this
#help-39
whole willow
whole willow
so 15:12:14
whole willow
12
hoary birch
Yes, you are correct then.
whole willow
thanks
pearl pondBOT
Available help channel!
lucid hazel
pearl pondBOT
lucid hazel
i have a question why is this 2sec^2(x)
why didnt we use power rule and do
d/dx ( 2 ) tanx + 2 d/dx ( tanx)
blissful cloak
d/dx ( 2 ) tanx + 2 d/dx ( tanx)
$\frac{d}{dx}[c]=0$
jolly parrotBOT
XxMrFancyu2xX
pearl pondBOT
pearl pondBOT
Available help channel!
wanton ledge
would f(7) = 2?
pearl pondBOT
would f(7) = 2?
wanton ledge
or is it 7
my question is since theres a hole in the function
but there is not any other place where the point is plotted
midnight haven
but there is not any other place where the point is plotted
There is
Like 5 points above it
wanton ledge
so it would be 7 got it
midnight haven
Yes
midnight haven
I mean it's not like your teacher is going be like "nope that's actually for 7.1 get fucked"
tepid panther
how would I start with solving this question?
pearl pondBOT
how would I start with solving this question?
leaden wadi
how would I start with solving this question?
Can you make a cutout less than zero?
tepid panther
no
leaden wadi
What are the dimensions of the piece of cardboard?
tepid panther
13 x 15
leaden wadi
Could you cutout a square piece that has dimensions of 13 x 13?
leaden wadi
My bad, let me rephrase that.
Could you cutout four square corners that are 13 x 13?
tepid panther
I don't think so
leaden wadi
Why not?
tepid panther
because 4(13x13) > 15x13(area of the box)
leaden wadi
So what do you think are the dimensions of the largest square corners that you can cutout?
tepid panther
1x1?
leaden wadi
Once moment, let me make an interactive graph that you can look at.
tepid panther
okay. Thanks.
leaden wadi
Imagine the sides folded up.
tepid panther
okay
leaden wadi
And the inner rectangle is the base of the box.
tepid panther
right
leaden wadi
And the grey area is the part that is cutout.
tepid panther
right
leaden wadi
How big of a piece can you cutout?
tepid panther
anything less then the area of the box
leaden wadi
How big of a piece can you cutout before the base in the center no longer exists?
tepid panther
you would have to cut a side + the base in the center
you would cut a side larger than the area of the center base
leaden wadi
Reload the page, I'm still finishing up the graph.
tepid panther
alright
leaden wadi
Ok, I finished. Reload it.
tepid panther
I see 4 sections
leaden wadi
That inner rectangle is the base of the box that you will be making. You cannot make a cutout that causes that inner rectangle to disappear or become a negative value.
leaden wadi
When the upper and lower sides are grey like that, that means the cutouts are overlapping.
You cannot overlap the cutouts.
That is an allowed cutout.
tepid panther
right
leaden wadi
What is the largest cutout that you can make that retains all four sides of the box?
tepid panther
a cut that doesn't exceed the inner rectangle?
leaden wadi
Yes.
tepid panther
but also isn't 0?
leaden wadi
Yes.
leaden wadi
What value did you find for the largest cutout that you can make?
tepid panther
13×15
leaden wadi
You're are cutting our four square pieces from each corner to make a box as shown in that grpah. The four cutouts will all have the same square dimensions.
What is the largest square piece that you can cutout from all four corners?
tepid panther
I don't know.
leaden wadi
It's half of the shorter side.
tepid panther
6.5
leaden wadi
Not only that, but if you cutout 6.6" from one side, you would only have 6.4" left which you would be unable to cutout a square with 6.6" x 6.6" dimensions.
So a 6.5" square is the largest square you can cutout, however, that would not leave a base for the box.
So 6.5 is an upper limit to your domain.
It cannot be 6.5 so it has to be less than 6.5.
tepid panther
and greater than 0?
leaden wadi
Yes.
leaden wadi
Correct.
tepid panther
and what would the explanation be? The box cannot be a negative number so it has to be greater than 0 and has to be less then the short side? (13)?
leaden wadi
The largest square you can cutout from each corner is half the length of the shortest side.
Does that make more sense? The dashed lines are where you fold the sides of the box up.
leaden wadi
Look at the graph. The question is asking approximately what value of x gives a box with the greatest volume. You don't need an exact value.
The graph shows the volume of the box on the y-axis and the size of the corner cutouts on the x-axis.
tepid panther
right
leaden wadi
This is where the domain you found earlier comes into play.
tepid panther
the volume is the greatest when y =200
leaden wadi
And for approximately what value of x does y = 200?
tepid panther
when x is 2 or 3
leaden wadi
Go with a value in the middle. You only need to approximate.
leaden wadi
As good an approximation as any.
leaden wadi
Ask away.
tepid panther
is this right?
I know when both sides end at the same point the degree is even
when they end in opposite sides is when the degree is odd.
leaden wadi
A general rule of thumb is to look at the number of turns in the graph and add 1.
leaden wadi
Yes.
tepid panther
for the second one
there is 1 turn
+1
=2
for the third one
3 turns
+1
=4
leaden wadi
Correct.
leaden wadi
Correct.
leaden wadi
In the first option, the linear factors are 2x, 2x-1, x-3, and x+4.
tepid panther
and that wouldn't be right, right?
tepid panther
okay.
leaden wadi
As an example, if x = 2 and x = -5 were zeroes of a polynomial function, you can determine that the linear factors of that polynomial function are x - 2 and x+5 which results in the polynomial P(x) = k*(x-2)(x+5).
tepid panther
so the equation must have the opposite of the zeroes listed?
leaden wadi
You are given the zeroes; -3, -1/2, 0, and 4; what are the linear factors?
leaden wadi
One thing I want to point out is that (x+1/2) can also be written as (2x+1).
tepid panther
how so?
leaden wadi
feral sedge
they're not equal but they have the same root
tepid panther
Okay.
leaden wadi
It's a weird distinction some textbooks and professors will make. I prefer the former x + 1/2 as it is unambiguous.
leaden wadi
Look at the options you are given and see if any match with the linear factors you found.
leaden wadi
Let me elaborate on why the third one is also correct.
tepid panther
okay.
leaden wadi
The zeroes of a polynomial tell you where an equation crosses the x-axis, but it does not tell in which direction the ends are going nor do they tell you how steep the curves are. The direction the ends are going is determined by the positivity or negativity of the polynomial. The steepness is determined by some constant outside of the linear factors.
That constant is represented by the k variable above.
tepid panther
k*x would be the steepness caviat
leaden wadi
Yes.
k can also be positive or negative which would also determine which directions the ends are going to as well.
tepid panther
right
leaden wadi
In option #3, the k value is the negative sign which is the equivalent of -1.
So option 3 does satisfy the zeroes given.
And (x-4)^2 also satisfies the x=4 zero as well.
tepid panther
right
so I had options 2,3,and 5 as correct.
are there any others which are right
leaden wadi
Does option 5 have the x=0 zero?
leaden wadi
And why is the last option not correct?
leaden wadi
No.
tepid panther
hold on I wasn't thinking straight
leaden wadi
If you expand the linear factors, you will get a polynomial in the form of ax^3 + bx^2 + cx + d.
tepid panther
right
#5 isn't right because there is no x determining the steepness
no conosant
leaden wadi
No. The important thing to note is that you have four zeroes, which implies that the polynomial has a minimum degree of 4.
tepid panther
right
leaden wadi
And if you look at the fourth option, it has a degree of 3.
leaden wadi
Also, if you did expand the linear factors, you would get this polynomial.
tepid panther
I'm guessing the 2 would be -2?
leaden wadi
This is just matter of doing the math and expanding the linear factors into the form on the right.
tepid panther
the actual zero would be -2 though right?
leaden wadi
The linear factor would be (x - 2).
tepid panther
like if the given was the function had a zero at -2
leaden wadi
Because when x = 2, x -2 = 0.
tepid panther
2 & 3 i meant to say.
leaden wadi
Correct.
leaden wadi
Do you have to use long division or synthetic division?
leaden wadi
Is that your work? That looks fine.
leaden wadi
Given (x + 3) is a linear factor, what is its corresponding zero?
tepid panther
x = -3
leaden wadi
And three of those graphs cross the x-axis at x=-3.
A simple option to eliminate possible choices is to set x = 0.
This results in f(0) = c.
In the given f(x), at x = 0, f(0) = 6.
leaden wadi
Yes?
leaden wadi
You know one point is (-3,0) and another point is (0,6)
f(0) = 6 and that corresponds to the point (x, f(x)) = (0, 6).
tepid panther
so (-3,6) needs to be visible on the graph?
leaden wadi
No.
Given that x + 3 is a zero, you can determine that one point on f(x) is (-3, 0). Does that make sense?
tepid panther
yes
leaden wadi
And solving for f(0) you get 6. That corresponds to the point (0, 6). Does that make sense?
tepid panther
yes
leaden wadi
So those are two points that should be on the graph of f(x).
Look at your options and see which graphs cross those two points.
leaden wadi
Correct.
tepid panther
the one I highlighted
Thank you so so much for your assistance @leaden wadi
Could we go back to the division polynomial problem? I think I made a mistake somewhere
leaden wadi
You're welcome.
tepid panther
how do I divide polynomials?
.
leaden wadi
Sure.
tepid panther
leaden wadi
I don't see any mistakes.
leaden wadi
-(-2x^2) = 2x^2
leaden wadi
The simplest way to check if you found the correct remainder is to use the Remainder Theorem. That basically says P(x)/(x-a) = Q(x) + R/(x - a).
This is a complicated way of saying that if you evaluate P(x) at x = a, then P(a) = R.
If you evaluate 2x^3 - 5x^2 + x + 2 for x = 1, it should equal zero.
tepid panther
so plug in x=1?
leaden wadi
Yes.
f(3) = 14. If you were to divide 2x^3 - 5x^2 +x + 2 by x -3, you should get a remainder of 14.
pearl pondBOT
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winged harness
!help
winged harness
why is this factual
(W - 1)(H - 1) choose (W - 1)
is the number of distinct paths in a W by H grid
only legal moves are down and right
pls someone
<@&286206848099549185>
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
pearl pondBOT
@winged harness Has your question been resolved?
winged harness
.
vestal tapir
you have to make (W - 1) + (H - 1) steps
all you can change is the order
e.g. xxxyyyy can be shuffled in 7!/3!/4! ways
winged harness
you have to make (W - 1) + (H - 1) steps
all you can change is the order
e.g. xx...
yeah thats what i thought
so it's (W - 1) + (H - 1) choose (W - 1)?
vestal tapir
yes
winged harness
yes
also what are some applications of pascal's identity, when u can literally just plug in nCr into calculator?
vestal tapir
no applications
winged harness
oh such as what?
vestal tapir
never in real life
winged harness
oh
winged harness
never in real life
can u help me with probability rq
suppose this is correct
then to caclulate P(A|B), you need P(A and B), but to calculate P(A and B), you need P(A|B)
isn't this a dilema?
pearl pondBOT
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winged harness
.
pearl pondBOT
@winged harness Has your question been resolved?
sturdy girder
Help please
pearl pondBOT
Help please
sturdy girder
pearl pondBOT
@sturdy girder Has your question been resolved?
lilac quartz
!status
pearl pondBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Prove that if $0<b\leq a$ then $\dfrac{a-b}{a}\leq \ln \left(\dfrac{a}{b}\right) \leq \dfrac{a-b}{b}$
jolly parrotBOT
CWolf
midnight haven
Pretty sure the proof involves the mean value theorem
toxic lichen
sure does
midnight haven
I guess first of all I should split up the ln
toxic lichen
||log(x) on [b,a]||
midnight haven
and then there should exist a c so that log'(c) = $\frac{\ln(b)-\ln(a)}{b-a}$
jolly parrotBOT
CWolf
midnight haven
which is ln(b/a) hmm
Anyways I guess the left and the right inequality follow out of $b\leq c \leq a$
jolly parrotBOT
CWolf
midnight haven
meaning $\frac{a-b}{b}\geq \frac{a-b}{c}$
jolly parrotBOT
CWolf
jolly parrotBOT
CWolf
midnight haven
.close
winter fjord
Let P : (1, 2, 2), Q : (2, 1, -2) and R : (2, -2, 1). The linear transformation F is an (orthogonal) reflection in the plane π and F(P) = Q, F(R) = R. Find the equation of the plane π.
Given solution:
The plane is given by the equation x-y -4z = 0. Use, for example, that F(P)-P = Q-P is a normal to the plane, and that the plane passes through the origin.
winter fjord
im just wondering how i work out that the plane passes through the origin?
P and Q both have abs value 3 from origin, is that it? 
pearl pondBOT
@winter fjord Has your question been resolved?
pearl pondBOT
@winter fjord Has your question been resolved?
pearl pondBOT
@winter fjord Has your question been resolved?
unique ibex
im just wondering how i work out that the plane passes through the origin?
because F must fix the origin
winter fjord
right, fixed origin is a property of linearity. but i still dont understand how the info that is given in the question tells me that the plane π passes through the origin 🤔
is π a transformation of the x,y plane?
unique ibex
right, fixed origin is a property of linearity. but i still dont understand how ...
This is because 0 is reflected to itself, so the plane has to pass through 0, or else it would be mapped somewhere else
winter fjord
sorry, im not following at all...
what i do understand from the problem: P and Q are each others reflections. R is its own reflection, which means it is in the plane π
unique ibex
Can you see that 0 must be reflected to itself?
winter fjord
hmmm i think so...
i mean, from what i understand, the linarity property fixes the origin in a transformation
unique ibex
So since 0 is its own reflection, it is in the plane π
winter fjord
i think im confused by the fact that theres two origins here... one for the room and one for the plane. but that shouldnt make a difference, because their origins are fixed on top of each other?
unique ibex
are you translating from another language?
winter fjord
yes:)
unique ibex
which one?
unique ibex
what is the origin of the plane?
winter fjord
(0,0)
unique ibex
that’s also the origin of the space
unique ibex
i think im confused by the fact that theres two origins here... one for the room...
so this is right
winter fjord
but the transformation/reflection could still be done over a plane that doesnt have its origin fixed on the origin of space? the transformation doesnt change the nature of the space or the plane, only of the point, right? and depending on where the plane lies in space, the transformation will be different
or, the resulting point will be different*
unique ibex
Then that wouldn’t be linear
winter fjord
really? 🤯
winter fjord
im gonna be honest, im having a hard time wrapping my mind around this. ill have to think more about this 🙂
unique ibex
but the transformation/reflection could still be done over a plane that doesnt h...
if you reflect across a plane that doesn’t go through 0, then 0 can’t go back to 0
winter fjord
yeah, that makes sense
the reflection of 0 should always be 0
anyway, thanks a lot. i think im making some small progress here
.close
dusky turret
how did they get the 4 and 0?
pearl pondBOT
how did they get the 4 and 0?
unique ibex
What is u(t)
dusky turret
its 0
unique ibex
where does it say that?
dusky turret
it was somewhere in the question
autumn topaz
it looks like u(t) = 0 if t < 0 and u(t) = 1 if t >= 0?
post the full question. we need all relevant info
near echo
u(t) is the step function
autumn topaz
ah, that's what I figured
near echo
do you know what the step function is @dusky turret
dusky turret
no i don't
near echo
it's 1 if the argument is less than or equal to 0, and 1 otherwise
for example u(1) = 1, but u(-1) = 0
does that make sense
dusky turret
but then how did that get a 0 on the lower integral?
near echo
do you know what the integral of 0 is?
dusky turret
0?
near echo
it's a constant
but the definite integral is 0 yes
so if you integrate 0 * some function from -3 to 0, you'll get 0
does that make sense?
pearl pondBOT
Available help channel!
stoic cove
pearl pondBOT
midnight haven
Product rule
stoic cove
so product rule is a formula to find the deravative?
empty pollen
so product rule is a formula to find the deravative?
Well its the formula to find the derivative of 2 expressions multiplied by each other
In this case, the expressions are x and f(x)
stoic cove
Well its the formula to find the derivative of 2 expressions multiplied by each ...
omg this is exactly what i needed
my teacher never taught us that clearly
empty pollen
omg this is exactly what i needed
Glad it helped!
stoic cove
umm im still confused tho
so i understand that x is equal to 4
this 4
but where is that 2 coming from?
<@&286206848099549185>
i have no idea where those -3 and 2 are coming from
based on the x input value 4..
im just not grasping product rule very well
glacial gale
there's not enough information, we need f(x) to verify those values
pearl pondBOT
@stoic cove Has your question been resolved?
covert sedge
I found this example on finding out which point estimator is most efficient but I don't understand why the last part was done how it was. As in I Get that whichever had the smallest variance is most efficient but I don't really understand why they are squaring stuff and why the variance simple is being divided by what it is being divided by, that type of stuff
glacial gale
i think they're applying a property of variance: Var[aX+bY]=a^2Var[X]+b^2Var[Y}
covert sedge
i think they're applying a property of variance: Var[aX+bY]=a^2Var[X]+b^2Var[Y}
Ah that helps, but I'm still not sure how they they decide what to divide the right side of the equation by?
glacial gale
they're adding the fractions
1/4+1/4=1/2, 1/16+9/16=5/8, etc
i'm assuming that Var(X1)=Var(X2)=sigma^2
covert sedge
i'm assuming that Var(X1)=Var(X2)=sigma^2
Yes
glacial gale
does that answer your question? or did you mean something else?
tiny ibex
pearl pondBOT
tiny ibex
Can someone help me with part b of this question?
pearl pondBOT
@tiny ibex Has your question been resolved?
tiny ibex
<@&286206848099549185>
pearl pondBOT
@tiny ibex Has your question been resolved?
unborn swallow
Can someone help me with part b of this question?
Standard calc find max
In part a you found some x that solves the dfq, then use the initially but to solve for the exact x(t) equation
we are given x(0)=0 and x’(0)=10 ^
Then solve for when x’=0 to get critical points
Compare critical point x values and endpoint x values (at t=0 and t=inf) one is a max
Capiche?
tiny ibex
Then solve for when x’=0 to get critical points
Yeah how do I do this?
pearl pondBOT
Yeah how do I do this?
plush bramble
Yeah how do I do this?
show your answer for part a
tiny ibex
Yeah I did
plush bramble
so where is it
jolly parrotBOT
plush bramble
You can't do b) without doing part a)
did you check your answer in a) by plugging it into the DE?
i.e. does your x solve this
plush bramble
and these initial conditions
tiny ibex
Yea
tiny ibex
E^-0.3t(-2cos0.2t + 47sin0.2t)
plush bramble
E^-0.3t(-2cos0.2t + 47sin0.2t)
you're missing a constant
plush bramble
,w d/dt (e^(-0.3t)(-2cos0.2t + 47sin0.2t))
jolly parrotBOT
plush bramble
exponential function is always positive so you can divide by that
then set the stuff in parentheses to 0
tiny ibex
Yeah I did that
plush bramble
and why are you stuck finding x' = 0
.
pearl pondBOT
@tiny ibex Has your question been resolved?
pearl pondBOT
pearl pondBOT
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junior pawn
i have to find the determinant of the matrix :
1 n ... n
n 2
. 3
.
. n-1
n ... n
(n everywhere except on the diagonal)
mortal island
try subtracting from each row/column the last row/column, linear combination, to zero out the n s
junior pawn
how can i show that P(x) = x^n - x +1 have n distinct root
saying the polynomial is degree n so it has n root doesn't seem correct
remote roost
junior pawn
?
feral sedge
Maybe show it doesn't show any roots with its derivative
jolly parrotBOT
Disorganized
junior pawn
wait what's that
vocal lark
wait what's that
it's that power of negative 1 times the product of all the trace elements
(elements on the main diagonal)
junior pawn
are you talking about the previous exercise?
vocal lark
are you talking about the previous exercise?
yes
junior pawn
ye i found that
limber oasis
how can i show that P(x) = x^n - x +1 have n distinct root
saying the polynomial...
Over the complex numbers I guess ?
junior pawn
yes
limber oasis
Show no root is doubled
Very useful lemma: if a root of a polynomial P is of multiplicity m, then it is a root of the first m derivatives of P
So if x is a doubled root of P, it's a root of P and of P'
junior pawn
then we have to prove it by recurrence
junior pawn
So if x is a doubled root of P, it's a root of P and of P'
ok
junior pawn
i don't see how to show that it's not root of P'
limber oasis
Look at P'
However you definitely know the roots of P'
So it's easy to show they're not roots of P
junior pawn
P' = nx^(n-1) - 1
limber oasis
So 1/n = x^(n-1)
So you can find the roots
Then it's just about checking that P(a root of P') is not 0
junior pawn
x = ln(1/n)/(ln(n-1)*(n-1)
it's not root
limber oasis
There's n-1 roots though
pearl pondBOT
@junior pawn Has your question been resolved?
midnight jacinth
i need help with part b, bc i have no clue how to find it at that exact point
midnight jacinth
this is calculus
pearl pondBOT
@midnight jacinth Has your question been resolved?
midnight jacinth
<@&286206848099549185>
pearl pondBOT
@midnight jacinth Has your question been resolved?
pearl pondBOT
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frozen sandal
I only get one more shot at this, can someone help?
pearl pondBOT
I only get one more shot at this, can someone help?
sharp quest
isn't this just sin(x) shifted by pi?
frozen sandal
is it?
wait also I realized i did my period wrong
I am doing it by pi
yeah it's supposed to be 2pi
does this look right to you?
sharp quest
is that shifted by pi?
frozen sandal
it's shifted -1/2
that's what I got for my phase shift
I know the phase shift is right
I just think I am doing it wrong
sharp quest
frozen sandal
OMG I was dividing by the period
I was doing -(pi)/2pi
when it's just -pi/1
so yeah left pi units
thank you
I see my mistakes now
.close
pearl pondBOT
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median shadow
please help
pearl pondBOT
please help
last moth
.close
pearl pondBOT
last moth
Closing this as you already have another channel..
pearl pondBOT
Available help channel!
vestal mauve
U
pearl pondBOT
@vestal mauve Has your question been resolved?
pearl pondBOT
pearl pondBOT
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tidal jewel
hlo
royal phoenix
@tidal jewel What is the shape of a piece of bubble gum?
tidal jewel
bubble gum looks like 3d rectangle
royal phoenix
Before I continue helping you, you need to close your 2nd help channel
tidal jewel
jus a sec
plush bramble
Closed your other channel
tidal jewel
done
royal phoenix
bubble gum looks like 3d rectangle
Have you ever seen a bubble gum?
The one you can blow with your mouth
tidal jewel
yes of course
royal phoenix
Do you think it looks like a rectangular shape?
tidal jewel
this looks like similar to rect? confuse
plush bramble
this looks like similar to rect? confuse
The problem specifically tells you it's a sphere
tidal jewel
ys i also assume that but stuck in solving
royal phoenix
@tidal jewel The gum is 4cm^3 before you eat it. You then eat it and blow a bubble right? You want to guess the thickness
The gum looks like a sphere and you want to guess its thickness
Now do a drawing of the sphere. It has 2 radius, inner radius that contains the air you blow and outter radius that has contact with ambiant air.
You want to guess the thickness, or the difference between these two radii
tidal jewel
jus a min
royal phoenix
@tidal jewel to achieve this, I will give you small tasks to do. First do a drawing and show me. Then give me formula for the volume of a sphere and try to guess the relation between the volume of the bubble and the thickness of the bubble. (This is literally what is written in your exercise. You are already well guided so you need to try what they ask)
tidal jewel
ok wait..
tender zenith
royal phoenix
@tidal jewel ping me if I don't see your messages haha
royal phoenix
volume = 4/3 pi r^3
Ok perfect, now what do you think is the relation between ΔV and Δr?
Try to justify what you think
royal phoenix
Ok perfect, now what do you think is the relation between ΔV and Δr?
Try to just...
To find this, you need to find what is the volume of the bubble
You can assume that you know r1 the inner radius and r2 the outter radius
tidal jewel
ΔV = 4/3pi( 3r^2) Δr ,
royal phoenix
How did you get that?
pearl pondBOT
@tidal jewel Has your question been resolved?
plush bramble
took derivative we want ΔV/Δr as yu pointed
Yea so can you find this algebraically
pearl pondBOT
pearl pondBOT
Available help channel!
proud nymph
Hello, could someone help me with this AWP?
pearl pondBOT
Hello, could someone help me with this AWP?
proud nymph
I dont understand how they started
what is that rule with the substitution?
I will send a pic of my method in a sec
dusk horizon
what substitution do you mean? Are you asking about z(t)?
I can't actually tell what you're doing? Where did g(t) and h(t) come from? How did you choose what they are?
pearl pondBOT
@proud nymph Has your question been resolved?
proud nymph
what substitution do you mean? Are you asking about z(t)?
I mean what they did in the white screenshot
I dont understand that
In my solution I used the formula to solve
I will send it wait
dusk horizon
This isn't a statement. This is just a definition.
dusk horizon
In this picture, they're finding y(t) by recognizing a product rule that happened
proud nymph
Which rule did they use for solving :(
I only know those two rules
and I thought you can apply this one
Why was my aproach wrong tho
dusk horizon
I still have no clue what you did. The thing you posted is just a definition. It doesn't mean anything without further clarification.
proud nymph
dusk horizon
But I understand the solution at the top. That's perfectly clear
proud nymph
I am sorry I forgot to send this
The definition I sent uses this
So I tried to put g(t) as t^2 - 1
because I thought its tha
t
dusk horizon
what you tried didn't work because the question would need to be (t^2 -1)(y/t) = yt - y/t
but the question is t^2 -y/t
true ruin
I dont get the point of PA = LU
pearl pondBOT
I dont get the point of PA = LU
true ruin
so once youve found the permutation to solve A into the upper triangular matrix
what is the next step?
like do you just try to find the lower triangular matrix?
tropic saddle
lets assume for a second that you dont have to switch rows during the gaussian elimination
so just A=LU
true ruin
right
tropic saddle
then what exactly is your question now?
why we do this?
why we write down the elimination in the form LU?
true ruin
the elimination in the form LU is just doing the operations to find the lower and upper tringular matricies right?
like for instance im trying to do this
so there i have found the upper triangular matrix
true ruin
sorry yeah i confused the lower
but now i would have to find the upper triangular matrix from after i swapped right
like so you do PA so that you can have a pivot to do the lower elementary operations
and then with the swapped result, you would find the respective lower and upper triangular matricies
which is PA = LU
also, my permutation should be correct but when i multipy, i dont exactly get the same result
pearl pondBOT
@true ruin Has your question been resolved?
true ruin
what is your L?
after i do the swap, will L be the result of applying the operations to obtain the lower triangular matrix?
tropic saddle
from the operations you do you read off the entries of L
true ruin
Im sorry i do not understand what you mean
midnight haven
Do you know algebra?
plush bramble
Can you help me
!help
pearl pondBOT
Can you help me
Please read #❓how-to-get-help
tropic saddle
the matrix $L$ is here $L=\begin{pmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 2 & 3 & 1 \end{pmatrix}$
jolly parrotBOT
Denascite
tropic saddle
compare with the operations you did and see if you see a connection
true ruin
compare with the operations you did and see if you see a connection
which operations
tropic saddle
the row operations
true ruin
so wne you multiply PA and LU they should be equicalent
im sorta having trouble getting to u
from [1 0 1; 0 1 0; 2 3 4]
tropic saddle
the U you computed was correct
true ruin
sorry the L
im sorry my brain is everywhere
im being overloaded with so much hmwk this week i want to die
tropic saddle
the operations you did were:
you replaced R2 with R2-0*R1
you replaced R3 with R3-2*R1
you replaced R3 with R3-3*R2
these 0,2,3
are the entries of L
in the appropriate places
true ruin
for U mine were sort of different
I did -2R1 + R3 and -3R2 + R3
I guess i technically did this R2-0*R1
pearl pondBOT
@true ruin Has your question been resolved?
true ruin
I dont know how to get to L
you get to L from whatever the result is from PA but i cant find the combinations
terse cave
I dont know how to get to L
lmk if u understand this
this is just an easy to visualise this @true ruin
true ruin
this is so helpful!!!
true ruin
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midnight haven
pearl pondBOT
midnight haven
hey so dv/dt is just another way of writing limit?
plush bramble
hey so dv/dt is just another way of writing limit?
otherway around. dv/dt is defined as a limit
wet dirge
how can i find he value of k?
pearl pondBOT
how can i find he value of k?
wet dirge
K(x)?
leaden wadi
Use the pair-wise elements given; eg. k(0) = 2 from the second element (0,2).
blissful cloak
I know what the binomial coefficient is, I've been using it since my algebra days. But I've been wondering where does $\binom{n}{k}=\frac{n!}{k!(n-k)!}$ even come from? I know that $\binom{n}{k}=\frac{{n}P{k}}{k!}$ but again I really don't understand the combination formula
jolly parrotBOT
MrFancy
lavish totem
i always understood it as n!/(n-k)! being your choices for k items from n without replacement
so n for the first, n-1 for the second up to n-k+1 for the kth
then dividing by k! because each of these can be ordered in k! ways
blissful cloak
so n for the first, n-1 for the second up to n-k+1 for the kth
yes and that's why we divide by (n-k)! to cancel out n-kth n-k-1th, etc
lavish totem
ye
blissful cloak
then dividing by k! because each of these can be ordered in k! ways
how does one describe this? 
lavish totem
how do you mean describe
like you have all possible subsets of size k from n items
but you're counting choosing an item first as differently from choosing it second
blissful cloak
ok not rather describe poor choice of wording on my part, but do you know like an example?
lavish totem
i guess you can think for small k
when k=2 you want to know how many ways to pick 2 things
and you're doing n*(n-1), n choices for item 1 and n-1 for item 2
but you're gonna count each combination of two items twice
first where you pick a first and b second
and second when u pick b first and a second
is that the kind of example u mean?
blissful cloak
but you're gonna count each combination of two items twice
ahh ok and for three items you could it by 6 because there's twelve combos
and ofc that's where the k!
comes from
alright
got it!
thanks @lavish totem! 
.close
midnight haven
pearl pondBOT
midnight haven
Can anyone help me conceptualize why are these true?
Graphically or algebraiclly...
I dont seem to get the intuition
actually only for number 2
i understnad 1
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
<@&286206848099549185>
pearl pondBOT
@midnight haven Has your question been resolved?
hybrid sorrel
well so for (a,b)=(0,0) the formula just simplifies to f(-x)=-f(x) which is what makes something an odd function (which is symmetric about (0,0)), so that makes sense.
then all we have to do is shift the function so that we get it around the point (a,b). so that would mean that f(x) is symmetric around (a,b) if f(x-a)-b is odd. that would mean that f(-x-a)-b=-(f(x-a)-b) implies f(-x-a)=2b-f(x-a). which is pretty close to what they give you. if we do a change of variables, u=x-a, then that gives f(2a-u)=2b-f(u) which is exactly the formula, except let x=u to get f(2a-x)=2b-f(x)
hybrid sorrel
well so for (a,b)=(0,0) the formula just simplifies to f(-x)=-f(x) which is what...
@midnight haven if you have questions on my explanation, feel free to ping me in the #prealg-and-algebra channel or something
hybrid sorrel
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queen hare
pearl pondBOT
plush bramble
Why do you need to multiply -1? to 1/2
You don't have to
silent wolf
it doesn't look like there was a good reason, looks like a quirk of whatever generated it
queen hare
ohhh
@silent wolf can I have a follpw up question?
i mean give another question
how it turn out to this?
from pic a to b?
queen hare
Please can you further explain? sorry
silent wolf
2(m+2) + (m-2)(-1) = 2m + 4 + (-m +2) = 2m + 4 - m + 2 = m + 6
the rest of the phrases all stayed the same
analog topaz
Please can you further explain? sorry
You just find the common denomiator which is 2(m-2) and multiply both the numerator and denominator by the value that gets you 2(m-2) which is seen in the first picture. The second picture just shows further simplification of the numerator.
queen hare
ohhhh Thank you @silent wolf, sorry for troubling you, I get it now
queen hare
You just find the common denomiator which is 2(m-2) and multiply both the numera...
Thank you too! 🙂
sorrry I forgot the basics
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solar gyro
pearl pondBOT
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
solar gyro
Here are my answers so far
Are they correct?
Plz someone help
I’ve got a test tmrw
pearl pondBOT
@solar gyro Has your question been resolved?
pearl pondBOT
@solar gyro Has your question been resolved?
pearl pondBOT
@solar gyro Has your question been resolved?
pearl pondBOT
@solar gyro Has your question been resolved?
proud nymph
Can someone tell me how to calculate 2022e^(i*2022) ? I know theres the formula cos(2022) + isin(2022), but what jappens to the 2022 in the front again
last summit
so
the formula you are talking about is
$$e^{i \theta}=\cos(\theta)+i\sin(\theta)$$
jolly parrotBOT
Austin
last summit
then if we have a constant applied out front
like in your question
this is
$$Ae^{i \theta}=A(\cos(\theta)+i\sin(\theta))$$
jolly parrotBOT
Austin
proud nymph
Oh thank youuuuu!!!!!
last summit
np
proud nymph
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pearl pondBOT
pearl pondBOT
Available help channel!
glacial sequoia
$\int_0^{\frac{\pi}4} \ln(\tan x) \dd x$
pearl pondBOT
$\int_0^{\frac{\pi}4} \ln(\tan x) \dd x$
jolly parrotBOT
NEON
glacial sequoia
Any ideas?
Wolfram just says it's "-C" and I don't find that constant on the wiki page for mathematical constants
glass salmon
Catalan constant
jolly parrotBOT
glacial sequoia
Fair
glass salmon
Ig it’s G or C
glacial sequoia
Is there a link between this integral and the alternating series representation for G?
oooo integration by parts maybe?
,w integrate x/(sin x cos x) from 0 to pi/4
jolly parrotBOT
pearl pondBOT
glacial sequoia
.reopen
pearl pondBOT
✅
plush bramble
Was gonna suggest Fourier but that's pretty ugly
light maple
how i’m supposed to tell when a curve will pass through an asymptote
dense flower
I can't read the page but it doesn't pass through an asymptote
the curve goes to infinity
wraith plinth
If your asymptote is y = 5 for example then you can try to see if there are solutions to f(x) = 5
pearl pondBOT
@light maple Has your question been resolved?
light maple
I can't read the page but it doesn't pass through an asymptote
it does
light maple
If your asymptote is y = 5 for example then you can try to see if there are solu...
is it necessary to test every asymptote i find?
dense flower
you find the asymptotes by looking at the denominator
since you cant divide by zero the function is undefined at -1 and 3
wraith plinth
You talking abt vertical aysmptotes but pretty sure they mean horizontal
dense flower
im lookin at da quesiton o
light maple
yeah that being said, y= 0 is an asymptote due to if you divide by x on both sides, y/x cannot equal 0 since it equals a fraction
x cannot be 0 anyway in that case
and neither can y
wait doesn’t that add another asymptote?
at x = 0
light maple
oh alright
dense flower
the function is defined at x=0
light maple
actually why is y=0 an asymptote anyway, just because it’s equivalent to a fraction?
but fractions with x in the numerator can be 0 at one point
jolly parrotBOT
bran
dense flower
you can solve for x
light maple
yeah what he said, it’s in the working they gave us right there
pearl pondBOT
@light maple Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
finite crown
Im currently studying simple linear regression bymself and im doing OLS
olive rover
pearl pondBOT
olive rover
Hello currently confused on this ik the answer is supposed to be 70 but I don’t know how to set it up
unborn abyss
work backwards in time
olive rover
I’ve tried and keep getting 112
unborn abyss
watch out for the "spent one third of his remaining money" part
olive rover
Would it not be set up as 1/2x+14+1/3(1/2x+28)
pearl pondBOT
@olive rover Has your question been resolved?
olive rover
Or would it be 1/3(1/2x+14)+14=0
olive rover
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