anyways after substituting the given values in we got this equation
#help-10
fresh pebble
no
ashen iron
Danggg
fresh pebble
to isolate for the variable work backwards with bedmas
yk bedmas right im assuming you do
fresh pebble
brackets exponents division multiplication addition subtraction
you might call it something else like pemdas or something
its just the order of operations
fresh pebble
yeah bedmas and pemdas are the same thing basically
ashen iron
So what do I write now
fresh pebble
so to isolate for the variable just work backwards in bedmas
fresh pebble
yeah well we have nothing to subtract and so we'll go to the next part which is divided and multiplying
ashen iron
Ok
fresh pebble
do you know how to cancel out the division?
ashen iron
No
fresh pebble
basically the opposite of dividing
ashen iron
So multiplication
fresh pebble
yeah
see how it says 21h divided by 2?
cancel out the divided by 2 by multiplying both sides by 2
ashen iron
Oh
So how would I do that
U know that 22 14 and 21 are in the triangle 2
Or are we not worried about them
fresh pebble
we dont really have to worry about them ig
cus we were given 2 important peices of info already which was the area and base
fresh pebble
well for the right side
whats the area times 2
the area being 136.5 so
136.5 times 2
fresh pebble
yeah
now that the division is cancelled out our equation is 273 = 21h
remember how we used the opposite of division to cancel out the /2?
ashen iron
Yes
ashen iron
Ok
fresh pebble
so what would be the opposite of multiplying?
fresh pebble
ai lemme see
fresh pebble
,rotate
warm shaleBOT
ashen iron
Same thing really
fresh pebble
6 3/4 being the area right?
ashen iron
Finding side length again
fresh pebble
same thing basically
ashen iron
6 3/4 being the area right?
It says 6 3/4 cm2
Does the cm2 in the picture matter
Look at it in picture
fresh pebble
It says 6 3/4 cm2
yeah it is the area
dont worry about the cm^2
its just a unit of measurement
ashen iron
Ohh
fresh pebble
however dont forget to express your answer as cm or cm^2
ashen iron
Ok
fresh pebble
but when working with it i jus leave out the units
anyways same thing as last time
a = bh/2
ashen iron
Ok
fresh pebble
quickly tell me what info were given?
fresh pebble
nah were given some dimension of the triangle and the area already
ashen iron
fresh pebble
,rotate
ashen iron
,rotate
warm shaleBOT
fresh pebble
since the traingle given was a right angle triangle
it means 3 is our height
so input the area and the height into the area formula
ashen iron
No I’m confused
ashen iron
Yessir
fresh pebble
ill just rewrite it as a improper fraction
27/4
so 27/4 = a
in the a = bh/2
we can rewrite a and 27/4
because they both have the exact same values hence the equal sign
so out equation wont get changed or ruined
you get it so far?
fresh pebble
if it helps you understand then go for it
incase you didnt understand the point i was tryna make i can try explaining it in simpler terms
ashen iron
My bad if I’m asking for a lot but can u just send me what to write
Just so I can get it over quickly
Teacher rushing me and shit
I’m still in class doing this rn I’m acting like I’m texting my parents
Appreciate it btw
@fresh pebble are u still gonna help me?
fresh pebble
go dms
obtuse pebbleBOT
@ashen iron Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wooden mortar
obtuse pebbleBOT
wooden mortar
Wanted to ask about the particular integrals
For the first set, with that Complimentary function
To find the particular integral apparently you would use format 1
But when I did a previous question as seen in set 2, the particular integral is formatted that the lamda doesn't disappear
The complimentary function for the first one would equal 0, because I see e^-x I thought those might disappear so ill place an x
unreal musk
But when I did a previous question as seen in set 2, the particular integral is ...
Wait how do you mean?
Generally you use the first one if that doesn't appear in the homogenous solution, but if it happens to be a solution of the homogenous solution, "multiply by x until it isn't"
So like the bottom one has both e^{-x} and xe^{-x} as homogenous solutions, so you need to multiply by x once again to get x^2 * e^{-x}, if that's clear?
wooden mortar
Then for the top one :0
Why is multiplying by x not necessary
Cause it has e^-× as homogenous
unreal musk
Well, notice cause you're multiplying by cos(3x) and sin(3x), so it isn't like it's "exactly" a solution by itself, if that makes sense?
Like $e^{-x} \cos(3x)$ and $e^{-x} \sin(3x)$ are "different" than $e^{-x}$ (for one, their derivatives are different)
warm shaleBOT
@unreal musk
wooden mortar
Ohh
But for the bottom one, the derivative of e^-x still looks like it
So it's like an exact solution? :0
Therefore need to multiply by the x accordingly
unreal musk
Also taking a guess that your original homogenous equation was effectively $\dv[2]{y}{x} + 2\dv{y}{x} + 10 = 0$, for which $y = e^{-x}$ isn't a solution if you try to check directly
warm shaleBOT
@unreal musk
unreal musk
And in the bottom one, cause you find e^{-x} in that homogenous solution, that would basically vanish if you tried substituting it, similar with xe^{-x}, so you'd keep going until you're not in the homogenous solution, which is x^2 * e^{-x}, and then you don't have the vanishing problem that you would with the homogenous solutions 
wooden mortar
I see
So mainly for the top one
Because there's no exact e^-x in homogenous solution, as it multiplied with the cos and sin
It won't vanish so can use the standard one
As in no need to times by x
I seee~~~☆
Thank you chartbit 😭👍✨
.close
obtuse pebbleBOT
unreal musk
Always a pleasure 
obtuse pebbleBOT
Available help channel!
spring fossil
obtuse pebbleBOT
spring fossil
Hello
I would like to inquiry how to find the null space of the above matrix
Much obliged
lusty badge
You're going to find x such that Ax = 0
obtuse pebbleBOT
@spring fossil Has your question been resolved?
sullen solstice
obtuse pebbleBOT
sullen solstice
How do I solve this? I would be dividing by 0 in the end when I substitute 0.6 in…
Help😭
<@&286206848099549185>
tranquil ginkgo
I dont think you have to simply 0.6 stuff
sullen solstice
Please expand, I don’t understand…
somber thistle
do you mind writing the last term with the ln and the sqrt here? i can't quite read it
sullen solstice
0.12(ln((5x/sqrt(9-25x^2))+(3/sqrt(9-25x^2))-5x/3)
<@&286206848099549185>
😭😭
This is what the graph looks like on Desmond
Desmos
Nooooplshelp
<@&286206848099549185>
sullen solstice
you forget the dx part
Wait, Even with that part included I would still be dividing by 0 though…
tranquil ginkgo
no. rewrite the dx part see what you get
obtuse pebbleBOT
tranquil ginkgo
wait it shoule be sin^2, and you use double angle formula
obtuse pebbleBOT
Available help channel!
ripe surge
Idk how to do this at all
obtuse pebbleBOT
Idk how to do this at all
warm shaleBOT
Monarch of Eternal Night
crude lynx
$128=4^3.2$
warm shaleBOT
Monarch of Eternal Night
ripe surge
So what’s the answer supposed to be
crude lynx
Well, I already told you the method
crude lynx
No
crude lynx
I didn’t pay attention when square roots was being taught
Since it's cube root, take the number with cube outside the root
crude lynx
So do I take 1458 and square root it by 9
Cube root it
obtuse pebbleBOT
@ripe surge Has your question been resolved?
ripe surge
Cube root it
How do I do it on the calculator tho
crude lynx
How do I do it on the calculator tho
For this question, you don't need it
ripe surge
Is it 3 for the first box
torpid tundra
would it be possible to map (0.5, 0.5) to the normalized 3d vector (0.91, 0.41, 0.03), if so, what's the formulas
obtuse pebbleBOT
would it be possible to map (0.5, 0.5) to the normalized 3d vector (0.91, 0.41, ...
@torpid tundra Has your question been resolved?
torpid tundra
<@&286206848099549185>
tired shell
would it be possible to map (0.5, 0.5) to the normalized 3d vector (0.91, 0.41, ...
not sure what this means, could you make a picture or something?
it's probably going to be a projection formula
torpid tundra
not sure what this means, could you make a picture or something?
for example:
(0.5, 0.5)
(0, 0, 1) will map to
(0.5, 0.5, 1)
(0, 1, 0) will map to
(0.5, 1, 0.5)
tired shell
still confused but you might be able to do that on (0.91,0,0), (0,0.41,0), and (0.03), normalize how you want then add them
torpid tundra
im trying to map them to a directional vector, (0, 0, 1) has the vector pointing in the z direction which allows the 2d vector to just be added normally. But if the directional vector is (0, 1, 0) the x, y wouldn't act the same way, which the mapping would look like (0.5, 1, 0.5)
tired shell
if your thing is vector + 0.5(perpendicular), there's many options but one is {x,y,z} is perpendicular to {-y,x,0} and {-xz,-yz,x^2+y^2}
torpid tundra
all the vectors i sent are examples because it's easier to explain with those vectors
the 2d vector is not a constant value
tired shell
3 examples on (1,0,0) (0,1,0) (0,0,1) give a unique matrix if your thing is linear, I just don't know what you're going for
torpid tundra
it's for a thing in minecraft, where the player would look in a direction and be able to go into a "2d screen" like mode. The mouse is what im trying to calculate where the location would be in the 3d space
tired shell
oh gotcha that's a big thing in unity
right now my guess is this for the 0.5's but I need to consider that video
torpid tundra
the 2d vectors are the mouse x and y coordinates
i used 0.5 as an example
and the 3d directional vectors were also examples
tired shell
there's a weird thing about 3d angles where there's no actual right way up
this sort of thing
torpid tundra
what
tired shell
concretely like if you face north then look up to (0,0,1), that's different from facing east then looking up to (0,0,1)
torpid tundra
are you talking about quaternion rotation?
tired shell
yea it's from quaternions not being commutative
torpid tundra
what do quaternions have to do with this
tired shell
like where do you want the x and y axis to point when looking up in the z-direction, there's no correct choice
this might be good
it just gets funky near the top
torpid tundra
if you're looking up it will always be (0, 1, 0)
im getting the vector from the pitch and yaw of the player
then normalizing it
which gives me a normalized directional vector
then i want to apply the 2d coordinates from the mouse vector, to the directional vector so i can then offset the mouse to it's proper location
tired shell
if your thing is vector + 0.5(perpendicular), there's many options but one is {x...
ok so back to this, it should be +(x mouse)*{-y,x,0}
can't tell if the other vector there points to the north pole or not to give the +y part
torpid tundra
+x???
tired shell
like {0.5,0.5} is the x and y of the mouse
and the function you want seems like direction vector + mouse distance along that viewing 2d plane
torpid tundra
and the function you want seems like direction vector + mouse distance along tha...
yeah but i cant just add it
tired shell
torpid tundra
because that only works if the z is 1
torpid tundra
what?
tired shell
if your thing is vector + 0.5(perpendicular), there's many options but one is {x...
if you angle it it's like the x and y axis of the mouse
idk how this compares to what you want
but it's like you draw a plane at the end of the vector, then add along that plane by the mouse horizontal and vertical
in minecraft it's just blocks so looking at a diagonal angle is going to be really ugly
torpid tundra
but it's like you draw a plane at the end of the vector, then add along that pla...
could you send me a formula of what you mean
tired shell
so normalized direction {x,y,z} with mouse {a,b} goes to
x-ay/sqrt(x^2+y^2)-bxy/sqrt((xz)^2+(yz)^2+(x^2+y^2)^2),
y-ax/sqrt(x^2+y^2)-byz/sqrt((xz)^2+(yz)^2+(x^2+y^2)^2),
z+b(x^2+y^2)/sqrt((xz)^2+(yz)^2+(x^2+y^2)^2
there's probably a 3d rotation matrix that does this cleaner welp
as (direction)+(3d rotation by direction)*(mouse)
torpid tundra
as (direction)+(3d rotation by direction)*(mouse)
(direction)?
remote needle
a
tired shell
the normalized 3d vector (0.91, 0.41, 0.03)
torpid tundra
(3d rotation by direction) im assuming is a quaternion from the vector
tired shell
yea just like pitch and yaw
torpid tundra
so grab the quaternion from the vector?
tired shell
I'm not sure how it works but yea with quaternion of the vector multiply with the quaternion of the mouse with depth=0
torpid tundra
and the mouse would be vector(x, y, 0) as a quaternion?
tired shell
I think so? there's a weird thing with mixing positions and angles in quaternions I don't remember
https://math.stackexchange.com/questions/40164/how-do-you-rotate-a-vector-by-a-unit-quaternion is saying it's qvq* for q=quaternion direction and v=(x,y,0)
q* as conjugate quaternion
tired shell
3d angles have a representation as quaternions
and you multiply them to compose rotations
torpid tundra
oh then you would rotate the vector around that?
but what's the point of converting it to a quaternion
obtuse pebbleBOT
@torpid tundra Has your question been resolved?
tired shell
quaternions are just one of like 3 ways to do 3d angle stuff
you can do coordinates xyz or pitch yaw trigonometry
obtuse pebbleBOT
@torpid tundra Has your question been resolved?
obtuse pebbleBOT
@torpid tundra Has your question been resolved?
median dome
Question: Find $$L=\lim_{x\to 0}\frac{e^{2x^2}-e^{\arctan(2x^2)}}{x^6}$$
warm shaleBOT
kheerii
median dome
I write this as $$L=\lim_{x\to 0}\frac{2\frac{e^{2x^2}-1}{2x^2}-2\frac{e^{\arctan(2x^2)}-1}{\arctan(2x^2)}\cdot\frac{\arctan(2x^2)}{2x^2}}{x^4}$$
warm shaleBOT
kheerii
median dome
the $\frac{\arctan(2x^2)}{2x^2}$ term becomes one, so we are left with $$L=2\lim_{x\to 0}\frac{\frac{e^{2x^2}-1}{2x^2}-\frac{e^{\arctan(2x^2)}-1}{\arctan(2x^2)}}{x^4}$$
warm shaleBOT
kheerii
median dome
am I incorrect up until here?
because if this is correct we should get 0, since the first term in the numerator gives us $1+x^2+\frac{2}{3}x^4+O(x^6)$ and the second term gives us $1+\frac1{2}\arctan(2x^2)+\frac1{6}\arctan^2(2x^2)+O(\arctan^3(2x^2))=1+(x^2+O(x^6))+\frac{2}{3}x^4+O(x^6)$
warm shaleBOT
kheerii
median dome
so their difference is just O(x^6)
frank monolith
**kheerii**
why dont you just use the series expansion at the start?
median dome
why dont you just use the series expansion at the start?
oh yeah, true
that completely slipped my mind for some reason
frank monolith
**kheerii**
also i didnt quite follow this step
median dome
also i didnt quite follow this step
if you look at the expansions, they cancel out upto the x^4 term
frank monolith
yeah they do
median dome
the remaining is just x^6 and above, which gives us the value of the limit as 0
which isn't the answer
frank monolith
if you do the same thing at the start, the x^6 term remains and you end up with 8/3
idk if you messed up the series somewhere
median dome
hmm
median dome
idk if you messed up the series somewhere
$e^t=1+\frac{t}{2}+\frac{t^2}{6}+\frac{t^3}{24}$
warm shaleBOT
kheerii
warm shaleBOT
kheerii
median dome
,w limit as x goes to 0 of (((e^(2x^2)-1)/(2x^2)-(e^(arctan(2x^2))-1)/(arctan(2x^2)))/x^4
warm shaleBOT
median dome
yeah both are
the first one was supposed to be (e^t-1)/t, my bad
what's wrong with the second one?
median dome
**kheerii**
also there's some issue in this step
which I can't figure out at all
ahhhhh wait there's a plus in tanx
so there should be a minus in arctanx
got it
,close
.close
obtuse pebbleBOT
fluid gulch
can someone help at help 24
obtuse pebbleBOT
Available help channel!
celest musk
hello can somebody please help me with iii
obtuse pebbleBOT
hello can somebody please help me with iii
celest musk
my solution was C4,3 * C8,2
considering that you pick 3 teachers out of 4 and then you pick 2 other people from the remaining 8
why is this wrong?
obtuse pebbleBOT
@celest musk Has your question been resolved?
polar fossil
you're double counting some combinations
eg if the teachers are ABCD and the rest are EFGHJKL then you could pick:
ABC and then DE
ABD and then CE
ACD and then BE
BCD and then AE
and these would all be the same combination but you've counted it 4 times
celest musk
eg if the teachers are ABCD and the rest are EFGHJKL then you could pick:
ABC an...
why are they the same combination?
2 and 3 are equal but 1 and 4 im confused
polar fossil
that's because I'm bad at typing hold on let me fix it
celest musk
oh ok dw
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hoary granite
was watching a lecture but the guy said let's skip over the derivation :< how do we get here?
obtuse pebbleBOT
was watching a lecture but the guy said let's skip over the derivation :< how do...
@hoary granite Has your question been resolved?
obtuse pebbleBOT
@hoary granite Has your question been resolved?
obtuse pebbleBOT
@hoary granite Has your question been resolved?
obtuse pebbleBOT
@hoary granite Has your question been resolved?
hoary granite
no sir
strong plinth
was watching a lecture but the guy said let's skip over the derivation :< how do...
is that C a binomial coefficient or so
hoary granite
yes
strong plinth
ah ok then it's just the binomial theorem, the only fucked up part about it is that it uses the generalization of the binomial coefficient to non-natural numbers
cus $(a + b)^x = \sum_{k=0}^\infty \binom{x}{k} a^k b^{x-k}$ holds for all natural x, but if you generalize the binomial coefficient properly, then it also holds for all real numbers x
warm shaleBOT
Lartomato
strong plinth
hmm i am wondering where the -1 went though
oh wait SORRY it could be that i'm talking total shit lmao
the binomial coefficient looks completely normal
hoary granite
yeah i dont get the "+r-1" following the n in the binomial coefficeint
strong plinth
hmm, let me think, i think a good avenue to try and derive this theorem would be the following
we know that $(1 - x)^n = \sum_{k=0}^n \binom{n}{k} (-1)^k x^{n-k}$
warm shaleBOT
Lartomato
strong plinth
and we also know that $(1 - x)^n (1 - x)^{-n} = 1$
warm shaleBOT
Lartomato
strong plinth
so if we assume $(1 - x)^{-n} = \sum_{k=0}^\infty a_k x^k$, then we can try to determine the coefficients $a_k$ by using the series representation of $(1-x)^n$ and the fact that the two series have to multiply to 1
warm shaleBOT
Lartomato
strong plinth
so we know $1 = (1 - x)^n (1 - x)^{-n} = \left(\sum_{k=0}^\infty \binom{n}{k} (-1)^k x^{n-k} \right) \cdot \left( \sum_{k=0}^\infty a_k x^k\right)$, and then we multiply the series on the right-hand side (this is where you can use the cauchy product formula)
warm shaleBOT
Lartomato
hoary granite
also im sorry for not mentioning it before, but n , x , r are all positive integers
strong plinth
by comparing each coefficient with the left-hand side, which is just 1, you will probably get some recursive description of the coefficients $a_k$
warm shaleBOT
Lartomato
strong plinth
also im sorry for not mentioning it before, but n , x , r are all positive integ...
that's ok i think that was clear
not for x, but i think it also doesn't matter much for x
okay but what i wrote above was kinda complicated
hoary granite
i understood it dont worry
strong plinth
alternative solution: you can do induction on n; for n = 1 you just have the geometric series, so that's easy
hoary granite
but im afraid that method is too lengthy 🤔
hoary granite
alternative solution: you can do induction on n; for n = 1 you just have the geo...
oh yes
strong plinth
the induction step is then $(1 - x)^{-(n+1)} = (1 - x)^{-1} \cdot (1 - x)^{-n}$
warm shaleBOT
Lartomato
strong plinth
the left factor is again just a geometric series, the right factor is your induction hypothesis
and then you again use the cauchy product formula to combine it all
and i'm guessing some standard binomial coefficient properties will give you what you want
maybe you can try that!
hoary granite
yeah let me try
strong plinth
if you struggle let me know but i'm guessing that the hardest part is just writing the cauchy product formula correctly
cinder hornet
was watching a lecture but the guy said let's skip over the derivation :< how do...
isnt this
the stars and bars approach/result for counting !!
hoary granite
if you struggle let me know but i'm guessing that the hardest part is just writi...
💀 i dont know about cauchy products yet, but i think theres another way to get their through induction so im trying that
strong plinth
hmm oh i guess if you translated this to stars and bars, each coefficient would be the number of solutions for $x_1 + ... + x_n = k$ ?
hoary granite
isnt this
the stars and bars approach/result for counting !!
no idea what that is
warm shaleBOT
Lartomato
strong plinth
💀 i dont know about cauchy products yet, but i think theres another way to get ...
it's the fancy name for $(\sum_{k=0}^\infty a_k x^k) \cdot (\sum_{j=0}^\infty b_j x^j) = \sum_{r=0}^\infty (\sum_{j=0}^r a_j b_{r-j}) x^r$
warm shaleBOT
Lartomato
hoary granite
interesting
strong plinth
hehe yeah this is exactly one of the stars and bars theorems
but it takes some work to see why
hoary granite
Got it guys!! Thank you so much for the help
had to do it thrice because I thought I wasnt getting n+1 term in the final form lmao 😭 I'm just dumb
@strong plinth thank you (letting you know im closing this channel, just in case)
ty methonmatics too
.close
obtuse pebbleBOT
strong plinth
awesome!
obtuse pebbleBOT
Available help channel!
timid silo
Stuck on this worksheet not really sure how to work out probabilities
obtuse pebbleBOT
Stuck on this worksheet not really sure how to work out probabilities
wraith barn
Ok for Q1-3, just start off by list the probabilities of rolling each colour
main raptor
need urgent help
obtuse pebbleBOT
need urgent help
main raptor
easy sequences question
if t1 = -5 and tn = -3t ↓ (n-1) + 8
find the first 6 terms
the n-1 is subscript of t
would you find t2 by doing t2 = -3(t1) + 8
t2 = (-3)(-5) + 8
t2 = 23
please help
proven aspen
what is this downward arrow sign?
eager niche
what is this downward arrow sign?
Subscript I believe
main raptor
thanks i got it, do you know how to find geometric sequence formula given the terms?
1, -2/3, 4/9, -8/27
obtuse pebbleBOT
@main raptor Has your question been resolved?
tranquil ginkgo
assume n starts from 1, you can seperate each term into two parts, one is the size of the number, the other is the sign of the numb
the sign of numb should be simple, then you find the pattern of the fraction
fallen inlet
Hello
bold bane
First, isolate the term that contains the variable c.
After that, divide by both sides by d to completely isolate c.
radiant marsh
How to do this???
if I'm correct this is pretty easy, what steps would you do when you try to find x in a normal equation?
let's take the example 4+4x = 10, you want to get rid of the 4 on the left side, how do you do that? -4 to the whole equation to get 4+4x-4 = 10-4 which is 4x = 6, then the opposite to multiplication would be division, you want to get rid of that 4 that's hugging the x right? They're a bit too close together, so we get 4x/4 = 6/4 which gets us x=6/4 -> x=3/2
obtuse pebbleBOT
@fallen inlet Has your question been resolved?
fallen inlet
First, isolate the *term* that contains the variable **c**.
I should minus ad ?
radiant marsh
do you know how to find x in 2+2x=4?
fallen inlet
if I'm correct this is pretty easy, what steps would you do when you try to find...
I would isolate x I think
Yes
radiant marsh
how would you do that
fallen inlet
Minus 2
radiant marsh
and then
radiant marsh
ok, what's the difference in your question?
radiant marsh
ab + cd = ef, you can treat ab and ef as whole numbers
fallen inlet
Ok
radiant marsh
as ab = number, ef = other number, I'll use n and o to shorten it and get
n + cd = o
now you can clearly see that all you need to do is get rid of that n to get cd = o-n
I hope my explanation makes sense
fallen inlet
Yes
fallen inlet
Yes
stiff hinge
i can't figure out what's wrong with my interval
obtuse pebbleBOT
i can't figure out what's wrong with my interval
stiff hinge
same thing with this problem
obtuse pebbleBOT
@stiff hinge Has your question been resolved?
stiff hinge
if someone could at least help me out w the principle of the intervals of convergence, i'd rlly appreciate it!
stiff hinge
i can't figure out what's wrong with my interval
im still confused for this one
worn yoke
you would generally expect the interval of convergence for a center a and radius R to look like
a - R < x < a + R (possibly including the endpoints). in this case your interval and radius/center don't agree
sudden axle
yo
obtuse pebbleBOT
@stiff hinge Has your question been resolved?
stiff hinge
you would generally expect the interval of convergence for a center a and radius...
it worked, it ended up being the following:
(3/8, 5/8]
thank u all!
glass zodiac
Can someone explain how the line integral along the counterclockwise path is zero? I figured it would be negative since it appears as if you are going against the vectors overall
obtuse pebbleBOT
Can someone explain how the line integral along the counterclockwise path is zer...
brave bramble
This all the context you have? They didn't happen to say the field is conservative, did they?
brave bramble
I think the question is more about the other two fields lol
glass zodiac
nah its all 3 i think
it makes no sense tho
the first 2 are obv 0 so im good with that
brave bramble
Oh like they all could be zero, I get it
glass zodiac
yeah
main raptor
what class is this
abstract snow
can someone please explain how you get the solution for the last part:
obtuse pebbleBOT
can someone please explain how you get the solution for the last part:
abstract snow
i tried asking chatgpt as it was urgent and it kept giving me nonsensical reasonings, i tried looking in stackoverflow and didn't find any solutions there either
i just need to know how to do the working
surreal forge
i just need to know how to do the working
number starts with 11... there are 6^4 ways
number starts with 121... or 122... there are 2 * 6^3 ways
number starts with 1231... or 1232... or 1233... there are 3 * 6^2 ways
number starts with 12341... or 12342... or 12343... or 12344... there are 4 * 6 ways
number starts with 12345... there are 5 ways
obtuse pebbleBOT
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shut crater
Unsure of how to approach this. Do I need the anti derivative?
obtuse pebbleBOT
Unsure of how to approach this. Do I need the anti derivative?
brave bramble
glass vapor
yes that
shut crater
Ohhh
brave bramble
From googling "average value of function"
shut crater
How do I use that though
glass vapor
do it?
shut crater
How?
glass vapor
integrate
shut crater
h o w
glass vapor
Oh💀
power goes up coefficient goes down
So
power becomes 2
divide 3 by 2
and 8 just becomes 8x
plug 6 in
shut crater
Ohhh, the anti derivative
shut crater
OHHH
glass vapor
same thing
obtuse pebbleBOT
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worthy prawn
i need help with this, not really but its just that my eyes arent to good and i see two of everything (monocular diplopia) and i have a lazy eye making my vision blurry and hard to see
obtuse pebbleBOT
i need help with this, not really but its just that my eyes arent to good and i ...
obtuse pebbleBOT
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sudden mist
How can polynomial identities be proven?
obtuse pebbleBOT
How can polynomial identities be proven?
hollow badger
Give me an example of one polynomial identity, something like (x + a)^2 = x^2 + 2ax + a^2, and we can try prove it
obtuse pebbleBOT
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lilac pebble
Use the second derivative test to find the local extrema of f(x) = 3x^4 + 4x^3 - 12x^2 + 2
obtuse pebbleBOT
Use the second derivative test to find the local extrema of f(x) = 3x^4 + 4x^3 -...
lilac pebble
So i found the first derivative and set it to 0
and i got x=-2 or x=1
then i found the second derivative and plugged those two values in
to get 72 and 36 respectively
but both of those are minimums
so are there no maximum/extremas?
hollow badger
and i got x=-2 or x=1
There’s one more solution (x = 0), which will give you a maximum 
weary heart
There’s one more solution (x = 0), which will give you a maximum <:catthumbsup:6...
yup
obtuse pebbleBOT
@lilac pebble Has your question been resolved?
lilac pebble
There’s one more solution (x = 0), which will give you a maximum <:catthumbsup:6...
wait how
its (x+2)(x-1)=0
nvm
nvm
nvm
.close
fiery breach
obtuse pebbleBOT
fiery breach
how to do disss :<
safe haven
what do you understand about 94% of the letters are within 12g of the mean
obtuse pebbleBOT
@fiery breach Has your question been resolved?
wintry mauve
obtuse pebbleBOT
wintry mauve
.reopen
granite fossil
Is the circled part the correct final answer?
obtuse pebbleBOT
Is the circled part the correct final answer?
earnest elk
whoops, youre right, itd be 4(1) - 9, and the end would be 30x^5 - 5 instead?
No, Almost there
What’s the derivative of a constant wrt x?
granite fossil
What’s the derivative of a constant wrt x?
im not sure, what is the constant wrt x?
earnest elk
9
urban kiln
well does a constant value change wrt any other changing value?
as you can see, any constant number, say k, is not in any way related to x, since it doesnt change as x changes, its rate of change is 0
ie d/dx(constant)= 0
granite fossil
as you can see, any constant number, say k, is not in any way related to x, sinc...
I think I remember that from a chapter before, the ending would be 30x^5 + 4(1) - 9(0) = 30x^5 + 4?
urban kiln
or, constant can be written as kx^0, when u differentiate it, u get 0.kx^-1 = 0
urban kiln
I think I remember that from a chapter before, the ending would be 30x^5 + 4(1) ...
yesss exactly
granite fossil
ok thank you
granite fossil
or, constant can be written as kx^0, when u differentiate it, u get 0.kx^-1 = 0
this is what I did before, thank you
Sorry but am I using the constant rule or the power rule?
granite fossil
ok thats what I thought, thank you for your help
granite fossil
.close
obtuse pebbleBOT
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dawn nest
how did the first line simplify to the second line? (the circled expression is given as 60)
obtuse pebbleBOT
how did the first line simplify to the second line? (the circled expression is g...
worn yoke
,, \log_{10} 10^{-3} = -3 \log_{10} 10 = -3(1)
warm shaleBOT
cloud
obtuse pebbleBOT
dawn nest
.reopen
obtuse pebbleBOT
✅
dawn nest
another question sorry
distant shadow
Hi
dawn nest
I'm trying to understand how we get the equation of this graph
distant shadow
So you know the y intercept
dawn nest
yeah
dawn nest
So it is satisfied by all exponentials
I see, but where did 1/3 come from
tardy tusk
(1/3)^(-1)=3
tardy tusk
So its of a fraction lesser than 1
Bigger than 0
dawn nest
oh so its -(3)^x ?, nah nvm
distant shadow
Again it cuts at -1, 3
When x= -1 y = 3
So y = (1/3)^-1
Generally y : (1/3)^x
tardy tusk
😦
dawn nest
When x= -1 y = 3
okay I get this part, but how did you exactly integrate this into the equation
muted stump
since they gave the point (-1, 3)
and you know it is exponential of the form $y=a^x$
then sub in (-1, 3)
to get $3=a^{-1}\$
$3=\frac{1}{a}\$
$a=\frac{1}{3}\$
$\therefore y=\left(\frac{1}{3}\right)^x$
warm shaleBOT
kotuseid
distant shadow
For you !
muted stump
😁
dawn nest
thanks @muted stump that's what I meant
and thanks @distant shadow I get it now
will close
.close
obtuse pebbleBOT
distant shadow
ofc bye
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spark iron
Assume the particle released from rest downwards, and I assumed upwards is postive direction. I dont get a terminal velocity once i derive and expression for v
obtuse pebbleBOT
Assume the particle released from rest downwards, and I assumed upwards is posti...
sonic forum
Assume the particle released from rest downwards, and I assumed upwards is posti...
it should be -ma = mkv- mg
since you took the axe upwards
spark iron
why tho?
sonic forum
because the particle is going downwards so the acceleration as a vector is down
spark iron
but we arent considering it as a vector
sonic forum
you consider it as a vector first then you project on the axe
spark iron
the value itself should pop out negative as mkv<mg
sonic forum
where a is the norm of the acceleration vector
sonic forum
this is mechanics
mechanics is all vectors
sonic forum
it should be -ma = mkv- mg
here a is >0
spark iron
wee difined the vecotr as postive
worn gazelle
I'm struggling with this
obtuse pebbleBOT
I'm struggling with this
worn gazelle
Is it true that $\frac{x}{\lambda} = \frac{y'}{\sqrt{1 + (y')^2}}$
warm shaleBOT
Jacob
glossy basalt
Is it true that $\frac{x}{\lambda} = \frac{y'}{\sqrt{1 + (y')^2}}$
seems legit, just missing a constant
worn gazelle
yeah ofc
worn gazelle
seems legit, just missing a constant
so do i need to rearrange to get whats shown?
glossy basalt
so do i need to rearrange to get whats shown?
yep, and you might also have to change the constant a bit at the end
"dummy variable"
worn gazelle
yup
glossy basalt
"dummy variable"
wait.... this term shouldn't be used like that lol
anyways i think you know what's happening after
worn gazelle
yeah just change/combine constants at the end
obtuse pebbleBOT
@worn gazelle Has your question been resolved?
worn gazelle
I don't think this rearranges to what's in the question
deft nacelle
What's the difference between a numerical sequence and a function?
obtuse pebbleBOT
What's the difference between a numerical sequence and a function?
kind hawk
a sequence is technically a function with domain N
but I am not sure thats what you are looking for
deft nacelle
In that case then why are they classified as an entirely different thing?
I agree with you that in theory, that's the only difference.
But i'm more interested in how they can be used practically.
novel knoll
Because it is more convient to write let … be a sequence
kind hawk
well they have quite different behavior. for sequences you can talk about the next point. for functions with domain R you cant
deft nacelle
OH YEAH
deft nacelle
well they have quite different behavior. for sequences you can talk about the ne...
LIGHT BULB LIT UP
THANK YOU
alright let me explain why I asked this question.
I'm trying to create models for different variables in finance using what I've learned during the last year of school.
Specifically, revenue streams (ex: evolution of a salary as per annual raise decided in contract and by labor laws, evolution of investment returns, etc..), savings and reinvestment of those savings.
deft nacelle
well they have quite different behavior. for sequences you can talk about the ne...
now, according to what you said, I can use sequences for short term calculations, and functions for long term yes?
Let me give an example so I can get some p2p review
kind hawk
I didnt say anything about short vs long term
deft nacelle
???
ohh right, functions can also do that job too
its just that according to my instrucitons, I should be able to integrate both functions and sequences
but honestly I feel like sequences become obsolete due to them literally being a function sub-type
Should I just do using fuctions?
kind hawk
use whatever works better for the model. but dont exclude sequences because they are a "subtype" of functions
obtuse pebbleBOT
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upper root
obtuse pebbleBOT
versed stratus
,rotate
warm shaleBOT
upper root
<@&286206848099549185>
distant shadow
Hi
Integrating factor
so x ^10
we get x^10 * y = int x^9 ln x
Now do by parts integration
upper root
shouldn't y' be alone in the left ranks?
distant shadow
No
im integrating using IF
See if you differentiate x^10 * y
You get thw question result
So multiply lhs and rhs with x^9
upper root
if you have pen and paper to hand, please send what you mean :))
distant shadow
Ok bro ofcourse
upper root
thank uu
obtuse pebbleBOT
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marble oak
I don’t understand this
obtuse pebbleBOT
I don’t understand this
marble oak
Can someone help me do it
flint flower
how do u calculate the area of a circle
marble oak
No clue
marble oak
Yes
marble oak
so they are expecting u to know how to calculate the area of a circle
How would I use this for these questions
tardy tusk
bro
It says to find exposed surface
It is area
diameter is 16ft
radius is half of diameter
so 8ft
So put in formula
A=πr²
marble oak
It says to find exposed surface
Does it matter to at is asking about exposed surface
tardy tusk
exposed means open
marble oak
So #1 just equals 8^2pi
marble oak
And that’s useful so he know how much space ig
tardy tusk
Ye
marble oak
Would #2 just be 128pi
tardy tusk
Hm
Two coasts what a hell
How can we have two coasts in cylinder
and how can you paint exposed surface
marble oak
Sigh
marble oak
We sre pretending the cylinder is a pool
marble oak
My geometry teacher is a little new
marble oak
Alr
tardy tusk
- V=A×h
marble oak
So 64*6
tardy tusk
ft³
marble oak
Would #4 just be the price times 384pi
tardy tusk
So #1 just equals 8^2pi
And here ft²
tardy tusk
Would #2 just be 128pi
And here ft²
tardy tusk
Ye
tardy tusk
Would #4 just be the price times 384pi
Ye
obtuse pebbleBOT
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Available help channel!
mild notch
how to integrate (x^2)(sin3x)
obtuse pebbleBOT
how to integrate (x^2)(sin3x)
tardy tusk
.close
mild notch
.close
obtuse pebbleBOT
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marsh trail
can someone help me very quick and simple
obtuse pebbleBOT
can someone help me very quick and simple
marsh trail
quartz tulip
what is your question?
obtuse pebbleBOT
@marsh trail Has your question been resolved?
obtuse pebbleBOT
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Available help channel!
rough stream
Does a Shapiro-Wilk test result of W=0.96 and p-value of 0.34 indicate that my data fits a normal distribution?"
obtuse pebbleBOT
Does a Shapiro-Wilk test result of W=0.96 and p-value of 0.34 indicate that my d...
@rough stream Has your question been resolved?
grizzled helm
Can anyone explain more what (b) is asking?
obtuse pebbleBOT
Can anyone explain more what (b) is asking?
grizzled helm
this is what chat gpt was getting but I don't understand how you can write a matrix from a transformation mapping to R^2x2
ah wait, they just stretched out the matrices into vectors
obtuse pebbleBOT
@grizzled helm Has your question been resolved?
obtuse pebbleBOT
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timid silo
can some one explain limits to me.
obtuse pebbleBOT
can some one explain limits to me.
timid silo
i graphed it. i can see it. and i thought i knew but i dont.
get common denominator
first
x?
no
i dont remember how to get to the common denominator revolving these problems
where x and 1 are both different.
u thought you would cross them over but that is mutiplication
come dm
i will show you
can someone explain limits to me?
latent frost
Quick question
obtuse pebbleBOT
Quick question
timid silo
idk
latent frost
is i(v2w3-v3w2) - j(v1w3-w1v3) + k(v1w2-w1v2) the same?
i guess it should be right?
latent frost
would prefer if you didn't respond then
timid silo
would prefer if you didn't respond then
Sure thing.
worn yoke
is i(v2w3-v3w2) - j(v1w3-w1v3) + k(v1w2-w1v2) the same?
yes, the video creator just flipped the sign on j without showing it. we can see algebraically that
j(v3 w1 - v1 w3) = - j(v1 w3 - v3 w1)
obtuse pebbleBOT
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fierce magnet
Help please i wanna cry
obtuse pebbleBOT
Help please i wanna cry
timid silo
what is tg
fierce magnet
tangens
timid silo
so tan?
fierce magnet
yes
fierce magnet
Im really sorry to ask you, could you maybe solve it? I have no idea how to do that
obtuse pebbleBOT
Available help channel!
strong forum
If X is normally distributed and Var(X)=2 and E(X)=3
Is Var(X+2X) different to Var(3X)?
obtuse pebbleBOT
If X is normally distributed and Var(X)=2 and E(X)=3
Is Var(X+2X) different to ...
wild swallow
is X + 2X different from 3X?
harsh remnant
is X + 2X different from 3X?
Looks like the left one used the canonical sum of products and the other being a minterm 😂
wild swallow
strong forum
is X + 2X different from 3X?
That's what I'm asking
I
I'm doing this question and I just did Var(X+2X)=Var(3X)=9Var(X)
But apparently
Var(X+2X)=Var(X)+4Var(X)
wild swallow
i have a feeling we are missing some context here
harsh remnant
<:what:561568026210730004>
Sorry, that was a bad boolean algebra joke
wild swallow
can you send the original question?
strong forum
Alright let me ss
strong forum
can you send the original question?
wild swallow
okay so it didn't ask you to calculate the variance of X + 2X exactly
you also have the -4Y part
wild swallow
Var(X+2X)=Var(X)+4Var(X)
this is incorrect
strong forum
you also have the -4Y part
Yeah but the solution did
Var(X+2X-4Y)=Var(X)+4Var(X)+16Var(Y)
I did
wild swallow
they are wrong
wild swallow
you are right
strong forum
Thank you
wild swallow
np
teal turret
Var(X+2X)=Var(X)+4Var(X)
||they forgot about the infinite variance glitch||
also, whats the reason it doesnt work? cuz of independence?
wild swallow
yes
teal turret
ah ok makes sense
novel knoll
also, whats the reason it doesnt work? cuz of independence?
dependence
teal turret
strong forum
||they forgot about the infinite variance glitch||
whats the infinite variance glitch
teal turret
lol
so like
it was a joke but i was referring to something like this
var(x + 2x + 4x + 7x) = varx + 4varx + 16varx + 49varx = 70varx VS var(x + 2x + 4x + 7x) = var(14x) = 196varx
novel knoll
more clear to do it like this:
var(x)=var(x+x-x) != var(x)+var(x)+var(x)=3var(x)