equality" doesn't have a different definition for each type of object
crude gale
does it not? For example, from how my book defined integers formally as "a--b", where a and b are naturals.
We then defined "a--b" to be equal to "c--d" iff a+d=c+b
It would have been possible to use a different definition of equality here albeit probably less useful?
astral bay
we then defined "a--b" to be equal to "c--d" iff a+d=c+b
...wait. what? that... huh
do you have a screenshot of the exact text of when they said that?
crude gale
the "-" here isnt the subtraction sign just a placeholder*
I guess what I am trying to say is that any other way to define equality here would be less useful, so I think if i were to say a-b=c-d iff a=b and c=d, it wouldn't really be the integers as I intuitively know it. But i think it still works as a valid notion of "equality"
crude gale
Yes I understand theres a difference between equality of sequences(terms match u...
^ which leads to this
But I guess there is something invalid about what i am asking since I am defining a sequence as a function so it already necessarily has a definition of equality from itself being a function
hm maybe i can just resolve my confusion by just treating equal and equivalence as completely separate terms
Also i think to flesh out my confusion maybe abit more clearly is that the "equivalence" here does satisfy reflexive,transvitiy and symmetry which made me think "is this not also another possible "equality""?
Thanks for all your time
.close
cedar kilnBOT
astral bay
.reopen
cedar kilnBOT
✅
astral bay
...tbh i would say that you can't "define equality" at all and that their definition of the integers is missing information
"a--b" and "c--d" aren't the same thing unless a=c and b=d, just claiming that they are doesn't somehow make it magically happen
the way i'd interpret the definition is that an "integer" is supposed to actually be an equivalence class
crude gale
but isnt that what is being done in the original definition? "a--b" and "c--d" are the same thing iff "a+d+b+c"
astral bay
yep, i'm syaing their definition is wrong
crude gale
oh okay
astral bay
(...and/or that what they meant is correct but you're taking it a bit too literally)
for any a--b you can take the set of all c--d such that a+d = c+b
crude gale
sorry continue
astral bay
for any a--b you can take the set of all c--d such that a+d = c+b
because of the fact that "a+d = c+b" is an equivalence relation, you end up getting that a--b and c--d are equivalent if and only if their equivalence classes are equal
for instance the equivalence class of 0--0 and the equivalence class of 1--1 are both {0--0, 1--1, 2--2, 3--3, 4--4, ...}
and that set is the integer "0"
crude gale
I never heard of the term and googled it but to just to make sure "equivalence class" means "An equivalence class is the name that we give to the subset of S which includes all elements that are equivalent to each other. “Equivalent” is dependent on a specified relationship, called an equivalence relation. If there’s an equivalence relation between any two elements, they’re called equivalent"
Let me rephrase abit, your saying that "a--b" is a set. The subset of integers(so must be of the form c-d) st a+d=c+b.
And i still don't see what would be wrong with a--b=c--d iff a=b and c=d as a definition. So continuing with your example of 0--0 and 1--1. If i were to define it this way, i still get that
0--0 is the set {0--0}
1--1 is the set {1--1}
So 0--0 =/= 1--1 which is definitely not what we want the integers to do but at the same time its still a valid definition.
astral bay
...well you wouldn't be "defining" a--b=c--d at all, but aside from that,
yes you could define the set of just all a--b, and that would be valid
it just wouldn't behave much like the integers
crude gale
...well you wouldn't be "defining" a--b=c--d at all, but aside from that,
oh okay you were trying to tell me this
Hmm I'm understanding this as your trying to give a more abstract/rigorous notion of equality rather than just a simple statement of defining equality as a=b iff a and b satisfy a certain property
astral bay
it's more that i'm giving a more rigorous version of what "defining equality" actually means
equality has already been defined, we can't just define it again
and in fact if you try to "define equality" to be something that's not an equivalence relation, you can get contradictions, because equality must be an equivalence relation
crude gale
Yes but the definition of sequences being equivalent do satisfy an equivalence relation right? I know I can't just undefined equality and redefine it this way though
astral bay
yeah the "sequence equivalence" there is an equivalence relation
crude gale
ah okay, i think i just need abit more time to think to declutter my mind abit, thanks again for your time
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
tropic socket
hi
tropic socket
If lim f(x) when x approaches a is b and lim g(x) when x approachees a dne
the only thing that we can say is lim (g/f) x goes to a dne
is this correct?
royal loom
No
I disagree
think about g(x)=sin(1/x)
when a=0
the limit g(x) approaches a does not exist
now take f(x)=1/x^2
the limit as a approaches a does exist
and so does the limit as g(x)/f(x) approaches a
lethal jackal
yeah but then lim x->0 f(x) dne?
dense hornet
technically you were almost correct lmao
royal loom
damnit
tropic socket
I thought if lim g/f exists, then g/f × f should exist therefore g exists so g/f dne
lethal jackal
basically if you go to epsilon-delta, you can see that if the wiggles in g don't go to zero, then dividing by something that approaches something is not going to make the wiggles go away
and this is what my proofs actually looked like
dense hornet
oh the ratio is actually g(x)/f(x), thought we are talking about the reciprocal of that
tropic socket
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
fluid pulsar
u can just turn one side
vagrant elbow
lg for log is a new one
muted bear
Oh you want to show equivalence
Take log base 2 of both sides
I thought you were looking at a solution and got confused mb
vagrant elbow
$a^{\log_b c} = c^{\log_b a}$
wraith daggerBOT
neonperseus
muted bear
Raise both sides to the power 4
If you take both sides to the power 4 the 4 and 1/4 cancel
Then you get the identity in its purest form
From the bottom line here, you can raise both to the power 4
Lol all good
Yeah
cedar kilnBOT
cedar kilnBOT
Available help channel!
magic solar
not too sure what to do after changing sin2x into 2sincos
cedar kilnBOT
not too sure what to do after changing sin2x into 2sincos
stark bronze
[\text{Use the difference quotient to find }\lim_{x\to0} \sqrt{x^2 -1}]
[\frac{\sqrt{(x+h)^2 - 1} - \sqrt{x^2 -1}}{h}]
[\frac{\sqrt{x^2+h^2+2xh - 1} - \sqrt{x^2 -1}}{h}]
wraith daggerBOT
dopediscorduser
cedar kilnBOT
@stark bronze Has your question been resolved?
bold lotus
what can you say about the two triangles formed
crude blaze
Hey
As u can see both triangles are congruent
So angle GPK= angle KPH
So we can say
a+8=3a-2
Oh
13
Sure I can try
Can u clarify?
Wait
Do u know the answer?
Yes
The answer would be 30
Cuz angle at U is 75 so angle at V would be 75 too
Since sum of angles is 180
So (75+75)-180 leaves 30
Reason:
The theorem states that if sides are congruent then their corresponding angles are congruent too
No problem
wild belfry
cedar kilnBOT
wild belfry
Im trying to see if theres a trend so I can think of the answer really quickly
There is with the odd numbers , √(nx) is (√n)/(2√x)
But I dont see a trend with the even numbers
Is there one that I dont see?
crystal raptor
you can just split sqrt(ax) up into sqrt(a)*sqrt(x)
then it becomes a lot clearer
tropic oxide
But I dont see a trend with the even numbers
there is no "trend"
$\sqrt{x}$ differentiates to $\frac{1}{2\sqrt{x}}$ and $\sqrt{ax} = \sqrt{a} \cdot \sqrt{x}$
wraith daggerBOT
Ann
tropic oxide
so the derivative of $\sqrt{ax}$ is $\frac{\sqrt{a}}{2\sqrt{x}}$
wraith daggerBOT
Ann
tropic oxide
whether this can be made to look any nicer is a different question entirely and you SHOULD NOT mix that in with the calculus
wild belfry
Ah ok my bad haha
Thats all I wanted to ask anyway haha
Thanks everyone
❤️
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
gritty lynx
The polynomial $px^3-3qx+r=0$ has a root of multiplicity two. Show that $4q^3 = pr^2$
wraith daggerBOT
chromium
gritty lynx
how tha hell do i do this
iron saffron
Do you know what does "has a root of miltiplicity two" mean?
iron saffron
what are the sum of the roots?
wraith daggerBOT
chromium
gritty lynx
i was thinking of this but don't know where to go
iron saffron
how do u get the sum of the roots?
gritty lynx
no idea lol
do you know how to answer the question?
or are you just figuring it out
iron saffron
i know, i'm just trying to know if you know the theory or not
gritty lynx
what theory?
iron saffron
one thing is you don't know a specific step in a problem
other is you don't know the definitions
gritty lynx
the sum of roots of a cubic is -b/a
but in this case there is no b
so the sum of roots is 0
so that's not going to help us much
unless maybe it does somehow lol
.close
lofty igloo
HI, I am Studying Probability Now i came to a question in here
You have 40 cards in four colors, 10 reds, 10 greens, 10 blues, and ten yellows. Each color has a number from 1 to 10. When you pick two cards without replacement, what is the probability that the two cards are not in the same color and not in the same number?
the steps i followed were to find the probability of P(2 cards are same color) and P(2 cards are of same number). Imagining 2 slots( 2 cards picked), 1st slot will be 40/40 for both and second will be 3/39 for same no. and 9/39 for same color. Now here what i did was ->
P(same color)= (1 * 9/39)
P( same number)=(1 * 3/39)
This gives the correct answer which is
1-(P(S C)+P(S Num))
But now if i wanted to first convert P(S C) to P(S C) and P(S Num) to P(NS Num)
Notations= S-> Same,C=Color, N=Not,Num=number
then use intersection between the two,
How can i achieve this?
cedar kilnBOT
HI, I am Studying Probability Now i came to a question in here
You have 40 card...
@lofty igloo Has your question been resolved?
soft owl
let say that :
- A : 2 card with the same color
- B : 2 card with the same number
you calculate :
- P(A) = 9/39
- P(B) = 3/39
And you want to calculate :
- P(¬A ⋂ ¬B) = ?
lofty igloo
yes
soft owl
hint1 : ||the events A and B are independent so : P(A ⋂ B ) = P(A) * P(B)||
lofty igloo
hint1 : ||the events A and B are independent so : P(A ⋂ B ) = P(A) * P(B)||
this is not equal to 27/39 which we get by using another solution
69.2 vs 71% would that be equal in terms of probability?
soft owl
69.2 vs 71% would that be equal in terms of probability?
of course not
soft owl
this is not equal to 27/39 which we get by using another solution
P(A ⋂ B ) = P(A) * P(B)
= 27/39²
is the probability of have 2 card with the same color and numbers
you need the second hint which is :
$P(\overline{A} \cap \overline{B}) = \overline{P(A \cup B)} = 1 -P(A \cup B)$
wraith daggerBOT
mehdi_moulati
soft owl
you just need to calculate P(A U B) and then you will find the answer
@lofty igloo is it clear ?
lofty igloo
Yes thankyou so much i got the answer
soft owl
Yes thankyou so much i got the answer
anytime bro
lofty igloo
.close
candid urchin
cedar kilnBOT
candid urchin
Find x
gritty lynx
christ that question is cursed
cedar kilnBOT
@candid urchin Has your question been resolved?
candid urchin
christ that question is cursed
Ik since I've been trying to solve this question for the last 40mins
And still haven't found a solution
gritty lynx
Ik since I've been trying to solve this question for the last 40mins
is that like an olympiad question or smth
that doesn't seem like the sort of question a school would give you for a test
candid urchin
that doesn't seem like the sort of question a school would give you for a test
Yup its not for a school test
candid urchin
is that like an olympiad question or smth
Not exactly
It's an exam that's similar to sat
gritty lynx
no way sat gives that sort of shit
sat is braindead
unless there's an easy solution to that lol
is the answer 40?
if it's 40 that'd be a meme
or is it 60
candid urchin
It's not sat It's a similar exam tho the math questions are quite different
candid urchin
or is it 60
That's what I git as my answer
cedar kilnBOT
@candid urchin Has your question been resolved?
uneven juniper
Just a trick during exam; to scale diagram lol
waxen basalt
hiu