have you done y yet? do that one before looking at z
#help-17
mild flower
wispy schooner
-2.8+y*1=.3
mild flower
i think you mean -2.8 + D*1 = 0.3
wispy schooner
Yes, sorry there’s so many variables
mild flower
you should end up with something that looks like y(t) = ___ + ___t, where there are numbers in the blank spaces
wispy schooner
I thought the t was the y*1 and the y(t) = .3
Because we subtract the points after
mild flower
i don't think I'm following you
our goal here is to come up with an equation for y in terms of t, we know it's going to be linear and we know it's going to pass through (0, -2.8) and (1, 0.3)
wispy schooner
I kinda get it, its because the equation before we used the equation for x(0) and x(1) that’s why I was following the rest of the equations as the set up (like -2.8+y*1=.3)
mild flower
yeah we did a very similar thing for x, to find an equation for x in terms of t
the procedure for finding x(t) and the procedure for finding y(t) [remember these are both equations, not values] are identical; the only thing that changes is the numbers we're working with
wispy schooner
Oh okay
So for the equation vector itself that means it’s 3.5-1.7t, 3.1t-2.8, and then lastly its 2.1
mild flower
yep which can be written as z(t) = 2.1 + 0t if you want to make it nice and symmetric; I'd recommend sticking to either ascending or descending order
vocal sleetBOT
hushed tree
heavy yoke
<@&268886789983436800>
lost yarrow
.close
mint remnant
What is the derivative of y=x^3*ln(1-x)?
vocal sleetBOT
What is the derivative of y=x^3*ln(1-x)?
vocal sleetBOT
What is the derivative of y=x^3*ln(1-x)?
Show your work, and if possible, explain where you are stuck.
paper depot
What is the derivative of y=x^3*ln(1-x)?
do you know in general how to take derivatives?
mint remnant
Yes but the multiple choice question didn’t seem to have it
I want to know if I did it correctly
outer warren
show what you did and the available options
(don't just show your final result, show all steps)
mint remnant
mint remnant
I can’t remember but the one I chose was almost like my one but the bracket contained x-1 instead
The other ones were obviously wrong and I sketched them to make sure
mild flower
it might be useful to recall that $1-x = -(x-1)$
twin meteorBOT
kitten.in.a.teacup
mint remnant
Is that a law for logs though?
-ln(x-1)=ln(1-x)?
I remember one of the answers were -3x/(x-1) and another was 3x^2*ln(1-x)
twin meteorBOT
regal bane
Why is Wolfram so eager to do weird factoring in the final answer
mild flower
it's a showoff
regal bane
Like "yes, I would like x² factored out of that, please"
vast shale
Like "yes, I would like x² factored out of that, please"
It is trying to be soo formal
vast shale
-ln(x-1)=ln(1-x)?
No , you can just take that -1 either to the power of number or of Base
mint remnant
i think the exam had no answer
it was designed by one teacher
only the end of year exams are written by a team
vast shale
i think the exam had no answer
Prolly they did error? Or want you to pick closest correct answer?
mint remnant
yep
vast shale
Hmm
mint remnant
it was a tech active exam so i sketched them all and not of them matched
vast shale
Well in that case you should just report that question
mint remnant
yep
vast shale
To the incharge
mint remnant
i’m not too stressed since these don’t go on reports, only for practise
but i’ll definitely talk
vast shale
✅
mint remnant
.close
unborn quail
if $2x^3 - 8x^2 + 3x - 4 = a(x-1)^3 + b(x-1)^2 + c(x-1) + d$ find a b c and d
twin meteorBOT
Big Chicken
tropic field
Expand and compare the coefficients I guess
unborn quail
surely there is a faster way
tropic field
Both part input 1 and find d
unborn quail
i did that
nvm i got it
u just keep on subbing in values for x
and u slowly get equations
that u solve simultaneously
also teh leading coeff can easily be eqaute
a = 2
thanks for u help
tropic field
But won’t expanding it be better
unborn quail
its slightly faster this way
tropic field
I see
vocal sleetBOT
twin meteorBOT
bitter copper
Use a new help channel this one may get moved because you closed it before it reopened
vocal sleetBOT
Available help channel!
unborn quail
vocal sleetBOT
unborn quail
,rotate
twin meteorBOT
unborn quail
i sent it again
tropic field
Although it is slow but you can plug in 3,2,1,0
unborn quail
but dont i need to expres it into the other form
unborn quail
its not equating tho
i have to change the equation
of the first one
into the form into the first one
tropic field
Find E you gotta sub in 0
Yes
It is kinda slow tho
Maybe there is a better way
Btw for “A”
unborn quail
A = 1
unborn quail
c = 4
tropic field
I guess you know how to do it
twin meteorBOT
onyx hound
What grade are you in?
tropic field
How’s it
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
i forgot what is the formula and how to answer the area of a circle
echo badger
πr²
real gale
https://youtu.be/D4nGkWOPb6M Watch this
fallen hedge
how do I prove this?
vocal sleetBOT
how do I prove this?
fallen hedge
im gtuessing that it extends off the double angle formula
fallen hedge
yes that's the most straightforward way
what are the steps of proving it?
paper depot
you think we will just give the entire solution to you?
paper depot
no such thing as "the" next step,
fallen hedge
clue
paper depot
but you could try to apply double angle identities where you see a way to do so.
vocal sleetBOT
@fallen hedge Has your question been resolved?
hasty wren
Is this a correctly executed Euler cycle?
In an Euler cycle, you can't go through the same point twice, right?
hasty wren
Or can you go through a point more than once, but not through an edge/side?
vocal sleetBOT
@hasty wren Has your question been resolved?
hasty wren
<@&286206848099549185>
vast shale
Or can you go through a point more than once, but not through an edge/side?
this is correct
and yes, that is an euler cycle
hasty wren
just read In Euler's cycle, which is a closed route in a graph, each edge is visited exactly once. This means you don't go through any point more than once.
which means opposite what you said
and believe what i read its inccorect bc i go thru X3 2 times
(red arrows are mine)
hasty wren
i know, but "means you don't go through any point more than once."
vast shale
it doesn't
hasty wren
Ok, hope your correct (ill read about it more later)
could you help me with this one:
vast shale
Ok, hope your correct (ill read about it more later)
you can look at the examples on wiki https://en.wikipedia.org/wiki/Eulerian_path
vast shale
could you help me with this one:
trial and error it
it shouldn't take you more than one or two tries
hasty wren
start from X2 (left up point) thats ok?
vast shale
yes
hasty wren
its too easy, feels like i do it incorrect
vast shale
euler cycles are easy
hushed atlas
for part c does it matter if
vocal sleetBOT
for part c does it matter if
river minnow
Both will work, but, obviously, solving f(x) = x is easier
vocal sleetBOT
vast shale
inverse wont be a function
vast shale
idk the condition for not 1-1 functions
river minnow
Missing
vast shale
yeah
vocal sleetBOT
Available help channel!
viscid ore
@open epoch here
vocal sleetBOT
<@736962279907524639> here
hushed atlas
disclaimer: its the same here because your f is an increasing bijection
idk what that means lol
vocal sleetBOT
idk what that means lol
vast shale
idk what that means lol
f is an increasing function
bijection = one-to-one and onto (which is required for the inverse to exist)
vocal sleetBOT
@hushed atlas Has your question been resolved?
delicate nymph
vocal sleetBOT
delicate nymph
can someone help me with ii
vast shale
which part of the solution do you not understand
delicate nymph
if the two vowels together count as one unit then why isnt it 1x6!x2!
delicate nymph
.close
obtuse field
hey i don't know if this is allowed since it is physics but it's pretty basic. I don't understand the small f going against F, because it says that the slab rests on a frictionless table ?
vocal sleetBOT
hey i don't know if this is allowed since it is physics but it's pretty basic. I...
obtuse field
That's all i'm not really understanding
mild flower
the table is frictionless but there's friction between the slab and the cylinder
mild flower
i think just so it's grouped with the other horizontal force
but yeah i'd have probably drawn it on top
mild flower
the force that the slab is applying to the cylinder is equal and opposite to the force the cylinder is applying to the slab yesj
wintry slate
in the bottom left box, we know 2 variables .. the slope of the red line (0.923077, 0.384615) and the coordinates of the start of the green line (15.3847, 222.117786)
we're trying to produce -200, 100 from the coordinates of the start of hte green line and the slope of the red line
can anyone help me?
vocal sleetBOT
in the bottom left box, we know 2 variables .. the slope of the red line (0.9230...
vocal sleetBOT
@wintry slate Has your question been resolved?
mild flower
i'd probably do all of this with coordinate geometry
slope of a perpendicular line is -1 / slope, find the intersection point of blue and red and then use distance formulas
vast shale
i tried many things but i can't mirror f_1 in the respect of f_2
vocal sleetBOT
i tried many things but i can't mirror **f_1** in the respect of **f_2**
Show your work, and if possible, explain where you are stuck.
vast shale
well i was i just messing around in calculator... was trying to mirror the f_1 coz i just studied about transformation in functions... so i was little curious what will be the eq if the quadratic eq doesn't meets with the x axis and is mirrored from a x axis with the height = N
now i am curious that how i am going to mirror the green line where x and y are in the 1st 2nd quadrant
with the respect of X = {y ∈ W : y ≠ 0; y<20} where X is x axis with height of y
<@&286206848099549185>
clear vault
yes?
clear vault
i don't know
wide rapids
lol
clear vault
i'm in year 8
vast shale
i'm in year 8
what do u mean
wide rapids
wdym mirror, like symmetry of the x axis?
vast shale
yea
clear vault
what do u mean
I mean I am in school year 8
wide rapids
y=-f(x) is the flip of the function y=f(x)
clear vault
13
wide rapids
across the x axis
vast shale
across the x axis
ik that
but i dont want that
i don't want to flip it across x axis
vast shale
show me the eq
vast shale
|y|-20 = ||x^2 + x + 1| - 2|
i mean
like
not particularly across f_2
like any vertical axis with the height of h = {y ∈ W : y ≠ 0; y<20}
which will be basically all integers but not 0
wide rapids
what can u clarify
u said u wanted to horizontally transform it
now you are across vertical axis
f_2 is a horizontal line
vast shale
now you are across vertical axis
sorry sorry horizontally.... i always get confused with vertical and horizontal
wide rapids
how does horizontal axis have height
vast shale
how does horizontal axis have height
like y = {y ∈ W : y ≠ 0; y<20}
wide rapids
are u trying to define a horizontal axis with y values in between 0 and 20?
vast shale
like these if u didn't get my point
vast shale
are u trying to define a horizontal axis with y values in between 0 and 20?
.... y = { -2, -1, 1, 2.... 20}
wide rapids
i dont know
wide rapids
.... y = { -2, -1, 1, 2.... 20}
so y=-2, y=-1
...etc
are the lines ur talking about?
vast shale
so y=-2, y=-1
yea
wide rapids
i see, its the same logic tho
u can use the y=0 as a reference and do -f(x)+y
and y depends on which
axis ur talking about
vast shale
|y|-20 = ||x^2 + x + 1| - 2| edit this eq and tell me what i have to edit
i can understand it way better when looking at the equation...
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
nevermind
i got it
i just had to change |y|-20 = ||x^2 + x + 1| - 2| this equation to something like
|y - a|-20 = ||x^2 + x + 1| - 2|
vocal sleetBOT
@vast shale Has your question been resolved?
strange wave
is thtis supposed to be 6 or 7?
strange wave
7
strange wave
x = 1 so you use the x>=1 definition
my dumbass put 6 and i got 97% 💀
strange wave
my dumbass put 6 and i got 97% 💀
i did that before ur explanation
vocal sleetBOT
vocal sleetBOT
Available help channel!
wide rapids
the strategy we use to find the period of the function f(x) = acos(kx) + bsin(kx)
vocal sleetBOT
the strategy we use to find the period of the function f(x) = acos(kx) + bsin(kx...
wide rapids
is basically finding out the period of cos and sin independently
then find their LCM?
this extends to ie f(x) = acos(kx) + bsin(kx)+ccot(kx)+xcsc(kx)
etc
any trigonometric function addition
is this true?
random gust
It extends for any periodic functions, and yes
wide rapids
It extends for any periodic functions, and yes
ok ty!!!
im gonna go eat
noodle
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
real pagoda
vocal sleetBOT
river minnow
Yes, it is a quadratic equation in sin(theta)
real pagoda
Yes, it is a quadratic equation in sin(theta)
so u do 2a^2+a-1 = 0
letting a be sinx
river minnow
Yes
viral copper
so a = -2 or 1
That doesn't seem right
real pagoda
a= 1 or -1?
river minnow
Still no
floral seal
how did you calc?
floral seal
yes
real pagoda
alright
floral seal
so 0.5,-1
real pagoda
and then i just inverse sin it and do the astc right
floral seal
yes
real pagoda
alright thanks
floral seal
No problem
vocal sleetBOT
vocal sleetBOT
Available help channel!
ivory spruce
K-2(x+1)^2x + x
vocal sleetBOT
K-2(x+1)^2x + x
ivory spruce
How would you determine the value of k to make a perfect square trinomial by chance?
Im aware k= 2ab
But in this instance, would it be
2(1)(2(x+1)^2)?
vocal sleetBOT
@ivory spruce Has your question been resolved?
late current
The linear combinations a1v1 + a2v2 and b1v1 + b2v2
can
only be equal if a1 = b1 and a2 = b2
.
vocal sleetBOT
The linear combinations a1v1 + a2v2 and b1v1 + b2v2
can
only be equal if a1 = b1...
late current
true or false
lyric fossil
what do you think?
late current
what do you think?
i mean true
late current
oh
i see
i have to think like that
but js to make sure
if they were not 0
then
it is true right?
sly sierra
no
suppose v1 = v2 = some nonzero vector for example
the statement is true under a specific assumption about v1 and v2, what assumption do you think that is?
late current
the statement is true under a specific assumption about v1 and v2, what assumpti...
orthonormal ?
sly sierra
yes, it's true in that case (if there is an inner product defined), but there's a more general assumption
late current
wait hold on
alright so yeah firstly v1 and v2 cant be equal 0 . bc if they are 0 then the equality will hold for all values for b1 a1 b2 a2 even if they are dissimilar therefore false . secondly if one of them is 0 then still the equality will hold therefore false . if both are non 0 .and if both are equal say 5v +6v . where 5 =a1 and 6 = a2 then there exists another a2 and b2 to yield an equal linear combination for example a1=a2 b1=b2 will yield the same vector as well as a1=b2 and a2=b1 so false again
i dont think that being unit vectors is important
or waitt
if they are not perpendicular
i.e linearly dependent
then
we would have inf number of b1 b2
right
so yeah
unit vectors are not important
but linear independance is important
right@sly sierra@lyric fossil?
sly sierra
but linear independance is important
yes, linear independence is exactly this
late current
yes, linear independence is exactly this
ahh u guys like U R REALLY AWESOME
i like it when u leave me to think
and not give me the ans direclty
thats smart
thank u so much guys again
sly sierra
sure, cheers!
late current
oh btw js a quick question
n dotted with (p-s) = 0
what is that called?
anyone knows?
it is an equation for a line
sly sierra
n.(p-s) = 0?
looks like the equation for a plane with normal vector n, containing the points p and s
or rather, containing the point s and every point p that satisfies the equation
fathom hedge
vocal sleetBOT
lyric fossil
they probably want you to keep it in terms of integers
fathom hedge
also you prolly don't need to write the span in the answer box
that was it i was kicking myself tyyy
Why is U a 4-dimensional hyperplane?
I kind of inffered it from the interaction of a.x = 0 in R^3 that it would be one degree lower but why
lyric fossil
a.x = 0 will give you a single equation with 5 variables
that means you have 4 free variables
fathom hedge
that means you have 4 free variables
how so sorry?
because I can write one variable in terms of the other?
lyric fossil
basically. it’s a “degrees of freedom” question
though the intuition you had is what you should be thinking of
fathom hedge
icic
i have another related question
im just going back through some stuff to make sure i understand
so for the first part
i get it
its orthogonal to the zero vector so it spans R^3
like it has no limits on it
idk how to work
fathom hedge
yaa
and then the second part
if only opne of a and b is the zero vector
then the other one is a non zero vector
intuitively its a plane but im not really sure how i would word it or explain it
if i was asked to explain that question
lyric fossil
it’s the same thing as the last example
we now have
a.x = 0
we again get a space of 1 lower dimension
lyric fossil
yes
fathom hedge
and then if they are non zero and parralel
thatll be thje same as the last one
like intuitively i get that
lyric fossil
yes, a.x = b.x = (c*a).x = c*(a.x)
then a.x = 0 as given
do c*(a.x) is still 0
so we just get a.x = 0
no new info
fathom hedge
ooh yes so its simplies
yeaa
and then the last part i think i get now following that
and last question is simple cross product
lyric fossil
yup
vocal sleetBOT
@fathom hedge Has your question been resolved?
fathom hedge
.close
vast shale
Hi
vast shale
So I'm doing limit of sequence and I kind of don't understand a proof
After the blue line thing
I don't understand
How's N = 1/E - 1
And what's integral part
rough ether
Integral part of a real number n is the same as floor of n
The thing that comes before the decimal point of that number
rough ether
Yep
rough ether
I guess here n is a integer?
vast shale
Yes
rough ether
So, n is greater than N implies n>= ceil of (1/epsilon) -1
random gust
The closest integer greater than or equal to the value
vast shale
Basically floor?
random gust
Yeah like the opposite of floor
rough ether
It's 8
rough ether
Reasoning is this ig
n >= 1 + floor(1/epsilon - 1) >= 1/epsilon - 1 which implies 1/(n+1) < epsilon
rough ether
So, n is greater than N implies n>= ceil of (1/epsilon) -1
Sorry if my explanation confuses u more :3
vast shale
No worries, atleast you're trying 🙂
Anyways ima find youtube video!!
Thanks for the help btw
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
terse dome
vocal sleetBOT
terse dome
What happened to the 1/x^2 under the root for it to turn into x^2? I thought if the -1/X^2 outside effected it would effect even the 1 won't it? why did it become a 1/x where did it's square go?
this is the original equation before deriving
where I stopped in my notebook is -1/x^2* (root1+1/x^2)
where do I go from there? or did I go the wrong way?
cobalt crypt
[
\f 1 {\sqrt {1 + \f 1 {x^2}}} \times \f {-1} {x^2} = -\f 1 {x^2 \sqrt {1 + \f 1 {x^2}}} = -\f 1 {\abs x \sqrt {x^2 \parens {1 + \f 1 {x^2}}}}
]
twin meteorBOT
cobalt crypt
you use the facts that
[
x^2 = \abs x^2 \textqq{and} \abs x = \sqrt {x^2}
]
to rewrite
[
x^2 \sqrt {1 + \f 1 {x^2}} = \abs x^2 \sqrt {1 + \f 1 {x^2}} = \abs x \sqrt {x^2} \sqrt {1 + \f 1 {x^2}} = \abs x \sqrt {x^2 \parens {1 + \f 1 {x^2}}}
]
twin meteorBOT
terse dome
oooh after you multiply the x^2 across the 1 +1/x^2 it becomes rootx^2 + 1
thank you very much good sir
.close
oblique rivet
vocal sleetBOT
livid grotto
,rccw
twin meteorBOT
oblique rivet
,rccw
livid grotto
take the picture the other way round please
livid grotto
many people in this server have stiff necks
twin meteorBOT
oblique rivet
Is this ok?
vast shale
Why did they put x=pi??
sin is 0 and cos is (-1)^n for x=pi
vast shale
yes but why not x=0
try it and see
vast shale
what is pointwise convergence
converges at each point to the limit
oblique rivet
converges at each point to the limit
is that what we do here
vast shale
I dont see any mention of that here
vast shale
its a case of "it works"
vast shale
sin is 0 and cos is (-1)^n for x=pi
the reason why x=pi was chosen is because of this
twin meteorBOT
twin meteorBOT
oblique rivet
Why did they do integral of 1 to pi instead of c to pi?
vast shale
because c=1
oblique rivet
why is c=1?
vast shale
it tells you in the question
vast shale
alg
oblique rivet
one last thing
what exactly is pointwise convergence
to prove it is which limits do we take?
oblique rivet
so basically if a piecewise is contiuosly differentiable does it mean it always converges pointwise
vast shale
no, that doesn't make any sense
a family of functions can converge pointwise
if you are talking about this, it should be a theorem in your book
paper lodge
Is this correct?
vocal sleetBOT
Is this correct?
left talon
I think you can check that its not that hard
for exmaple, for the first one you can do this:
y = ax^2 + bx + c
you can do 3 equations with 3 parameters and then you can solve em
for function 2, we can see that it is a linear look when you change x by 1 you cahnge y by the same amount
for example when you cahnge x by 1 the y cahnges by 6 in every iteration
4 -- > 7
5 ---> 13 (7+6)
6 ----> 13 + 6 = 19
7 ---- > 19 + 6 = 25
so its a linear
vocal sleetBOT
@paper lodge Has your question been resolved?
paper lodge
4 -- > 7
5 ---> 13 (7+6)
6 ----> 13 + 6 = 19
7 ---- > 19 + 6 = 25
So it is right
I did I check but i js wanna be sure
<@&286206848099549185>
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
I am stuck here..
weak cobalt
where are you stuck exactly 😳
weak cobalt
you know that n! can be written as n * (n - 1) * (n-2)!
that's the definition of the factorial
weak cobalt
so that we can cancel it from the denominator
ashen saffron
bois
ashen saffron
say I was to buy a body pillow
(im not going to 100%)
its 150 x 50cm would it fit into 4ft
wait so its a case going onto a pillow
case being 150 x 50cm and pillow itself 4ft
paper depot
well, do you know how many centimeters a foot is?
paper depot
30.48 is the exact value, but yes, 30 is good enough for quick or non-high-precision calculations
so how long's your pillow in centimeters?
paper depot
120-ish.
you have a 120 cm pillow being put in a 150 cm long case.
will it fit in?
ashen saffron
no
paper depot
why not?
ashen saffron
but yes
ashen saffron
no because it wouldnt fill it out
yes because it wont fill it
pretty much same answer for both
paper depot
i mean the pillow can go into the case physically
it is just that the case is too large for it
ashen saffron
yes but not as intended
paper depot
whether that is a bad thing for you is for you to decide
ashen saffron
so 5ft would be fine?
paper depot
again
you decide
are you ok with a pillow being put in a case that's 30 cm too large for it
summer ore
vocal sleetBOT
summer ore
Can anyone tell me how I solve this? and is my (a) did correctly?
<@&286206848099549185>
vocal sleetBOT
@summer ore Has your question been resolved?
vocal sleetBOT
@summer ore Has your question been resolved?
wary flame
Looks good to me
summer ore
Looks good to me
May I know how to determine the transfer function?
wary flame
H(s) = Y(s)/X(s) (H = Q(s) and X = R(s) in your case)
summer ore
H(s) = Y(s)/X(s) (H = Q(s) and X = R(s) in your case)
I don’t understand, because just now i was thinking Q(s) = 1/(s^2 +8s+15)
wary flame
Its oke
summer ore
Its oke
Can I add you and ask you more in direct message since in my area, it almost 3am😅
summer ore
what u ve got is right to me
Hmm, because if I’m using what I defined, I can’t proceed, anyway, tomorrow I’ll ask you in PM🥹
Thanks
.close
ocean reef
vocal sleetBOT
vocal sleetBOT
@ocean reef Has your question been resolved?
river minnow
Note that you can rewrite it as $(1 + \frac2{3n - 1})^n$
twin meteorBOT
A Lonely Bean
ocean reef
yeah
river minnow
Then you could do a substitution, let some t = (3n - 1)/2
river minnow
And use the limit definition of e
ocean reef
is that the only way?
river minnow
If you are lazy, but know the method, you might as well use software
river minnow
is that the only way?
Taking log and then using l'hop works as well
river minnow
**A Lonely Bean**
But I would go like this
river minnow
Then you could do a substitution, let some t = (3n - 1)/2
That's why you should do this sub
So that it becomes 1 + 1/t inside the brackets
ocean reef
what about the n outside lol
ocean reef
Then you could do a substitution, let some t = (3n - 1)/2
why did you add 2 under this
vocal sleetBOT
ocean reef
.reopen
river minnow
.reopen
vocal sleetBOT
✅
river minnow
why did you add 2 under this
So that it will be 1/t
river minnow
If you immediately recognize it as a e^2 and want to skip several steps, sure 
ocean reef
thanks so much
vocal sleetBOT
@ocean reef Has your question been resolved?
vocal sleetBOT
jovial wind
I think it’s asking for the factors of 30. But 30 has to be the first common multiple
Like 30 and 1. First common multiple is 30
5 and 3. While it is factor of 30, it’s first common multiple is 15
So start by getting all the factor pairs of 30
It’s asking for multiple not factor
Probably not
I would think so? I haven’t thought of any other method rn
A wha
That sounds harder
hazy sparrow
vocal sleetBOT
hazy sparrow
hello its not about the integral
i just want to know how you get this derivitive
i know the chain rule
so its 1/2root(x-1) YES
but why is it *x then
cyan talon
yeah the 1/x is from the chain rule
1/(1 + (sqrt(x-1))^2)
that's your derivative of arctan
evaluated at sqrt(x-1) (the inner function)
@hazy sparrow
hazy sparrow
im trying to understand
cyan talon
how do you do the chain rule for this function?
just so that I can use your notations
hazy sparrow
cyan talon
yeah exactly
hazy sparrow
this is correct?
hazy sparrow
cyan talon
why do you even have a cube root is my question
cyan talon
you're complicating this too much
hazy sparrow
; (
cyan talon
you just want to know why there's an extra 1/x factor
why are you expanding everything out
cyan talon
this should be just enough
hazy sparrow
yow
hazy sparrow
yes
vast shale
oh ok
hazy sparrow
but i didnt get the answer
vast shale
well idk how to do it
cyan talon
rip
hazy sparrow
its ok, i just want to understand XD
cyan talon
anyway let's go step by step
hazy sparrow
aPlatypus pls can you write this out for me
cyan talon
i'm chatgpt now
vast shale
its ok, i just want to understand XD
ok
cyan talon
aPlatypus pls can you write this out for me
I mean how did you write out the chain rule at first
to see where there is a problem
hazy sparrow
cyan talon
yes ok
hazy sparrow
so i take the root x-1 from the inside took the dirivitive
cyan talon
so that's what you computed on your own right ?
hazy sparrow
i got 1/2 (...) to the negative power
hazy sparrow
so that's what you computed on your own right ?
yes
cyan talon
ok
hazy sparrow
i got 1/2 (...) to the negative power
times the dirivitive of arctan but where the x is i placed the root
cyan talon
then $\frac{1}{1+(\sqrt{x-1})^2} = \frac{1}{x}$
twin meteorBOT
_aplatypus
cyan talon
what I'm saying is that this is the source of your 1/x
hazy sparrow
cyan talon
?
hazy sparrow
wtfffffffffff
how
did i not see this
im so sad, tomorrow i have exams of integrals but i failed at dirivits (idk what its called) thx man
wtf
thx really
cyan talon
gl
mellow rampart
I want to confirm something: the goal of svd is to find vectors that are orthogonal before and after linear transformation?
vocal sleetBOT
I want to confirm something: the goal of svd is to find vectors that are orthogo...
mellow rampart
The orthogonal matrices U and V are obtained from the eigendecomposition of AA^T and A^TA.
This is assured as both AA^T and A^TA are symmetric, meaning positive eigenvalues
verbal bison
vocal sleetBOT
west raptor
Do you know the quadratic formula?
verbal bison
No
west raptor
Have you heard of completing the square?
verbal bison
No
west raptor
Do you know how to factor quadratic polynomials?
verbal bison
We didn’t learn that
west raptor
Ok, I'll explain it:
Note that (x+a)(x+b)=x^2+(a+b)x+ab
So we can use this fact to convert the left hand side into the form (x+a)(x+b)
We know a+b=5 and ab=6 from the question
The only way to solve this is to try values one by one
west raptor
No, not these
Because they don't apply here
Are you sure your teacher did not teach you this, because it's the most basic quadratic equation solving method
verbal bison
Ya
west raptor
Here's the quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ when $ax^2+bx+c=0$
twin meteorBOT
Math Is Fun
west raptor
It's the only way I know to solve these without factoring it
verbal bison
That’s for next year.
I’m year 9
We learn that in year 10
Wait
Let me just show u a pic
verbal bison
Shouldn’t
Shouldn’t you do
Find something find when u add to gives 5 something when you multiply it gives 6
west raptor
What?
verbal bison
The hell is a polynomial
west raptor
This
verbal bison
I Never heard it in my lifeeee
west raptor
$ax^2+bx+c$
twin meteorBOT
Math Is Fun
west raptor
I'm basically refering to the x^2+5x+6
mild flower
nomenclature aside, can you do a similar thing to that x^2+5x+6? Yes you're looking for two numbers that multiply to 6 and add to 5
verbal bison
How do solve perfect squares by using (a+b)^
cedar pewter
anything i can help with @verbal bison? your question seems to be unanswered.
vocal sleetBOT
@verbal bison Has your question been resolved?
ruby epoch
How do solve perfect squares by using (a+b)^
perfect squares are given to you looking like this $c - d$
twin meteorBOT
jumpydino
verbal bison
I did. the perfect square
But I want as easier wayyy
my teacher told it to me
And I forgot
The answer be like
(A+b)^
mild flower
tbh the answer is "do like 200 of them so you recognize the numbers and don't have to think about the fact that x^2+14x+49 = (x+7)^2"
in the same way that you don't have to count on your fingers and toes for 6*7 = 42
verbal bison
I figured itnout
vocal sleetBOT
I figured itnout
verbal bison
Like for example
calm charm
verbal bison
X^+14x+49
ya
Rlly just wanna make sure if I’m correct
So to find the. Perfect square
u find like when u add something it gives u 14 but when u multiple it gives 49
in this it’s 7
cuz when u add 7+7 u get 14
When u multiple
49
so the answer would be (x+7)^
@mild flower
Is it correct
twin meteorBOT
kitten.in.a.teacup
mild flower
which is distinct from $(x+7)^3$ and $(x+7)^{26}$
twin meteorBOT
kitten.in.a.teacup
verbal bison
**kitten.in.a.teacup**
That’s what I wrote
vocal sleetBOT
@verbal bison Has your question been resolved?
old schooner
Can someone help with something real quick
vocal sleetBOT
Can someone help with something real quick
old schooner
fringe venture
drop it
old schooner
anyone know how to approach this
fringe venture
cos rule
old schooner
tried doing that but I keep getting the wrong values
fringe venture
c^2=a^2+b^2-2bccostheta
old schooner
so what would I do to get A and B exactly ?
old schooner
okay
mild flower
mild flower
A, B, and C are the angles; a, b, c are the side lengths opposite those angles
old schooner
so how would I find A and B as asked
mild flower
we already know C, right? and we know the side length of the opposite side (c)?
(I know it's not labeled as C but it's the one that isn't A or B)
mild flower
we also know the length of b, which is the opposite side of the angle B
old schooner
mild flower
so we have $$\frac{\sin C}{c} = \frac{\sin B}{b}$$ and we know 3 of those values
twin meteorBOT
kitten.in.a.teacup
