Let's label |T| as j
#help-26
acoustic tangle
serene lodge
ok
acoustic tangle
So you can get any T by just choosing j elements out of those n - i elements from A\S
Meaning the numbers of all such T with cardinality j would be n-i choose j
serene lodge
What do you mean by 'choose j'?
acoustic tangle
What do you mean by 'choose j'?
$\binom{n-i}j$
thorny flameBOT
A Lonely Bean
acoustic tangle
And, since j varies from 0 to n-i, we should evaluate the sum
[ \sum_{j=0}^{n-i}\binom{n-i}j ]
thorny flameBOT
A Lonely Bean
acoustic tangle
Do you recognise this?
serene lodge
I see what you mean but I don't recognise that specific formula
acoustic tangle
Here we can use the fact that
[ \sum_{k=0}^m\binom mk = 2^m ]
thorny flameBOT
A Lonely Bean
acoustic tangle
**A Lonely Bean**
So this basically evaluates to $2^{n-i}$
thorny flameBOT
A Lonely Bean
acoustic tangle
Okay, so, to recap, we have shown that given S has i elements, the number of T sets such that (S, T) is in the set is 2^{n - i}
acoustic tangle
Again, there are n choose i ways to choose i elements out of n elements, so now we need to evaluate the sum
[ \sum_{i=0}^n\binom ni 2^{n-i} ]
thorny flameBOT
A Lonely Bean
acoustic tangle
how does this link back to the cardinality?
We have calculated the amount of ordered pairs given that S has i elements, now we let i go from 0 to n and count along adding
acoustic tangle
Yes
serene lodge
until n
acoustic tangle
**A Lonely Bean**
And for convenience let's rewrite this sum
[ \sum_{i=0}^n \binom ni 2^{n-i} = \sum_{i=0}^n \binom n{n-i} 2^{n-i} = \sum_{i=0}^n \binom ni 2^i ]
thorny flameBOT
A Lonely Bean
acoustic tangle
Do you want a hint for evaluating this?
serene lodge
Yes please ๐
acoustic tangle
Can you recall the binomial theorem?
acoustic tangle
[ (a + b)^n = \sum_{i=0}^n\binom ni a^ib^{n-i} ]
Plug in $a = 2$ and $b = 1$, what do you get?
thorny flameBOT
A Lonely Bean
serene lodge
3^n
acoustic tangle
Yup
serene lodge
Why is a=2 and b=1?
I see that's the cardinality but don't understand how you got there using this method
acoustic tangle
Why is a=2 and b=1?
We simply chose a and b to be like that
acoustic tangle
I see that's the cardinality but don't understand how you got there using this m...
It's kind of a trick I guess
Whenever you have n choose i and x^i where i is the running index, you can make use of the binomial theorem
green abyss
Find an Eulerian Circuit
Is this just trial and error or is there logic to this?
green abyss
i keep hitting dead ends
I'm here on MS Paint just drawing lines trying to find a circuit
odd pagoda
how do you keep hitting dead ends
green abyss
Because I can only use each vertex once right?
torpid matrix
yeah it should just work
odd pagoda
there is quite literally nothing you can do wrong here btw. you can just try running
green abyss
sorry about that
yeah i know
i hit 'dead ends' because i thought i could only use a vertex once
thank you
.close
fast monolith
topaz sinewBOT
opaque oasis
What substitution would I use for the following differential equation? I'm stuck.
fast monolith
Sorry neo
opaque oasis
np!
fast monolith
I have this?
opaque oasis
also for this, are you familiar with synthetic polynomial division?
It may help you to familarize yourself with it
fast monolith
You mean my question? I am trying to work out how to solve it ๐
it looks really simple
bitter hemlock
You mean my question? I am trying to work out how to solve it ๐
you can always use this:
cubic formula : )
opaque oasis
Also recall that all potential solutions of the cubic are factors of the first coefficient and the last constant.
fast monolith
you can always use this:
There is no easier way to solve it by hand?
opaque oasis
there is an easier way
lets look at the factors of the first coefficient and the last term
opaque oasis
What is your first language?
opaque oasis
oh alright
bitter hemlock
coefficients are like a, b, c, d in ax^3+bx^2+cx+d
the constants in front of the terms
fast monolith
factor of the first coefficient is 3 and last term is 2
fast monolith
the constants in front of the terms
got it
bitter hemlock
factor of the first coefficient is 3 and last term is 2
huh? first coefficient is just 1
all you need to test are 1, -1, 2, -2 i guess?
fast monolith
I just need to test stuff until it works? How do I know what to test. I know you tried to explain already but I don't get it
bitter hemlock
Also recall that all potential solutions of the cubic are factors of the first c...
doesn't this only work assuming that the factors end up being whole numbers? what if they are fractions \ rational numbers?
opaque oasis
doesn't this only work assuming that the factors end up being whole numbers? wha...
yeah i realized that
it's not always applicable
but it is a good start
With this equation it does not have integer roots
so you would have to go with a different method
What are they asking you to do niri?
bitter hemlock
There is no easier way to solve it by hand?
there is no easy way to solve cubics unless you can factor by grouping, spot a factor by just looking at it etc.
fast monolith
I am trying to solve when the x is 0
bitter hemlock
in general, no they are not easy to solve
fast monolith
okay. So it just looked much simpler than it really was. I am in high school so I might've made a mistake to get here ๐
opaque oasis
wait.
bitter hemlock
lol that's not solving the equation, that's just plugging in x = 0 : )
opaque oasis
Are you trying to find the value when x is zero or when y is zero?
bitter hemlock
when x = 0, y = 2
fast monolith
let me check for mistakes.
found it
no need for cubic equations
sorry, how do I close this and thanks for the help ๐
still good to know
bitter hemlock
actually wait
fast monolith
yeah?
bitter hemlock
you might be able to do some trickery here using difference of cubes
maybe i dunno nm, keep playing it i guess
: )
gl
!done
topaz sinewBOT
If you are done with this channel, please mark your problem as solved by typing .close
stiff ferry
cinder owl
im ngl how do you find the basis without necessarily putting it in rref?
sweet shard
if you're working on a problem, just show it
cinder owl
im not
but on my exam
my teacher will legit be like
find the basis, without using rref
like for diagonalization, it would be the eigenvector that corresponds with the eigenvalue that is 0
that makes sense to me
but what if you are just given some arbitrary matrix
odd pagoda
unless its a special matrix or the basis is obvious, you use rref
thats what rref is for
well, ref is enough
cinder owl
like as in symmetric? or orthonormal?
cinder owl
well, ref is enough
why just the upper tri?
odd pagoda
well you only need to know where the pivot columns are
the actual rref is rarely ever needed
well I mean if you know it is orthogonal then you know its invertible and so the columns are linearly independent
cinder owl
does a matrix being invertable imply all of its columns are linearly independent?
jaunty phoenix
Not native sorry ๐
it's a hidden quadratic
odd pagoda
its equivalent, yes
cinder owl
does invertable ensure that all the spaces are linearly independent
ie column, row, left null, null space?
odd pagoda
it makes no sense to talk about spaces being linearly independent
invertible
all rows lin independent
all columns lin independent
row space equal to R^n
column space equal to R^n
left/right null space equal to {0}
all equivalent
cinder owl
also what is the relation of svd and diagonizeable matricies
odd pagoda
well svd always exists
its a generalization of eigendecomposition
if both exist then they arent necessarily equal
unless you have something like symmetric pos definite
topaz sinewBOT
@cinder owl Has your question been resolved?
earnest gorge
topaz sinewBOT
earnest gorge
I am not quite sure if it's saying the first thing or second thing
peak scarab
the 2nd one
You generally cannot inverse existence and universal quantificators
Parentheses might make it clearer if you're confused
see for more
earnest gorge
https://cstheory.stackexchange.com/questions/4473/techniques-for-reversing-the-o...
Thanks
c.lose
close.
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
brisk geyser
Where do I start???? so confused and i have no clue how you can get this answer from that
topaz sinewBOT
Where do I start???? so confused and i have no clue how you can get this answer ...
broken niche
Where do I start???? so confused and i have no clue how you can get this answer ...
What is f(x)
wooden osprey
Where do I start???? so confused and i have no clue how you can get this answer ...
the equation of the graph's tangent at $x_{0}$ can be expressed as $y=k(x-x_{0}) + y_{0}$
thorny flameBOT
FungusDesu
wooden osprey
where $k = f'(x_{0})$
thorny flameBOT
FungusDesu
brisk geyser
this is all that it says unless this is part of the question (which i already did)
unique crypt
you have f'(x) so plug in 4 to find f'(x)
brisk geyser
wait
brisk geyser
hold on
can i reopen this
real quick
i got this except plus 7/3 did i do something wrong
kindred cloud
does anyone have any tips on how to improve at Ap calculus ab
elfin sparrow
i got this except plus 7/3 did i do something wrong
+7/3 is right, it's a typo
topaz sinewBOT
@brisk geyser Has your question been resolved?
hearty drum
topaz sinewBOT
hoary vigil
Given $f(x) = \frac{1}{\sqrt{x}}$ and $a = 4$, find $f^{\prime}(a)$
thorny flameBOT
kyhua
hoary vigil
Posting what I've tried so far in a sec...
At the end I started to take the conjugate of the denominator but I stopped because I figured it might start being circular.
My issue is I can't seem to find a way to get rid of this sqrt(x) no matter what I try
And I know I have to cancel the x's out somehow based on previous problems that were easier, but I can't seem to figure out how to do that for this problem
I know the answer should be -1/16, but I'm missing something and I'm not quite sure what it is
Any help would be appreciated 
cyan mesa
$\frac{\frac{1}{\sqrt{x}}-\frac{1}{2}}{x-4}\\$
$\frac{\frac{2-\sqrt{x}}{2\sqrt{x}}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}$
@hoary vigil
thorny flameBOT
Combustion
cyan mesa
i can't really read what you wrote after the third step so i can't see where you went wrong
hoary vigil
Shouldn't be a multiply, should be an arrow ๐
I multiply by the conjugate to get to the 2nd part
cyan mesa
$\frac{\frac{1}{\sqrt{x}}-\frac{1}{2}}{x-4}\to\frac{\frac{1}{x}-\frac{1}{4}}{\left(x-4\right)\left(\frac{1}{\sqrt{x}}+\frac{1}{4}\right)}$
thorny flameBOT
Combustion
hoary vigil
**Combustion**
For this, on the right hand side denominator, it should be
$$(x-4) (\frac{1}{\sqrt{x}} + \frac{1}{2})$$
thorny flameBOT
kyhua
hoary vigil
right?
cyan mesa
oh yeah my bad
cyan mesa
**Combustion**
also only one step is really necessary for this
cyan mesa
**Combustion**
just do what i wrote above and you'll be set
$\frac{\frac{1}{\sqrt{x}}-\frac{1}{2}}{x-4}\to\frac{\frac{2-\sqrt{x}}{2\sqrt{x}}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}$
hoary vigil
I am
thorny flameBOT
Combustion
hoary vigil
no way
I completely forgot about difference of squares in the denominator
I think i see it now
Hm
I ended up at
$$\frac{-1}{2x+4\sqrt{x}}$$
thorny flameBOT
kyhua
hoary vigil
How is this the final answer...? I'm not quite sure. I thought I was supposed to be finding f'(4)
cyan mesa
oh yeah just plug 4 in
hoary vigil
Dang, I see that it works but now I'm even more confused haha. But that's really cool! Thanks :D
cyan mesa
cyan mesa
it's the x value you want to evaluate the derivative at
thorny flameBOT
kyhua
hoary vigil
This is the equation of the secant line
By plugging in a = 4, what purpose does that have?
I can see that by taking the derivative of 1/x^2 we get :
$$\frac{-1}{2x^{3}}$$
hoary vigil
we're not just plugging a = 4 to get the derivative
Right, but what purpose does it have when it's by itself?
thorny flameBOT
kyhua
hoary vigil
Ah wait
cyan mesa
hoary vigil
$$f^{\prime}(x) = \lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}$$
thorny flameBOT
kyhua
hoary vigil
By comparison, when plugging in only a = 4 we're finding something similar to the derivative of the function, to which at the end we can take the limit of from x -> 4 (as you said earlier) which would give us the derivative of f'(a)
I think I get it
cyan mesa
i think i get what you mean yeah
half blade
is it possible to Add two numbers together using only multiplication and divison? Lets say I want to add 5 + 10 = 15, how can I use 5 and 10 to get 15 without adding, but using multiplication and/or division?
topaz sinewBOT
is it possible to Add two numbers together using only multiplication and divison...
wispy tiger
hollow drum
is it possible to Add two numbers together using only multiplication and divison...
Can you use 5 and 10 multiple times?
half blade
yes
well actually no
i can only use those two numbers once
5 is in a placeholder 10 is in a placeholder and i need to get 15 as a result using only multiplying or dividing
i dont think this is possible is it...
hollow drum
I mean if 5 and 10 are just example numbers, then you can do 3 * 5 = 15
broken niche
There are only 4 combinations then right?
10(5), (5)10, 5/10, 10/5. Clearly none of these are 15
hollow drum
i cannot change those integers
If you are only limited to using 5 and 10 and only using it once, then no it's not possible to result in 15
half blade
what i meant was
i can do 5 x 10 = 50 x whatever# divided by whatever#
or im allowed to do 5 / 10 = 0.5 x whatever # dided by whaetever#
i want to see if i can get a result as close too 15
almost like adding
but without adding
you know how 5 + 10 = 15
imagine i can do 5 x 10 = 50 / whatever * whatever / whatever again to get 15 as a result
is there a set formula for that
broken niche
Let a and b be numbers. You want a+b=abc for some c, so just solve for c
half blade
im not sure i understand
broken niche
Lets use ur example
hollow drum
i can do 5 x 10 = 50 x whatever# divided by whatever#
or im allowed to do 5 / 10...
Your instructions really aren't clear. You said you are limited to only 5 and 10 and you only use it once. What do you mean by this part?
broken niche
im not sure i understand
You want to get 5+10 with multiplication. 5+10=5(10)(c) where c is some number
So you can solve c=(5+10)/50
So you can get 5+10 by doing 5(10)(15/50)
I hate discord
hollow drum
So you can get 5+10 by doing 5(10)(15/50)
You need to put spaces between the *
broken niche
You need to put spaces between the *
I see
half blade
So you can get 5+10 by doing 5(10)(15/50)
how cani make this work with any numbers?
5 + 10 = 15 aka 5*10 (15/50) = 15
what about if 5 + 10 changes all the time
like for example soemthing random like 20 + 35
broken niche
Let a and b be numbers. You want a+b=abc for some c, so just solve for c
That is when this comes into place
This is just the general form
Solve for c first, we get c= (a+b)/(ab)
So with your new example let a=20, b=35. With this we know c=(20+35)/(20(35)). So subbing that into a+b=abc we get
20+35=20 * 35 * (20+35)/(20 * 35)
half blade
OHHH
MY GOD
okay i get it now
that is so cool
that is actually amazing
thank you so much
so that works with ANY two integers
broken niche
Yeah
broken niche
thank you so much
Np
half blade
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
pine anchor
Can anyone help me figure this out?
topaz sinewBOT
Can anyone help me figure this out?
topaz sinewBOT
@pine anchor Has your question been resolved?
sweet shard
try ratio test
pine anchor
It's giving me 1 i think
vernal matrix
Noting that $\ln(x) < x$ for any positive $x$, you could make use of that
thorny flameBOT
@vernal matrix
vernal matrix
(note that x=n may not be the choice you want to make here!)
faint musk
how do i do this one
topaz sinewBOT
how do i do this one
vernal vale
how do i do this one
what have you tried?
vernal vale
im confused on the interval part
its just how long the thing is allowed to move
usually its to avoid weirdness in the function they give you
like log 0 isnt defined here that might be a problem
even though its included
topaz sinewBOT
@faint musk Has your question been resolved?
faint musk
its just how long the thing is allowed to move
ok so i first find the derivative of the velocity function they give me right
vernal vale
ok so i first find the derivative of the velocity function they give me right
for which part?
the velocity gives you direction so you can just work with that
topaz sinewBOT
@faint musk Has your question been resolved?
vague gull
how do i do this one
yeah you need to find the derivative in terms of time for acceleration
im not too sure about the intervals stuff ive just been exposed to these types of questions but in basic terms
once you find dv/dt you can replace all the values of t with 2 for the expression which should work out
vague gull
how do i do this one
so acceleration would be 1/t - 4
for time intervals where it's zero just equate 1/t - 4 = 0
1/t = 4 implies t = 1/4
at 1/4 seconds a = 0
for a and b i assume you can integrate wrt. time for displacement and then try? im not very sure, sorry
faint musk
alright thanks
silk wing
topaz sinewBOT
silk wing
,rotate
thorny flameBOT
pastel salmon
you need to multply and divide by the same conjugate experssion
$a-b=\frac{a^{2}-b^{2}}{a+b}$
thorny flameBOT
Joanna Angel
thorny flameBOT
silk wing
My handwriting is terrible but is it something like this?
pastel salmon
resulst is absolutely wrong
first step you did ok, but you wrote + 1 and you shud write -1
in nominator
in secodn step, do not take any n^2, from sqaure root
since, you will have - 1 in nominator
and denomiantor wil go to infinitie
so you have symbol like
1/infinmity
hence limit = 0
thorny flameBOT
pastel salmon
here, the trick is more complexed, one moment
silk wing
3โ(a)-b= (a-bยณ)/((3โ(a))ยฒ+(3โ(a).b) + bยฒ)???
silk wing
3โ(a)-b= (a-bยณ)/((3โ(a))ยฒ+(3โ(a).b) + bยฒ)???
Idk what I'm writing at this moment
pastel salmon
$a-b=\frac{a^{3}-b^{3}}{a^{2}+ab+b^{2}}$
silk wing
Ohhhhh
thorny flameBOT
Joanna Angel
pastel salmon
and you will see that the nominator will be linear, since the term wil be -2n, but denomiantor wil be expression of degree 2, , that means the degree of denomiantor wil be higehr than nomantor, so limit = 0
bu tyou need to write it nicely only
thorny flameBOT
pastel salmon
yes
silk wing
and you will see that the nominator will be linear, since the term wil be -2n, b...
I get it now ty
,close
pastel salmon
yw
silk wing
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
drowsy oasis
how to graph x/x^3 - 1
topaz sinewBOT
how to graph x/x^3 - 1
glad crater
transformation
or just sub in points
the thing is the same as
1/x^2-1
unless u didn't add bracket
topaz sinewBOT
@drowsy oasis Has your question been resolved?
glad crater
what is t.p
junior patio
would need help with this one - i tried adding rows and columns but it didnt work and got messy... maybe there is another solution?
topaz sinewBOT
would need help with this one - i tried adding rows and columns but it didnt wor...
@junior patio Has your question been resolved?
junior patio
<@&286206848099549185> help if possible:)
subtle elm
its 'b' or 'a' that you cut at the last colum
junior patio
it was an "a" but should be a "b"
i mean the prof corrected that (probably typing mistake)
polar torrent
Did you try to use row operations? It looks like you might be able to get a diagonal matrix
junior patio
mmh ill try that and post my try here in a moment
polar torrent
Start with r1 + r3 I think youll get a leading 1 that way
topaz sinewBOT
@junior patio Has your question been resolved?
polar torrent
midway there - can i swap columns aswell?
Yes you can swap columns, but remember that it will affect your determinant by multiplying by a factor of -1 (just like a row swap)
polar torrent
yea its a mess again
This looks better than before, you should now be able to do cofactor expansion along particular columns that have a lot of zeroes
junior patio
Yes you can swap columns, but remember that it will affect your determinant by m...
aah good idea! (not good in english - is that where i look at the 3x3 matrices and multiply it by the corner so to speak?)
polar torrent
Im on the bus atm but can give it a shot when i get to my office and see what i get as a final answer
junior patio
would be awesome- ill try out your method in the meantime
polar torrent
Yeah you can start with the 1 in upper left and then multiply by the 3x3 det you get from crossing out the row and column
junior patio
currently trying that:) thanks and then you get +0+0+0. looks doable at least
junior patio
so thats my solution so far - kinda looks messy still but im acutally sort of happy with it...
junior patio
im still new to this discord so i dont know how everythign works but i think im still occupying this help channel so you might want to post this somewhere else next time
as for the answer: x/6+x/3+x/18=180 -> solve for x (=324)
polar torrent
just got to my office, solving it now
we will get an answer in terms of a and b only by the look of the question
Here are my first few steps. I might have picked easier operations to work with than you (I wanted to prevent fractions)
I ended up with this as a final anwer:
Yours looks like it might simplify to something similar, but I probably don't have enough time to check your algebra, sorry!
neon iron
im still new to this discord so i dont know how everythign works but i think im ...
Can you write in your notebook cuz I didn't understand this
junior patio
well that look correct! thanks for the huge help very nice of you
polar torrent
well that look correct! thanks for the huge help very nice of you
YW
oblique venture
can somone help me with this question pls?
topaz sinewBOT
can somone help me with this question pls?
south cedar
how 3
oblique venture
that's like the least number of stations i can think of
south cedar
but there are 12 stations ?
i dont think i really got the question
how did u find 3
topaz sinewBOT
@oblique venture Has your question been resolved?
bright dagger
I need help for part B
topaz sinewBOT
I need help for part B
forest bloom
,, \delta (t-a) * \delta (t-b) = \delta (t-(a+b))
thorny flameBOT
kanna
bright dagger
ok
thorny flameBOT
kanna
forest bloom
For the first one
bright dagger
so delta[n] is delta(t-0) ?
forest bloom
so delta[n] is delta(t-0) ?
?
I'm just using a different variable
but yes delta[n] = delta[n-0]
it just means it never shifted
forest bloom
of course
bright dagger
I just copied from the professor slides, but since I there is no video about it, Im kinda lost
thats why im asking
would the second one be: delta(t -(1-1)) = delta(t)
?
forest bloom
i'm going to take a nap, but you might want to check the second line here
forest bloom
would the second one be: delta(t -(1-1)) = delta(t)
the convolution of those dirac delta functions... you just use the format i wrote to you
topaz sinewBOT
forest bloom
would the second one be: delta(t -(1-1)) = delta(t)
yeah
topaz sinewBOT
Available help channel!
neon iron
subtract x^2 -6x from 5x^2-7x-10
topaz sinewBOT
subtract x^2 -6x from 5x^2-7x-10
neon iron
subtract x^2 -6x from 5x^2-7x-10
What is
$$5x^2 - x^2$$
thorny flameBOT
neon iron
yh i can see ur question
neon iron
answer this first
Ok
So Iโm trying to subtract x^2-6 from 5x^2-7x-10
But idk where to start
neon iron
So Iโm trying to subtract x^2-6 from 5x^2-7x-10
yeah and what would 5x^2 - x^2 be
What were subtracting
x^2 from 5x^2
neon iron
So Iโm trying to subtract x^2-6 from 5x^2-7x-10
This
neon iron
4x^2
yup
Ok
if i asked you to subtract 5 from 10 what would you do
Whatโs next
Subtract
? - ? = ?
5
5-10=5
from 10
5?
topaz sinewBOT
topaz sinewBOT
โ
what
neon iron
Sorry my brother
why did you close we havent even got to your question
, if you dont understand something lmk
It wasnโt me
My brother
neon iron
it would be 10 minus 5
its okay, anyways do u understand
A bit
okay now answer this, subtract $6x^2$ from $10x^2$
thorny flameBOT
neon iron
if i asked you to subtract 5 from 10 what would you do
think back to @neon iron
4
?
Idrk sorry
neon iron
if i asked you to subtract 5 from 10 what would you do
we did
10 - 5 = 5 right
neon iron
6-10
and no that would give you -4 not 4
Oh yh
Wrong way
i think ur still lost on the first example
what is 3 subtracted from 7
Yeah Iโm new to this
Brain hasnโt really processed it yet
I think Iโll just leave it here
Itโs getting late so I gotta go to sleep
neon iron
Yeah Iโm new to this
which part dont you get
The subtraction part
Iโm really good at this in adding
But subtracting is just more difficult for me
neon iron
The subtraction part
well you havent given me a wrong answer to correct you on
Do u wanna add me so we can do this tomorrow
neon iron
Do u wanna add me so we can do this tomorrow
nope i dont add anyone
Oh ok
Np
Have a good day or night
.close
distant lintel
Could someone help me with this problem?
topaz sinewBOT
Could someone help me with this problem?
@distant lintel Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
night wharf
topaz sinewBOT
night wharf
I really don't know where to start with this problem
i think you are supposed to use lhospital rule
but i am confused on how to make it into that form
i already tried just putting it to root 10 and then putting the exponent to infinity making it one but that was wrong so idk at this point
night wharf
could you do the problem on a piece of paper and then let me interpret it? because idk what you mean be e^log(..)
like do you want me to put the problem in the (...)
?
fluid belfry
no, im not familiar with calc sir
vale furnace
Then use property of log and continuity of e
I see. U need to learn from student Chris
night wharf
if i type property of log and continuity of e into youtube will i get a tutorial on how to do. it
fluid belfry
yessir
night wharf
?
vale furnace
One sec
night wharf
ok i will try that
night wharf
thanks
vale furnace
Itโs pretty much the same method done slightly differently
night wharf
.close
knotty tusk
i moved all to right and got 0 => 2x^3 +4x^2 -2x -4, should i factor out x first? than i can factor that inside of x
knotty tusk
but im not sure if that would guide me to the correct answer
$\2x^3 +4x^2 -2x -4$
$0 \geq 2x^3 +4x^2 -2x -4$
thorny flameBOT
jetblacksalvation
knotty tusk
$x(2x^2 +4x^1-2-\frac{4}{x})$
thorny flameBOT
jetblacksalvation
ivory wave
knotty tusk
lol
topaz sinewBOT
@knotty tusk Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
thin jolt
hello, could someone guide me on how to calculate determenants of these?
i feel like i have to use determinant's properties here but i really have no idea where to start
topaz sinewBOT
hello, could someone guide me on how to calculate determenants of these?
i feel ...
ruby tree
Adding a scalar multiple of a row to another row does not change the determinant
topaz sinewBOT
@thin jolt Has your question been resolved?
thin jolt
Adding a scalar multiple of a row to another row does not change the determinant
yeah i remember this one, but is there a way to make these two look like triangular?
second one looks like there's, considering that I can make all B elements turn to 0, so det would be a^n
im not that sure about the first one tho
ruby tree
Not sure about your claim for the second one
For the first one, what happens if, for every row except the last, you subtract the next row to it?
topaz sinewBOT
thin jolt
.reopen
topaz sinewBOT
โ
thin jolt
For the first one, what happens if, for every row except the last, you subtract ...
this will turn the first column to 0
except for the last row
and some of the other elements will turn to 1, not sure because of x๐ซ
thin jolt
For the first one, what happens if, for every row except the last, you subtract ...
or wait
It'd make the 1st column turn to 0 except for the last row
also It'd make X's disappear and my main diagonal would look like 1-x and all the elements above it would be 1?
except for the last row once again
ruby tree
Yes
thin jolt
oh and then I can move the last row and make it first?
ruby tree
No, just try to simplify the last row
thin jolt
lemme play around with it for a bit
thin jolt
No, just try to simplify the last row
I can make it turn to
1 0 0 0 0 ... 0
using the first row right?
cuz the first one now looks like 0 1 1 1 ... 1
so if I multiply it by x and substract the the last row it'd make it look like 1 0 0 0
ruby tree
Not quite
thin jolt
oh right
ruby tree
Yeah except the first column
ruby tree
oh and then I can move the last row and make it first?
You know what I think that was actually the correct call 
thin jolt
lol
ruby tree
Wait no
thin jolt
pens up๐๐ป
ruby tree
The whole upper-right triangle is 1's and the whole diagonal is 1-x except the first column
thin jolt
yes
ruby tree
And now the whole lower-left triangle is 0 except the first column
ruby tree
For the first one, what happens if, for every row except the last, you subtract ...
So you can do that again
But scaled by 1/(1-x)
Except if x = 1 but in that case the determinant is just 0 right?
thin jolt
yes cuz it makes the entire main diagonal turn to 0๐ค
ruby tree
I don't think the main diagonal being 0 is a correct argument
$$\begin{vmatrix}
0 & 1 & 1 & ... & 1\
0 & 1-x & 1 & ... & 1\
0 & 0 & 1-x & ... & 1\
... & ... & ... & ... & ...\
1 & 0 & 0 & ... & 1-x
\end{vmatrix}$$
thin jolt
well
determinant equals to 0 if either there's a row that consists of only 0's or there're linearly dependent strings
thorny flameBOT
Nel
ruby tree
Is this correct?
thin jolt
yep I have the same matrix written
thin jolt
yeah me too, I have literally 3 tasks left to finish
these 2 and one more, related to matrix algebra
and yeah im kinda frozen
ruby tree
If x = 0 then the determinant is 0 because the two first rows are identical
Otherwise:
second row - first row -> 0 -x 0 0 ...
then first row + second row * 1/x -> 0 0 1 1 ...
Repeat with every row in place of the second
Except the last
$$\begin{vmatrix}
0 & 0 & 0 & ... & 1\
0 & -x & 0 & ... & 0\
0 & 0 & -x & ... & 0\
... & ... & ... & ... & ...\
1 & 0 & 0 & ... & -x
\end{vmatrix}$$
thorny flameBOT
Nel
thin jolt
this one looks mirrored
thin jolt
-x^(n-2) becase we have 1's in the first and in the last row right๐ค
ruby tree
It's still -x in the diagonal
thin jolt
yea i mean diagonal is 1 -x -x -x ... -x 1
thin jolt
oohhhhhhh
ruby tree
= (-1)^(n-1) x^(n-2)
thin jolt
i guess i got the point
ruby tree
So if x = 0 it's 0, otherwise if n is odd it's x^(n-2), otherwise it's -x^(n-2)
I guess the x=0 part is redundant
(-1)^(n-1) x^(n-2) would be my answer
You may want to double check
thin jolt
I'll try my best but you seem to be muuuuch more confident with matrix than I am
ruby tree
That doesn't mean I don't make mistakes
thin jolt
(-1)^(n-1) x^(n-2) would be my answer
where does n-1 in -1^(n-1) comes from tho?
its 2am I love matrixes very much, especially this kind of tasks
ruby tree
-(-x)^(n-2) has n-1 minus signs
thin jolt
ah
muted bridge
Can someone pls help with finding derivative here
topaz sinewBOT
Can someone pls help with finding derivative here
muted bridge
Am i meant to use chain rule on both sides?
gleaming reef
Can someone pls help with finding derivative here
Implicitly diff
And solve for dy/dx
gleaming reef
Am i meant to use chain rule on both sides?
Yes
muted bridge
So for the left side: 4(x^2+y^2)(2x+2y*dy/dx)
is that correct?
not sure if im using the chain rule correctly
<@&286206848099549185>
frail fiber
yes correct!
frail fiber
yes
polar veldt
any formulas for this problem and solutions?
topaz sinewBOT
any formulas for this problem and solutions?
sleek quartz
Can someone pls help with finding derivative here
I'm not sure, but I think it is 9/13
muted bridge
I'm not sure, but I think it is 9/13
thats right. can you show me your work pls
I have no idea where Iโm messing up
muted bridge
ok i see what you did
topaz sinewBOT
@polar veldt Has your question been resolved?
topaz sinewBOT
Can someone check my C
topaz sinewBOT
@tepid cliff Has your question been resolved?
topaz sinewBOT
@tepid cliff Has your question been resolved?
topaz sinewBOT
@tepid cliff Has your question been resolved?
proper dagger
topaz sinewBOT
half edge
There was a little quadratic substitution
Substitute g = 2^a
Then we get g^2 -15g -16 = 0
(g - 16)(g+1) = 0
(2^a - 16)(2^a + 1) = 0
@proper dagger
lyric lynx
How do I find the line that best approximates a given function in a given interval?
Note that I do not know much statistics or calculus and I'm doing this for myself
My try right now:
Find line l(x) that best approximates f(x) in [a, b]
m = (f(b) - f(a))/(b-a)
l(x) = m(x-a) + f(a) + c
e(x) = |l(x) - f(x)| (error function)
What do i do next?
topaz sinewBOT
How do I find the line that best approximates a given function in a given interv...
lyric lynx
I think I need to do something with the integral but I'm unsure what
topaz sinewBOT
@lyric lynx Has your question been resolved?
topaz sinewBOT
@lyric lynx Has your question been resolved?
daring acorn
How do I find the line that best approximates a given function in a given interv...
NOT REALLY SURE WHAT UR ASKING, BUT U SHOULD GIVE LEARNING CALCULUS A TRY
daring acorn
How do I find the line that best approximates a given function in a given interv...
THIS IS GOOD STUFF BTW
ONLY CHANGE ID MAKE IS GETTING RID OF C HERE ENTIRELY; C IS ALREADY IN THE FORMULA, C = -MA + F(A)
craggy umbra
Can someone help idk what I did wrong
topaz sinewBOT
Can someone help idk what I did wrong
topaz sinewBOT
@craggy umbra Has your question been resolved?
craggy umbra
U did the wrong operation first
????????!!!
topaz sinewBOT
topaz sinewBOT
Available help channel!
unique shuttle
How do you do long division. Topic is polynomials and i need someone to teach me because i cant work out how to do them. Im in grade 10
topaz sinewBOT
How do you do long division. Topic is polynomials and i need someone to teach me...
unique shuttle
The steps are complicated and i need a way of remembering them
deep crow
Do u have a probelm i could work with
grim jacinth
I don't remember exactly, but I'm sure there are YT vids on polynomial long division
grim jacinth
Do u have a probelm i could work with
?
unique shuttle
Yeah i tried looking at youtube videos
Ill get a question
Uhh
I dont know how to do this on phone
Wait
This confuses me
deep crow
Ok so
neon iron
yello
neon iron
Yeah i tried looking at youtube videos
yk how to do factoring??
actualy
that isnt the best way to teach
unique shuttle
Cross multiplication or what
neon iron
what?
deep crow
You want to only care about the first number you are dividing by
neon iron
You want to only care about the first number you are dividing by
yeah listen to him
deep crow
So how much times does x go into x^2
neon iron
how many times does x go into x^2?
deep crow
Do i divide by thr x+2
yea twice
neon iron
x goes into x^2 x times
neon iron
so you do x * x+ 2
neon iron
yeah this
deep crow
Oh did i
neon iron
yeah
deep crow
Which part
neon iron
its +2x
deep crow
Oh whoops
unique shuttle
Im sorry this is making me frustrated
neon iron
Why is there -x^2
bc u multiplied the divisor by x
so the full equation gets multiplied by x
unique shuttle
Whatabou5 the +2
neon iron
hence x^2 + 2x
neon iron
Whatabou5 the +2
gets multiplied by x
neon iron
hence x^2 + 2x
so it gives u this
unique shuttle
I hate long division
unique shuttle
Which number
neon iron
and being left with -5x+10
unique shuttle
What is the big number
neon iron
u want to always remove the biggest numbers
neon iron
What is the big number
x^2 -3x -10
unique shuttle
o
unique shuttle
But thats the uh
neon iron
so look at the first number of BOTH numbers
unique shuttle
Expression right?
neon iron
Expression right?
yeah im js referring to it as that
unique shuttle
So x and x^2
neon iron
yeah
unique shuttle
Right?
neon iron
so what do u multiply x by to get x^2
unique shuttle
by itself
neon iron
yeah x
so u multiply x by not only x itself
but 2
bc thats the other part of small number
unique shuttle
Cant you just say its 2x?
neon iron
what do u fet?
unique shuttle
It makes it easier
unique shuttle
Uuh
So wouldnt it like cancel it out
Isnt there just steps that you could tell me
How am i going to remember this pattern
neon iron
How am i going to remember this pattern
i really cant
i dont have paper
so i cant show u
deep crow
Neither dont i and worse im at a party rn
Do u want the answer?
i wrote out all my work
unique shuttle
Sure
Working out probably wont help tho because i have no jdea where everythibg goes
Im so screwed for this exam ๐ช
deep crow
multiply where?
unique shuttle
In other questions i saw you had to multiply
deep crow
multiply by -?
unique shuttle
Idk
Look its what i saw im probably wrong but uh okay
So for the x+2 do you just make it 2x and always multiply by that whole expression?
I meant divide
deep crow
So for the x+2 do you just make it 2x and always multiply by that whole expressi...
Depends on the expressions
In this case we do cause we muktiply (x+2) by x
and when u distribute that you get x^2 + 2x
unique shuttle
I cant do this
deep crow
You got this
unique shuttle
Im having a hard time understanding
deep crow
It might be that im explaining this badly
unique shuttle
Im a visual learner and i would probably need someone to point to the numbers and explain that way
Step by step
Im sorry for wasting your time
topaz sinewBOT
@unique shuttle Has your question been resolved?
proper dagger
topaz sinewBOT
proper dagger
I understand question b, but I got something different
I noticed that the maximum velocity of the particle will be 6.
To find the time, I could simply put it back into the equation?
6=2-4cost
cos(t)=-1
I get a working angle of pi
Cos is negative in second and third quadrant
pi + pi = 2pi
pi - pi = 0
Calculated the working angle incorrectly
realised I went straight to the answer rather than getting the correct working angle
apologies
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
plush flicker
topaz sinewBOT
topaz sinewBOT
@plush flicker Has your question been resolved?
lyric lynx
a = 0