it's sine, notice how in the question the two form they provided have no phase shift
#help-10
crystal moss
frozen wadi
ahhh smart thank you
crystal moss
ahhh smart thank you
ur very welcome ヾ(•ω•`)o
frozen wadi
+close
crystal moss
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frozen wadi
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stable oxide
help
stable oxide
One is added to a three-digit number that is a multiple of 6, and it becomes a multiple of 7, and one more unit is added, and it becomes a multiple of 8. Find the sum of digits.
pls help
main lodge
100a + 10b + c = 6j
100a + 10b + c + 1 = 7k
100a + 10b + c + 2 = 8l
Maybe... linear algebra 
obtuse pebbleBOT
main lodge
obtuse pebbleBOT
Available help channel!
sleek marsh
How do i prove that $f:\mathbb{R}^2\rightarrow\mathbb{R}$ defined by $$f(x,y)=\frac{x^3}{x^2+y^2}$$ when $(x,y)\neq (0,0)$ and $$f(x,y)=0$$ if $(x,y)=(0,0)$ is differentiable at $(0,0)$?
obtuse pebbleBOT
How do i prove that $f:\mathbb{R}^2\rightarrow\mathbb{R}$ defined by $$f(x,y)=\f...
warm shaleBOT
ALBERTO BALSAM
brave bramble
Just need to show the partial derivatives are continuous
chrome furnace
chrome furnace
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
neat valley
simple stats question but what is level of significance referring to here
hushed hinge
obtuse pebbleBOT
obtuse pebbleBOT
@hushed hinge Has your question been resolved?
untold cave
hushed hinge
hb this one bro?
obtuse pebbleBOT
@hushed hinge Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
woven parcel
obtuse pebbleBOT
woven parcel
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lapis acorn
obtuse pebbleBOT
lapis acorn
so basically we have to put in distance formula and so did i
im afraid i cannot send you what i havedone cuz im on my pc
im in a hurry so can someone just...?
pallid yew
I mean if we can't see what you've done then we can't say whether it's correct lol
You've just got to check how many distances are equal
lapis acorn
i just have a question
its silly but
what is (-root 2 + root 2 )^2
that'll clear my doubts
pallid yew
0 but I'm not sure where that's coming up
lapis acorn
well its the distance of PQ
pallid yew
sqrt(2) - (-sqrt(2)) not sqrt(2) - sqrt(2)
pallid yew
under those powers of two it should be sqrt(2) - (-sqrt(2)), you should take the position vectors away from eachother then look at the length of that
Otherwise you get length of PQ = 0 which is nonsense because P and Q are diff points
lapis acorn
under those powers of two it should be sqrt(2) - (-sqrt(2)), you should take the...
i dont get it?
okokkok
i got it
THANK YOU!!!
.CLOSE
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glass palm
given 2 roots and a y intercept how do i know the range of a function
obtuse pebbleBOT
given 2 roots and a y intercept how do i know the range of a function
high lily
insufficient info
obtuse pebbleBOT
@glass palm Has your question been resolved?
glass palm
insufficient info
thats what i got on my external
it gave me roots at -2 and like 4 and y intercept at 4
answers were like y greater than or equal to 3.5 and other stuff
patent owl
did the question mention that the function is quadratic
high lily
are you omitting any important info
glass palm
did the question mention that the function is quadratic
forgot but i dont think so
when i find the exact question ill ask
.close
obtuse pebbleBOT
high lily
otherwise there are infinitely many functions that have those properties
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
what a scam
obtuse pebbleBOT
@fiery tiger Has your question been resolved?
obtuse pebbleBOT
@fiery tiger Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
Why tanx=-1 is undefined
nocturne minnow
Because the range of arctan is [-pi/2, pi/2] I believe
timid silo
Could you explain simpler?
nocturne minnow
That still doesn’t answer my question on why you thought tan x = -1 was undefined
nocturne minnow
,w tan x = -1
warm shaleBOT
nocturne minnow
See, not undefined
waxen walrus
uh, i think if it is equal to -1
then sin2x is equal to -1
and cos2x is equal to 0
1 + cos2x + sin2x = 0
so it's undefined
timid silo
Thank you
charred remnant
@timid silo i believe you can close this now
timid silo
.close
noble kindle
obtuse pebbleBOT
noble kindle
For b), how do I argue that $${2,3,4,...} \subseteq g(\mathbb{N})$$
warm shaleBOT
Kurama
sage wolf
Hello
obtuse pebbleBOT
@noble kindle Has your question been resolved?
sage wolf
noble kindle
This channel is occupied
sage wolf
Ok sorry
noble kindle
.close
timid silo
they said real number but they using rational number ,
is this book printed wrong ? or something wrong with me ?
obtuse pebbleBOT
they said real number but they using rational number ,
is this book printed wro...
nocturne sun
they said real number but they using rational number ,
is this book printed wro...
to prove a statement false, you just need a single example
their example happened to be a rational number
it could've been a natural number too
doesn't matter as long as it's a real number
rational numbers are real numbers, and so are natural numbers
obtuse pebbleBOT
timid silo
.reopen
obtuse pebbleBOT
✅
timid silo
but [x+y] = [x] + [y] is a true statement ,
if x = y = 4
[4 + 4 ] = [8]
[4] + [4] = [8]
getting equal answer then why they said it is false ,,
nocturne sun
but [x+y] = [x] + [y] is a true statement ,
if x = y = 4
[4 + 4 ] = [8]
[4] + [...
if you want to show it's true, you need to prove it works for all real numbers
but for disproving a single example is enough
nocturne sun
if you want to show it's true, you need to prove it works for all real numbers
otherwise I could say $a + b = 7$ is true for all real numbers because $a = 3, b = 4$ satisfies the property
warm shaleBOT
Doggo
crisp sable
If I have an event x it's chance of occurring is y and I do it z times what is the chance of it happening
Yup ik pretty pathetic
obtuse pebbleBOT
If I have an event x it's chance of occurring is y and I do it z times what is t...
crisp sable
<@&286206848099549185>
mint bronze
If I have an event x it's chance of occurring is y and I do it z times what is t...
Hi, so we can use a binomial distribution to help us here
Please feel free to ask any questions btw, there are no pathetic questions
So we can imagine that at every one of the z times you do the action, there is a probability y of X occurring and a probability 1-y of X not occuring
So the probability of there being n successes in z trials is given by
,,P(n)=\binom{z}{n}y^n(1-y)^{z-n}
warm shaleBOT
Social Capital Gainer
mint bronze
So the probability of having any non zero amount of successes will be given by 1 - P(0) where P(0) is the probability of having no successes
Therefore the probability you are looking for is given by
,,1-(1-y)^z
warm shaleBOT
Social Capital Gainer
drifting wraith
if you do it 1/y times (e.g. 700 for one on seven hundred chance) this will be generally 63%
there's a limit that you quickly reach
crisp sable
Ok
drifting wraith
if it's like in percents
crisp sable
X100
crisp sable
Ah yeah I thought you meant to make it a precent
To make sure I am not getting it wrong if y=0.0656 precent chance
And z=160
What can I expect to get
Cuz rn it does not add up
The number is either waaaay too small or waaay too high
mint bronze
Is your chance given as a percentage?
mint bronze
What number is it
drifting wraith
and what is it?
mint bronze
How many percent
crisp sable
The precent is 0.06265
Wait
OH MY GOD
I was taking a decimal as a precent
It is 10 precent not 0.1 precent
Woopsies
mint bronze
Ok, well you do just put the numbers in I think. To put it in perspective, the chance of getting heads from tossing a coin is 0.5. So if you toss a coin 10 times, the chance of gettig heads at least once is 0.999
crisp sable
Yeah it approaches 1 but never reaches it
crisp sable
If it did reach 1 it would mean the event is guaranteed which its not
mint bronze
Yea
mint bronze
.close
obtuse pebbleBOT
crisp sable
Nope I defnitly meant that
mint bronze
Bye now
mint bronze
No problem
stark ether
is that a dot product?
quick vault
it isn't even addition. xD
stark ether
I don't think that identity holds for vector dot product
quick vault
meager osprey
I’m really dumb and tired never mind and thank you
obtuse pebbleBOT
Available help channel!
fluid snow
How do I know when two traingles are similar?
obtuse pebbleBOT
How do I know when two traingles are similar?
fluid snow
Are EBF and CDE similar?
Are EFC and ECD similar?
are EFB and EFC similar?
do you just eyeball it?
I know that if 2 angles are the same, then the triangles are similar
but here, you don't know any angles except some right angles and can still say that some of them are similar
kindred moss
ECF: 180 - (20 + 90) = 70
kindred moss
Are EBF and CDE similar?
Don’t think so
fluid snow
we can also see two similar triangles, $\triangle BFE \sim \triangle DCE$
warm shaleBOT
Kepe
fluid snow
How do they see this
kindred moss
What is 20 a side of
fluid snow
AC = 20
kindred moss
Oh the whole line?
warm shaleBOT
Kepe
fluid snow
But how do they see this?
kindred moss
Both are right angle triangles
You can use trigonometry for DCE
It’s got a 90 degree angle
Or it’s got a horizontal line followed up by a vertical line going straight up
obtuse pebbleBOT
@fluid snow Has your question been resolved?
kindred moss
A right angle is a triangle that has an right angle or two sides that are perpendicular
It doesn’t need to have 2 angles that are the same
obtuse pebbleBOT
fluid snow
A right angle is a triangle that has an right angle or two sides that are perpen...
I meant for 2 triangles to be similar
warm canopy
what are you trying to do?
fluid snow
nothing, I was just messing around
but everything I did was correct?
but it turns into 75 - 10x - 5x²= 5x² + 10x - 75
that cant be right
warm canopy
not true for every x
but true for x that make either one zero
which is what you mean when you write $ax^2+bx+c=0$
warm shaleBOT
iCaird
warm canopy
you're finding x that make that true, not saying that the whole thing is zero always
fluid snow
so
$$75 - 10x - 5x²= 5x² + 10x - 75$$
is correct?
warm shaleBOT
Kepe
warm canopy
not for every x
warm canopy
no
fluid snow
if you multiply both sides of 75 - 10x - 5x² = 0 by -1
you will get 5x² + 10x - 75 = 0
warm canopy
you need to understand when an expression is true for all x
and when its true for some x
fluid snow
you need to understand when an expression is true for *all* x
its true for one or two x here
warm canopy
right so you need to be clear about that when you write equalities like that
fluid snow
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hot vigil
obtuse pebbleBOT
hot vigil
i need help with this pls
drowsy cosmos
do you know what factors of a polynomial are?
hot vigil
nope
drowsy cosmos
you could call them building blocks of your polynomials
it makes it easier to see where the polynomial is zero
for example
$$x^2-1=(x-1)(x+1)$$
warm shaleBOT
Enoo58
hot vigil
those are the 4?
drowsy cosmos
no this only has two
drowsy cosmos
yes
hot vigil
mugiwara
drowsy cosmos
and one of the ways to find them is to find where your polynomial equals zero
hot vigil
would the other 2 be x+5 and x-5
drowsy cosmos
and one of the ways to find them is to find where your polynomial equals zero
Try finding the roots of your polynomial
hot vigil
.close
crystal stream
Hi there, Can someone help me with this one? I proved (a), now I am not sure how to prove (b) and (c).
obtuse pebbleBOT
Hi there, Can someone help me with this one? I proved (a), now I am not sure how...
crystal stream
crystal stream
Why does it mean that ToS is also invertible?
twin sapphire
that its Ker is = {0}
so 0 is not an eigen value
so you have Ker(SoT)={0} => 0 is not an eigenvalue of ToS
so by negation: 0 is an eigenvalue of ToS => Ker(SoT)=/={0}
crystal stream
Yeah
crystal stream
but it means ToS is also invertible
But why is that?
twin sapphire
the mmiddle step
is that SoT inversible means that both S and T are inversible
you can see all of this using the determinant
det(SoT) =det(S)det(T)
crystal stream
What is the determinant of a transformation o.O
twin sapphire
its the determinant of its matrix
its independant of the basis in which you express the matrix
so we just call it the determinent of the transformation
obtuse pebbleBOT
@crystal stream Has your question been resolved?
crystal stream
.close
nocturne sun
can you use a calculator or?
nocturne sun
it's divisible by 18 I think
long sinew
Are you sure it isnt 46216?
nocturne sun
it's divisible by 18 I think
nahh nvm
long sinew
Huh...?
nocturne sun
I'm too lazy to answer sorryyy
long sinew
Stop spam
nocturne sun
stop it
obtuse pebbleBOT
urban ridge
velvet sigil
how are these two equal?
hollow plank
It's just a common denominator thing
you have sqrt(sin)/sqrt(cos)+sqrt(cos)/sqrt(sin) = sqrt(sin)*sqrt(sin)/sqrt(cos)*sqrt(sin) + sqrt(cos)*sqrt(cos)/sqrt(sin)*sqrt(cos)
Hmm
$$\frac{\sqrt{\sin x}}{\sqrt{\cos x}}+\frac{\sqrt{\cos x}}{\sqrt{\sin x}} = \frac{\sqrt{\sin x}\sqrt{\sin x}}{\sqrt{\cos x}\sqrt{\sin x}} + \frac{\sqrt{\cos x}\sqrt{\cos x}}{\sqrt{\sin x}\sqrt{\cos x}}$$
warm shaleBOT
Blaxapate
hollow plank
There
limber quartz
Not staying long?
trim island
nah i hate the message comes after i post my message
This is my working out
,rotate
warm shaleBOT
trim island
my answer for C & D are correct
but lets say that the x coordinate had to be negative
would i have to use the r formula
to workout a negative answer ?
limber quartz
Aren't we supposed to remember something about point P to solve this?
This is part C of a multi-part problem
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
$\frac{1}{n-4}$
warm shaleBOT
jpjthunder
fierce lagoon
Nice fraction
wicked tundra
$\frac{1}{n-4}-\frac{1}{n+4}$
warm shaleBOT
jpjthunder
fierce lagoon
Nice fractions
wicked tundra
idk how to get the sum right
wicked tundra
just know it sums from 5 to infinity
limber quartz
let me get he sum right
Lol, its ok. There is a channel for testing LaTeX code
wicked tundra
im exhanstated lol
fierce lagoon
**jpjthunder**
Make a telescoping series
limber quartz
wicked tundra
@fierce lagoon where the reference for this language
fierce lagoon
wicked tundra
I just want to solve this
fierce lagoon
Or desmos
wicked tundra
fierce lagoon
Ah yes
fierce lagoon
That will be $\frac{7}{8}\sum_{n=5}^{\infty}\left(\frac{1}{n-4} - \frac{1}{n+4}\right)$
warm shaleBOT
Umbraleviathan
fierce lagoon
Let's see
Well
You're gonna have to write a total of 32 terms to see that it's telescoping lol
wicked tundra
this is the sequence I found
$\frac{7}{8}(\frac{1}{1}-\frac{1}{9} + \frac{1}{2}-\frac{1}{10})$
warm shaleBOT
jpjthunder
wicked tundra
it goes on to infinity
fierce lagoon
Slowly, things will start cancelling out
wicked tundra
im tryting to cancel it out
wicked tundra
I thought it was this
fierce lagoon
(1/1 - 1/9)+ (1/2 - 1/10) + (1/3 + 1/11) ... + (1/9 + 1/17)
The sum will be (1/1 + 1/2 + 1/3 ... 1/8)
wicked tundra
$\frac{7}{8}(\frac{1}{n} - \frac{1}{n+8})$
warm shaleBOT
jpjthunder
fierce lagoon
The sum will be (1/1 + 1/2 + 1/3 ... 1/8)
• 7/8
wicked tundra
wait how is it cancelling out to that sequence
fierce lagoon
(1/1 **- 1/9**)+ (1/2 - 1/10) + (1/3 + 1/11) ... + (**1/9** + 1/17)
Look
You might start noticing that things will eventually cancel out
What will be left is just (1/1 + 1/2 + ... 1/8)
Of course I'm too lazy to write 16 to 32 terms
But if might notice
(1/1 - 1/9)+ (1/2 -1/10)+ (1/3 + 1/11) ... + (1/9 - 1/17) + (1/10 - 1/18) + .... (1/17 - 1/25)
@wicked tundra you notice now?
wicked tundra
wait is 1/9 again?
wicked tundra
oh
1/11 appears
I couldnt find it cuz I didnt put enough terms
wish I can get a calcualtor to lay out this sequence instead of writting it a bunch of times
fierce lagoon
Lmao
Yeah so
Whenever you see like
Fractions that subtract
Write out a ton of terms
But also notice patterns
Which you did
It ends up being
wicked tundra
will there be 1/inf
fierce lagoon
1/n + 1/(n+8)
fierce lagoon
will there be 1/inf
Yeah but that's just 0
dreamy scroll
you can do partial fraction decomposition to get it directly, as well
wicked tundra
I have to write down everything to see this sequencel ike how many trees do I have to kill
so much paper
dreamy scroll
you actually dont
wicked tundra
I could just use demos calculator
dreamy scroll
that is not a way
there is a way to do it rigorously by hand that is fast but it requires you to get pretty comfortable manipulating sigma sums
wicked tundra
ok
dreamy scroll
you had this after PFD, right?
wicked tundra
yea
wicked tundra
wait I see it now
fierce lagoon
Something like this
wicked tundra
(1/n) eventually equals to (1/n+8)
fierce lagoon
Except expanded since there's a denominator difference of 8
wicked tundra
so it cancels out
fierce lagoon
Yeah
dreamy scroll
right, but how much of it cancels? the answer to that question give you the limit
wicked tundra
$s_n = \frac{1}{n}$
warm shaleBOT
jpjthunder
wicked tundra
wait that might be wrong
fierce lagoon
Well
dreamy scroll
do you know what an index shift is?
fierce lagoon
Something like this
This basically means "the sum is whatever is left"
dreamy scroll
right
but you need to do algebra to find that
and algebra that includes the characters "..." is not rigorous algebra
fierce lagoon
(1/1 **- 1/9**)+ (1/2 **-1/10**)+ (1/3 + 1/11) ... + (**1/9** *- 1/17*) + (**1/1...
_ _
Once you realize this
Can't you just jump to the conclusion
dreamy scroll
to show it rigorously you must only manipulate the sigma sums
acceptable for a calc 2 class to write it like that? maybe. it depends on the teacher
dreamy scroll
the idea is that any summation of the form $$\sum_{n = m}^{\infty} \frac{1}{n+a}$$ is secretly just a shifted version of the summation $$\sum_{n=1}^{\infty} \frac{1}{n}$$
warm shaleBOT
JamesH
dreamy scroll
with some number of terms possibly missing from the beginning
dreamy scroll
so lets talk about how to actually solve a problem like this
we can do a similar example together, then you can figure out how to use the same strategy for your problem
lets skip the PFD part, which you seem to have figured out
and say we wanted to calculate $$\sum_{n=5}^{\infty} \left(\frac{1}{n+1} - \frac{1}{n+3}\right)$$
warm shaleBOT
JamesH
dreamy scroll
we can rewrite that a difference of two series,
$$\sum_{n=5}^{\infty} \frac{1}{n+1} - \sum_{n=5}^{\infty}\frac{1}{n+3}$$
warm shaleBOT
JamesH
dreamy scroll
to calculate this sum, we need to take the limit of the sequence of partial sums. i.e. $$\lim_{N\to\infty} \sum_{n=5}^{N} \frac{1}{n+1} - \sum_{n=5}^{N}\frac{1}{n+3}$$
warm shaleBOT
JamesH
wicked tundra
does it not appoarch 0?
dreamy scroll
no
we are getting there
in order to calculate this limit, we need to cancel out most of the infinitely many terms
wicked tundra
I think the reason I struggle with this is because idk how to solve limits as well
there were other ways to solve it but I just try to put in a really big number to see wat it appoarches too
dreamy scroll
that is a decent way to get some intuition, but is not reliable
also notice that it is $N$ approaching infinity
not $n$
which are different variables here
the thing that is approaching infinity is the length of the finite sums written in the limit
not the actual index variable n
do you see the distinction?
dreamy scroll
bro
do you want to learn how to solve these or just get to the answer asap
i am willing to teach you how to solve it
but i am not interested in guessing answers
wicked tundra
sorry Im having a hard time focusing right now
dreamy scroll
thats ok
warm canopy
Uh you shouldn't have split up the sums, on their own they do not converge
warm canopy
gotcha
wicked tundra
I think the reason why I kept getting it wrong is because the calutor keeps bugging out
I refresh the question turns out hte answer was 761/320
but same concept just with 25 this time
dreamy scroll
what are you even putting into the calculator?
dreamy scroll
the numbers should not be that big
dreamy scroll
which is infinite
but when you are telescoping you are taking only finitely many terms from the beginning
the number you listed there is between 2 and 3
the result comes from adding fractions. it seems that your webassign expected an exact answer, not a decimal
you seem more interested in finding the correct answer than understanding how to do the problem, so good luck
wicked tundra
I think I really need to take a break but I cant
I am on a schedule
I was suppose to finish this a few hours ago and I am stuck on this one problem
obtuse pebbleBOT
@wicked tundra Has your question been resolved?
scarlet gale
Both have y equal to something.
Write y = y, then replace the left side with one of those x sides and the right side with the other one of those x sides.
@feral cosmos
little obsidian
if you watch the next 10 seconds he is trying to rearrange r/h = sqrt(3)/3 to isolate h
but i think he does something wrong because he gets h = sqrt(3)r
and im not sure how he got that
warm canopy
What's 3/sqrt(3)?
warm canopy
There you go
little obsidian
but where does 3/sqrt(3) even come from
twin sapphire
little obsidian
i got h = r/[sqrt(3)/3] somehow
little obsidian
oh you can simply it down
oh i remember u lol
i watched some of 3blue1browns videos
pretty good explanations
little obsidian
yes
asked about differentiation
one question tho i dont get how r/[sqrt(3)/3] simplifies down to r x 3/sqrt(3)
warm canopy
Times the top and bottom by 3
little obsidian
when you multiply dont you have to multiply both sides of the equation
little obsidian
so you dont have to multiply h by three?
i am really lacking basic knowledge lol
warm canopy
No because we're really just timesing the right hand side by 1
But writing it as 3/3
little obsidian
but we're multiplying it by 3?
warm canopy
$\frac ab = \frac{ac}{bc}$
little obsidian
is it really the same as multiplying by 1 if it the fraction simplifies down to 1
warm shaleBOT
iCaird
twin sapphire
yeah
little obsidian
how is it the same as multiplying by 1 tho just because the fraction happens to simplify to 1 does it really mean its equivalent to timesing by 1 and we can leave the other side of the equation alone?
warm canopy
$\frac cc = 1$ so $\frac ab = \frac ab \cdot 1 = \frac ab \cdot \frac cc = \frac{ac}{bc}$
warm shaleBOT
iCaird
warm canopy
Take c=3 if you like, but can be anything apart from 0
little obsidian
brb
alright i think i see
so if we had an equation h = 2/6 and we decided to multiply by 3
because then 2/6 would turn into 6/6
we wouldnt have to multiply the h by 3?
little obsidian
oh
warm canopy
If you did that then we would have to multiply by 3
But we're not multiplying by 3
We're multiplying by 1
Which we are writing as 3/3
little obsidian
we would have h = 6/18 in the example i just gave?
little obsidian
why do we multiply the h by three tho
little obsidian
h = 2/ 6 multiply both sides by three 3h = 6/6 so h = 1/3
warm canopy
h = 2/ 6 multiply both sides by three 3h = 6/6 so h = 1/3
Right but like I said, that's not what I've been talking about
little obsidian
oh we didnt multiply by three in my original question
we multiply top and bottom by 3
warm canopy
Yes
little obsidian
so like multiplying by 9/3?
warm canopy
What
little obsidian
or is it still not the same thing
warm canopy
That's 3
little obsidian
LMAO
im a goner
yeah i see
its some special rule then i guess
havent done anything like that when isolating terms in equations
i didnt even know that was a thing
multiplying both top and bottom of a fraction by a constant to make the fraction equal to 1
let me try to think of an example then just to make sure i get it
warm canopy
multiplying both top and bottom of a fraction by a constant to make the fraction...
This is NOT what's happening
little obsidian
..
little obsidian
and why are we doing that again
i see what u mean but what was the purpose i forgot
oh
to cancel out the 3 on the denominator right
warm canopy
Yes, we had a nested fraction we wanted to make simpler
little obsidian
so ok
by that logic then
the fraction is equivalent right even after applying that
cos if we r just multiplying it by 1
its value stays the same no
little obsidian
im braindead
i havent come across that i guess i have major gaps in my knowledge
sucks cos that seems really basic and the work im doing is gonna go up to second and third order differential equations lol
warm canopy
Maybe go over how fractions work would be a good start
warm canopy
Only way is up my guy
little obsidian
well i think my question has been answered thanks for the help
got a lot of studying i need to do lol
👍
warm canopy
Stick at it
obtuse pebbleBOT
@little obsidian Has your question been resolved?
sour egret
obtuse pebbleBOT
sour egret
I am confused on why this answer is true and how I would get this answer.
obtuse pebbleBOT
@sour egret Has your question been resolved?
lilac glacier
@sour egret do you know the binomial expansion of (x+y)^n
sour egret
no i dont
lilac glacier
vagrant osprey
Hi — i was wondering about this step in a linear algebra problem
obtuse pebbleBOT
Hi — i was wondering about this step in a linear algebra problem
obtuse pebbleBOT
@vagrant osprey Has your question been resolved?
vagrant osprey
<@&286206848099549185> ^^
dreamy scroll
can you remind me of the definition of antisymmetric?
vagrant osprey
can you remind me of the definition of antisymmetric?
A^T = -A
sorry i’m late on this response
dreamy scroll
no problem
i wish i could help more directly but i am slightly rusty on this stuff, though i have seen it many times
the conjugate of a complex-valued vector $z = (z_1,z_2,z_3)^T$ is given by $\overline{z} = (\overline{z}_1, \overline{z}_2, \overline{z}_3)$, is that accurate?
warm shaleBOT
JamesH
obtuse pebbleBOT
@vagrant osprey Has your question been resolved?
vagrant osprey
the conjugate of a complex-valued vector $z = (z_1,z_2,z_3)^T$ is given by $\ove...
im not sure about this but i’m willing to say yes???
i know virtually nothing about conjugates when transposes get involved
dreamy scroll
im not talking about that matrix transpose at all
im just talking about how the entries of z relate to the entries of z bar
dreamy scroll
**JamesH**
i am pretty sure if this is accurate, that thing you wrote is true by definition
not every true statement warrants a theorem 🙂 but it may be that it is listed in a big list of properties of complex vectors
fallen willow
obtuse pebbleBOT
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
tame valve
x = -40.71465
Did I get it correct here?
obtuse pebbleBOT
x = -40.71465
Did I get it correct here?
royal basin
,calc (-4 * log(3) - 3 * log(7))/(2 * log(3) - log(7))
warm shaleBOT
Result:
-40.71465244487
checks out
obtuse pebbleBOT
tame valve
Lol sorry i always forget
obtuse pebbleBOT
Available help channel!
brisk arrow
obtuse pebbleBOT
brisk arrow
The question ask for it value
Here’s my attempt
But sin360 would be 1/0 which is illegal I guess
royal basin
no
sin(360°) is 0
it isn't 1/0
sin(x) is never 1/0
but also 160*2 isn't 360 so that's where you screwed up
brisk arrow
but also 160*2 isn't 360 so that's where you screwed up
I see
its solved, thank you ann
.close
ebon garden
hiii 🙂 i have this question but i dont understand how to get to -14y, can anyone help?
obtuse pebbleBOT
hiii 🙂 i have this question but i dont understand how to get to -14y, can anyon...
gaunt shell
Hi, can somebody explain me on how to get the quartile and decile or just give an example? I'm quite confused. 🙃
tardy epoch
Hi, can somebody explain me on how to get the quartile and decile or just give a...
This channel's occupied. Read #❓how-to-get-help
nocturne sun
hiii 🙂 i have this question but i dont understand how to get to -14y, can anyon...
$$(a + b)^2 = (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2$$
warm shaleBOT
Doggo
nocturne sun
so,
$$(y - 7)^2 = (y + (-7))^2 = y^2 - 14y + 49$$
warm shaleBOT
Doggo
obtuse pebbleBOT
@ebon garden Has your question been resolved?
timid silo
@dusk turret
obtuse pebbleBOT
<@271692959164923904>
timid silo
Look
Mean 581, Std 970
But upper whisker is not equal to mean+3sd
That's only true for normal distribution
dusk turret
There's no reason to expect it to be, yeah.
The "quantile" formulation is extremely general.
timid silo
But you said in the last channel that usually mean+3sd is considered outliers
dusk turret
For a normal distribution, mean plus/minus 3SD is considered an outlier. I'm sorry if I was unclear.
This is a decidedly non-normal distribution.
obtuse pebbleBOT
Available help channel!
deft girder
Question is to find ab. Do I have to find 17! or there is other ways to do?
royal basin
i think you have to find 17!
hollow garnet
how would i go about doing this
obtuse pebbleBOT
how would i go about doing this
visual onyx
how would i go about doing this
try to factorise/completing the square/others to make it the standard form (x-h)^2 + (y-k)^2 = r^2
hollow garnet
how do i factorise it
visual onyx
x(x-2)
not in this form
in (x-h)^2
which we need to find h
cause do you recall the standard format of a circle
visual onyx
yes
we want to transform this to this format
now we got the x terms
x^2 - 2x
for (x-h)^2 = x^2 - 2hx + h^2 correct??
hollow garnet
yes
hollow garnet
i dont get that
visual onyx
we are missing the constant
hollow garnet
yes
visual onyx
we can see that the constant for x term is -2h in (x-h)^2
now in the question is -2
therefore, h = 1
so the constant term we need to add is 1
x^2 - 2x +1 -1 +y^2 +6y -15 = 0
hollow garnet
okay yeah that makes sense
visual onyx
could you try it for y terms
brisk slate
How do I find x in
Y = mx+c
obtuse pebbleBOT
How do I find x in
Y = mx+c
charred remnant
How do I find x in
Y = mx+c
algebra.
charred remnant
put c into the LHS
brisk slate
Make it -c=mx
charred remnant
then divided both side by m
charred remnant
Make it -c=mx
Nope
Y/m-c/m=x
@brisk slate if that all
you can closed this channel
charred remnant
yes
grave halo
If I have a matrix equation like for example P = M A H (all of these being matrices
obtuse pebbleBOT
If I have a matrix equation like for example P = M A H (all of these being matri...
grave halo
If I want to move a term to the otherside for example H, I need to take its inverse
but how to I know if I put it before or after P
warm canopy
well what are you going to do to the right hand side to eliminate H?
grave halo
*H^-1
warm canopy
on which side of MAH?
warm canopy
yes
grave halo
Ok thanks a lot
grave halo
.close
timid silo
i need help
obtuse pebbleBOT
i need help
timid silo
x^2+x-6
high lily
with?
polar harbor
So you have to use factorisation
high lily
consider a pair of values that multiply to -6 and sum to 1
timid silo
1
high lily
1 isn't a pair of values
timid silo
oh
high lily
1 is just 1 value
timid silo
1 and 6
timid silo
You have make x into two values and it has to equal to 6
mhm
high lily
1 and 6 neither multiply to -6 nor do they sum to 1
high lily
-6 + 1 isn't 1
timid silo
-6 + 1 isn't 1
its -5 i yhink
high lily
-6 + 1 isn't a pair of values
high lily
-5 which isn't 1 which isn't what you want
timid silo
yh x=1 or sum
high lily
consider a pair of values that
multiply to -6 and
sum to 1
timid silo
So like think about the different combinations of two values you can get
so like 3 and 2
polar harbor
so like 3 and 2
Correct
high lily
no
timid silo
OMG REALLY?
high lily
not quite
timid silo
wat?..
high lily
3 and 2 don't multiply to -6
nor do they sum to 1
high lily
typo
timid silo
and when u take away u get 1!
high lily
missed a - sign
timid silo
oh so then like -3 and 2
polar harbor
3 and 2 don't multiply to -6
nor do they sum to 1
but 3 times -2 equals to -6
timid silo
:0
high lily
-3 + 2 isn't 1
polar harbor
-3 + 2 isn't 1
but negative 2 makes sense and positive 3 as well
polar harbor
-3 + 2 isn't 1
+3 and - 2 equals to -6
timid silo
soooo
timid silo
So you have to use these two values in order to find the solution
yeh is it 3 and 2 or not?
high lily
no
high lily
no
timid silo
i cant think of any other ones
polar harbor
+3 and - 2 equals to -6
^^ Think about it for a second
high lily
make sure that your pair of numbers satisfy BOTH conditions
multiply to -6 and
sum to 1
timid silo
oooooh
high lily
if they don't satisfy both, then that pair of numbers isn't what you're interested in
high lily
something to do with those numbers yes,
but get your signs right
high lily
yes
high lily
$$(x+m)(x+n) = x^2 + (m+n)x + mn$$
warm shaleBOT
ℝamonov
timid silo
wat?...
high lily
when considering a pair of numbers like that, those will be the values of m and n above
high lily
yes
timid silo
REALLY??
high lily
yes
timid silo
LFG