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#help-17
dusk sluice
vocal sleetBOT
dusk sluice
From physics, but my issue is with the trig.
Why is the vertical component cos and the horizontal is sin?
I don't get it
lone linden
dusk sluice
Yea I know that, but it's not helpful
lone linden
in relation to the angle beta
the green is your adjacent
and the hypotenuse is n
dusk sluice
Yea, I see it from that diagram, but the picture doesn't seem to have the angle pictured that way
lone linden
and the hypotenuse is n
so you can say that $\cos \beta=\frac{\text{adjacent}}{n} \implies n\cos \beta=\text{adjacent}$
twin meteorBOT
Civil Service Pigeon
lone linden
Yea, I see it from that diagram, but the picture doesn't seem to have the angle ...
wdym
dusk sluice
Why isn't the angle like this
They draw it like this
Like I don't understand how the angle is on the top part
rain yarrow
Like I don't understand how the angle is on the top part
because the bottom part has been removed due to budget cuts
it doesn't matter
dusk sluice
dusk sluice
it doesn't matter
If the angle is on the bottom, then the verical component would be sin wouldn't it?
dusk sluice
They're saying the vertical component is cos
dusk sluice
I would get the wrong answer, because I would have done the EXACT same calculations as them, but with sin instead of cos
So that is a problem, no?
I would have done the same work as this
But switched sin and cos
which would give a different answer
rain yarrow
reflections always swap, tho
dusk sluice
I don't understand
why is anything even being reflected
and I don't know what you mean by "reflections always swap"
rain yarrow
if you have the angle on the y axis
you are reflecting it across the hypotenuse, kinda
and that swaps sin and cose
also you can easily find sin and cos
by just seeing WHICH ONE TOUCHES THE ANGLE
dusk sluice
I get that sin is the side opposite of the angle divided by hypotenuse
and cos is adjacent over hypotenuse
I completely understand that
but they're taking a completely different triangle from me
and I don't understand why
rain yarrow
can i see the problem
dusk sluice
dusk sluice
rain yarrow
oh
dusk sluice
Well it's not style because I get a different answer
rain yarrow
maybe read the problem more carefully next time?
dusk sluice
It's an example to help me understand the content
Except I don't understand the example, so I can't understand the content
I read the question carefully, I still don't know why they are doing it that way
and I read their solution
they don't give a good explaination as to why they take that angle
rain yarrow
then I don't know
I'm not the teacher
they take it to show you that you will be faced with trick questions
dusk sluice
The teacher does not allow me to contact them pretty much
I have to do the course via textbook only more or less
This is from the textbook
Hence why I am trying to get help online
rain yarrow
mostly to screw w/you
you will be faced with trick questions like this
and it shows you that
dusk sluice
I need to be able to identify those trick questions then lol
I don't think it's a trick question though, I need to know when to use cos and sin
I'm pretty sure this is very fundamental to understanding physics and modeling problems
I get an answer of 76 degrees when the answer should be 14 degrees if I swap them, that's a huge difference
dusk sluice
I have no idea how to even estimate that, nor would I know how to check the answer.
dusk sluice
All I would know is that the angle is probably somewhere between 0 and 90 degrees lmfao
I would have no idea where
dusk sluice
It doesn't though, because they move the triangle...
They use a different triangle essentially
So using the soh-cah-toa thing doesn't help in the slightest if its a different triangle
rain yarrow
THERE IS ONE RIGHT ANGLE IN THE TRIANGLE
whoops had capslock on
sry
anyways, find that angle
and apply my rule
not hard
dusk sluice
Ok, I found a right triangle
The right angle is in the bottom
And I got the wrong answer because I used sin for the vertical
Turns out, they use a different triangle where the right angle is on the top. I have no idea how they got that triangle, it doesn't make sense given the question.
rain yarrow
well, could you walk me through the question?
making vague allusions to it doesn't work
dusk sluice
I posted the question before, it is asking at what angle does a banked curve have to be for a car to turn on it without requiring any friction (centripital force only) at a speed of 25m/s
It has a picture
This is the picture
rain yarrow
it's simple
dusk sluice
The normal force is the force exerted on the car by the road. This would just be equal to the weight of the car if the angle were 0 degrees.
However, because it's angled the normal force has vertical and horizontal components
It is saying the vertical component of the normal force is cos(angle) * total normal force
and the horizontal is sin(angle) * total normal force
If you draw a triangle, I can EASILY identify what would be cos and sin
The problem is, I am using the wrong triangle apparently
I don't know why they use the triangle that they do
rain yarrow
because you are going forward and right
but forward first
i think?
the legs go up and to the left
either way you start at one of the corners without the right angle
that triangle that they used fit the road
ask classmates
i have to go
dusk sluice
The only explaination I can get is "Beta is the angle between the horizontal and the surface, which is the same as the angle between the normal line and the vertical."
I don't know what that means
rain yarrow
basically, the angle is different, so the triangle is different
vocal sleetBOT
@dusk sluice Has your question been resolved?
sand hedge
how do you set this up?
vocal sleetBOT
how do you set this up?
sand hedge
i thought you would with dot product buy my friend is saying cross
i thought cross was perp
flat whale
i thought you would with dot product buy my friend is saying cross
Cross product of what
And dot product of what
sand hedge
you would take the direction vector of the scalar equation
(1,2) and (4,a) for a
i feel like you would just take the dot product
flat whale
i feel like you would just take the dot product
That can work
vocal sleetBOT
@sand hedge Has your question been resolved?
sand hedge
That can work
what else should i do
sand hedge
the angle between the direction vectors wouldnt change wherever theyre shifted
so if i just find the direction vector and dot product them shouldnt it work?
flat whale
Then you're just overcomplicating it
Lines are parallel if their slopes are the same
Put both lines into slope intercept form
flat whale
Yea that one requires dot prod
vocal sleetBOT
@sand hedge Has your question been resolved?
vocal sleetBOT
@sand hedge Has your question been resolved?
vocal sleetBOT
@sand hedge Has your question been resolved?
karmic mica
id use tan(a+b) = tana+tanb/1-tanatanb
tan(alpha) = |the slope|
if 0<=alpha<90
@sand hedge
crimson pumice
vocal sleetBOT
crimson pumice
,rotate
twin meteorBOT
crimson pumice
How do you prove something like this?
final zephyr
Technically you should also integrate from -inf to inf
brittle minnow
I mean rice is just technically wrong
final zephyr
Technically you should also integrate from -inf to inf
(integrate f(x)) I mean
crimson pumice
so technically I should intergrate from -inf to inf
final zephyr
yes
crimson pumice
but technically this also works
brittle minnow
no
final zephyr
no
final zephyr
you have to integrate from -inf to inf them split into 3 integrals
because piecewise
crimson pumice
I think -inf to inf of 0 is still 0
final zephyr
yes
cobalt crypt
no
this is just being pedantic, it is clear that integrating over the rest of the domain gives you 0
crimson pumice
so i can intergrate at 0 to 1
cobalt crypt
if you realise that thats the only part of f which matters, yes
final zephyr
it is clear that any multiple of 4 is a multiple of 2, but to prove it you still have to write 4k = 2(2k)
cobalt crypt
thats just being pedantic
final zephyr
I'd argue it's being more precise
crimson pumice
actually I kinda agree with that
it kinda writing ab = ba
at the end of the day it still makes the same thing
but moving on
I got the right answer which is 1
brittle minnow
while I somewhat agree with snow here, it's for the better to do than not
In the best case you write some extra stuff in the worst you might lose some marks in exam
crimson pumice
well thanks for the help
cobalt crypt
highly doubt anyone would penalise you for not writing $\int_{-\infty}^\infty f(x) , dx$
twin meteorBOT
latent robin
Something/52 = 0,13
vocal sleetBOT
Something/52 = 0,13
river minnow
Quick I’m in test
Unfortunately we are not allowed to help then
karmic imp
Quick I’m in test
Cheating is a bannable offense
vast shale
We're not allowed to help + there are other better options than this server for fairly simple question.
vocal sleetBOT
@latent robin Has your question been resolved?
fading forum
Hi, how can I find the arc length
vocal sleetBOT
Hi, how can I find the arc length
fading forum
$y = \int_{-2}^{x} \sqrt{3t^4-1} dt, -2≤x≤-1$
twin meteorBOT
Ñøïr
inner magnet
maybe you can sub 3t^4= cos^2 x
fading forum
maybe you can sub 3t^4= cos^2 x
Since L = int(sqrt(1+[d/dt(f(t))]^2) I tried to cancel out dt in denominator and the one in the function, is it wrong?
Derivative of integral
inner magnet
sorry yes you are correct dont need to find rthe integral
fading forum
I couldn't get far tho because I don't know how lower bound of -2 affects
inner magnet
i think if for definite integral need to work it out but for indefinite which doesnt have lower bound can just cancel
vast shale
i'm pretty sure you're just supposed to get a number
viral copper
What's the original question
fading forum
Value is sqrt(3)t^3/3, if I am not mistaken, but what are the bounds?
fading forum
$y = \int_{-2}^{x} \sqrt{3t^4-1} dt, -2≤x≤-1$
Arc length for this
viral copper
Is that the integral that is giving us the arclength or..?
You need a function to calculate the arclength of
viral copper
you can use an integral to calculate arclength as well
can we see the question in the original wording
fading forum
Not much of help tbh
viral copper
That's helpful
reef scarab
Ah
viral copper
Which one are you doing?
twin meteorBOT
viral copper
Ahhh I get what's going on here
The curve itself is $y = \int_{-2}^x \sqrt{3t^4 - 1} \dd t$
twin meteorBOT
NEONPerseus
reef scarab
Ah
inner magnet
yes thats what i said
viral copper
Do you know the formula for the arclength of a curve in terms of its slope? @fading forum
viral copper
yes thats what i said
You did?
fading forum
Yes
viral copper
I apologise then
fading forum
dt's cancel out, then square and root cancel out, +1-1
viral copper
uh
fading forum
Sorry, i couldn't word it well
viral copper
$\int_a^b \sqrt{1 + \left ( \dv{y}{x} \right )^2} \dd x$
You must be aware of this formula
twin meteorBOT
NEONPerseus
viral copper
This is the formula for the arclength of a curve from x = a to x = b, correct?
fading forum
yes
viral copper
**NEONPerseus**
Do you know how to find dy/dx from this?
fading forum
Since function is an integral itself, can't we just remove it?
viral copper
indeed in this case you can
$y = \int_{g(x)}^{h(x)} f(t) \dd t \ y' = h'(x)f(h(x)) - g'(x)f(g(x))$
Have you seen this before?
twin meteorBOT
NEONPerseus
fading forum
I think yes, but I can't really remember
viral copper
It's alright, not really relevant, I just wanted you to know that it's not always the case that they simply cancel out
In this case they do cancel out
inner magnet
**NEONPerseus**
thank you for showing me
right?
viral copper
No need for a y
reef scarab
Right mb
twin meteorBOT
Kiameimon | Welt Rene (glomed)
reef scarab
It's just an application of FTC + chain rule
viral copper
@fading forum now that you have dy/dx can you put it in the formula?
inner magnet
or can you evalutate trhe integral and then take derivative?
reef scarab
or can you evalutate trhe integral and then take derivative?
Well it works
But why go through the trouble
viral copper
or can you evalutate trhe integral and then take derivative?
I doubt that integral is even elementary tbh
,w int sqrt(3t^4 - 1)
twin meteorBOT
viral copper
Can't integrate it
vast shale
Wtf, I've never seen that in a problem set
viral copper
You're not meant to integrate it
vast shale
An integral that can't be solved with elementary functions?
reef scarab
Ye
vast shale
oh
reef scarab
fading forum
$y = \int_{-2}^{x}\sqrt{1+\sqrt{3t^4-1}^{2}} dt, -2≤x≤-1$
twin meteorBOT
Ñøïr
viral copper
Replace whatever ts you have with xs
And the limits of integration are from -2 to -1
Not -2 to x
And it's not equal to y, it's equal to the arclength
fading forum
And it's not equal to y, it's equal to the arclength
Mb
viral copper
we had y as a special integral function
And we differentiated it to find dy/dx
These are all functions in x
t was a dummy variable
fading forum
$L = \int_{-2}^{1}\sqrt{1+\sqrt{3x^4-1}^{2}} dx$
twin meteorBOT
Ñøïr
viral copper
Indeed
Did you understand why I asked you to change the limits and replace the xs with ts
fading forum
But if integral had lower bound different than x's, what'd I do?
viral copper
wdym
fading forum
Did you understand why I asked you to change the limits and replace the xs with ...
Yes
fading forum
wdym
Like, if question was
$y = \int_{-2}^{x}\sqrt{1+\sqrt{3t^4-1}^{2}} dt, -3/2≤x≤-1$
twin meteorBOT
Ñøïr
viral copper
Uhh
I think you've mixed the steps up again
the procedure is always the same:
- Find dy/dx (MUST BE A FUNCTION OF X)
- substitute dy/dx into the integral formula
- Put your integration limits from x = a to x = b (will be given in the question)
fading forum
Lower bound of x was -3/2 instead of -2 for instance
viral copper
Doesn't matter
As long as it's a constant
That was not right to say
As long as the lower bound is a constant, and the upper bound is x, you will get back whatever is inside the integral upon differentiating
fading forum
Lower bound of x was -3/2 instead of -2 for instance
So I would integrate for -3/2 lower bound then?
Or shouldn't I replace -2?
viral copper
So I would integrate for -3/2 lower bound then?
yes if you're being asked to calculate the arclength between those points
viral copper
no worries
timber cypress
Hello I need a help
vocal sleetBOT
Hello I need a help
vocal sleetBOT
@timber cypress Has your question been resolved?
vocal sleetBOT
@timber cypress Has your question been resolved?
timber gate
That's the Lami's Theorem
timber cypress
But doesn't it say to the ratio of sines opposite to the forces?
timber gate
But doesn't it say to the ratio of sines opposite to the forces?
its just bit modified , the sines of lami theorem have been replace by sides using the sine rule
the ratio is preserved
timber cypress
Can you show me how they did it in that question?
vocal sleetBOT
@timber cypress Has your question been resolved?
ember tendon
what happens when you try to find the transformation matrix of an affine transformation?
vocal sleetBOT
what happens when you try to find the transformation matrix of an affine transfo...
sleek flame
This looks to be true, but my work shows it’s false? Am I on the right track to solving this?
vocal sleetBOT
This looks to be true, but my work shows it’s false? Am I on the right track to ...
vast shale
you want to show that u=c_1 v + c_2 w can be written as a linear combination of v+w and w-v
hint: notice that (v+w)+(w-v) = 2w
vocal sleetBOT
@sleek flame Has your question been resolved?
vast shale
you cant multiply vectors
random gust
but what if you wanted to @vast shale
sleek flame
only cross and dot, right
vast shale
but what if you wanted to <@456226577798135808>
then make sure to define it and be very precise
sleek flame
sleek flame
thank you! 🙂
vast shale
thank you! 🙂
yo don't forget to close the channel when your question is answered
vocal sleetBOT
@sleek flame Has your question been resolved?
deep bane
I dont even know where to start
vocal sleetBOT
I dont even know where to start
vocal sleetBOT
vocal sleetBOT
Available help channel!
signal relic
Can anyone help me with part b) of this problem? I am not sure how to solve this.
vocal sleetBOT
Can anyone help me with part b) of this problem? I am not sure how to solve this...
regal bane
Try the squeeze theorem. Notably, -1 ≤ sin(x) ≤ 1
urban laurel
or just evaluate the limit of 1/x (as x approaches infinity) and write this -1 ≤ sin(x) ≤ 1
since sin(x) is bounded and the limit of 1/x is 0 then the lim of sin(x)/x is 0 (as x approaches infinity)
vocal sleetBOT
@signal relic Has your question been resolved?
signal relic
Sorry guys. @regal bane, I am not sure how to apply the squeeze theorem. (In reality, I forgot.) And @urban laurel, I don't think my professor will accept your first proposed solution, since it is not written "mathematically" correct. Nevertheless, do you mind explaining what you meant in your second comment?
vocal sleetBOT
regal bane
-1 ≤ sin(x) ≤ 1
-1/x ≤ sin(x)/x ≤ 1/x
Take both to infinity.
signal relic
.reopen
vocal sleetBOT
✅
urban laurel
you can also apply the queeze theorem here like Kaynex said
vocal sleetBOT
@signal relic Has your question been resolved?
misty viper
For mathematical induction, does that case for p(k+1) look okay?
misty viper
(I feel like the left side is right, but the right side is wrong)
random gust
For the last step you need to take the difference between k+1 th and k th and show that that is the correct difference.
vocal sleetBOT
@misty viper Has your question been resolved?
misty viper
What do you mean by the th? And why difference?
random gust
Because your P function is a sum
In order for the RHS to be correct increment k by 1 has to have the same effect as increasing it by 1 in the actual function
So you need to check that @misty viper
vocal sleetBOT
@misty viper Has your question been resolved?
compact zealot
vocal sleetBOT
compact zealot
Having trouble with another question lol
How did they find the SA=64=6x+2xh+12h using V=6xh?
I'm trying to logic it out, can't seem to figure it out
6x is because there are 6 sides I presume
worthy citrus
its just the surface area of a box with sides 6, x and h
worthy citrus
label the box in the picture with 6, x and h
find the area of each face in terms of those
worthy citrus
and the box has 5 faces because its open on the top
worthy citrus
yes
compact zealot
Thats also what confuses me
6x would be the 6 sizes
but the top is open?
So its just being considered in the volume
worthy citrus
6x is the area of the bottom face
compact zealot
6x for the base
2xh for the two longer sides
12h?
Because the front and back faces is 6*2?
worthy citrus
what the the side lengths of the front and back faces
worthy citrus
and
compact zealot
base length is 6
worthy citrus
so area of one of them is?
compact zealot
6h
worthy citrus
so two? 🙂
compact zealot
I guess I'm just confused as I felt it would be expressed differently
6h+6h
I guess its only 6h^2 if it was being multiplied
But in this instance its just the added area of all the sides
worthy citrus
yep exactly
compact zealot
Yep, small brain moment forgetting basic geometry, thank you!
worthy citrus
no worries:)
compact zealot
.close
bright nest
Anyone know how to do this
vocal sleetBOT
Anyone know how to do this
vocal sleetBOT
@bright nest Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
tepid jewel
Hey guys, if i change the interval to [-2,2] isnt the result will still be true?
lyric fossil
is the function defined on that interval?
tepid jewel
Yes, with imaginary
lyric fossil
do you know the definition of continuity over the complex numbers?
or were you just introduced to the definition for real valued functions
tepid jewel
Just introduced
And i'm kinda confused what if there is a hole in the middle of the function graph?
lyric fossil
Just introduced
i would go search up the definition of continuity over the complex numbers
lyric fossil
And i'm kinda confused what if there is a hole in the middle of the function gra...
i don't understand what you mean
royal mortar
i would go search up the definition of continuity over the complex numbers
well
just limit on complex number
$\forall \epsilon > 0 \exists \delta > 0 \forall |x-x_0| < \delta, |f(x)-f(x_0)| < \epsilon$
twin meteorBOT
1048576Prog
royal mortar
is a function is continious on $x_0$
twin meteorBOT
1048576Prog
tepid jewel
i don't understand what you mean
I mean what if the function at a/b is not defined
lyric fossil
I mean what if the function at a/b is not defined
what is a/b
royal mortar
oh maybe
tepid jewel
Random number, since if the function is continue at an interval it has to be defined for every number in the interval
royal mortar
like $\dfrac 1x on x \in \mathbb R$
twin meteorBOT
1048576Prog
royal mortar
right?
lyric fossil
are you asking if the function is continuous on the interval if it has a hole in the interval?
tepid jewel
Yes
hollow raptor
The proof shows that the limit is just f(a) for any a between -1 and 1, so it doesn't have any holes
lyric fossil
if you are undefined at a point, you cannot be continuous there
royal mortar
just follow the definition
tepid jewel
But if the interval is changed to [-2,2] than using same formula, it becomes true too(?)
tepid jewel
Yes related
hollow raptor
But if the interval is changed to [-2,2] than using same formula, it becomes tru...
No, you would need to change the function so it stays in the reals
tepid jewel
More like how the solution
royal mortar
But if the interval is changed to [-2,2] than using same formula, it becomes tru...
What you need to prove is only the limit rule is true on $\mathbf C$.
twin meteorBOT
1048576Prog
tepid jewel
No, you would need to change the function so it stays in the reals
So the function should be defined too?
lyric fossil
No, you would need to change the function so it stays in the reals
i think they've said they're assuming the function goes f:[-2,2] -> C
lyric fossil
What you need to prove is only the limit rule is true on $\mathbf C$.
\mathbb
royal mortar
and the proof based on limit rules doesn't need change,
tepid jewel
Yeah if i change the solution to -2<a<2 isnt it still the same
lyric fossil
Yeah if i change the solution to -2<a<2 isnt it still the same
basically yes
i would suggest you read about continuity on the complex numbers
and then reason out why it would still be continuous
tepid jewel
I havent learn about complex number
hollow raptor
That's beyond the exercise lol
royal mortar
$\textbf{Theorem.} \text{An elementary function is continuous over its domain of definition}$.
twin meteorBOT
1048576Prog
lyric fossil
That's beyond the exercise lol
they're asking the question
it's not beyond the scope of their question, and they've shown interest in the complex behavior
lyric fossil
I havent learn about complex number
i don't know what to say then. your function is not defined on the reals between -2 and 2
hollow raptor
Yeah, but you guys may be confusing them with something he hasn't learned yet
lyric fossil
they are the ones who brought in complex numbers
maximo: is the function defined on that interval?
Rise: Yes, with imaginary
tepid jewel
I only know about imaginary number
lyric fossil
1 - i is not an imaginary number
it is a complex number, it has a real part (1) and an imaginary part (-i)
if this is new to you, you won't have the tools to answer if the function is continuous from -2 to 2
hollow raptor
> maximo: is the function defined on that interval?
> Rise: Yes, with imaginary
That's why you can't use the larger interval, because then you need to use complex numbers
tepid jewel
So the formula from the solution only works for real numbers?
lyric fossil
the answer you should think as of right now is
"f(x) is not defined on the interval [-2, 2]"
well f(a) is not defined for all a in the interval
so it doesn't make sense to say f(a)
tepid jewel
Im confused
lyric fossil
what is f(2)
tepid jewel
If using graph there is none
twin meteorBOT
maximo
lyric fossil
is this a real number
tepid jewel
No
lyric fossil
then you can see how f(x) is not defined for all values between -2 and 2
there are some values that you can put in
that give you numbers that aren't real numbers
does that make sense so far?
tepid jewel
Yeah
lyric fossil
now for us to talk about continuity
we need to have the function be defined at the x value we want to analyze
so asking "is f(x) continuous at x = 2"
doesn't make sense, because f(2) is not defined (as we just saw)
that's the answer in relation to your question above
what is even more imporatnt is that if we change the domain to [-2, 2], then the function is not well defined at all
have you ever seen the notation
f : [-2,2] -> R
tepid jewel
No, i havent
lyric fossil
then never mind that notation
for a function to be good, well behaved, or well defined
we want it to give us a single number for every value we plug in
tepid jewel
So would the solution be better if i can show that it is defined on real numbers for the interval(?)
lyric fossil
i don't understand your question
tepid jewel
Like f(2) is not a real numbers
tepid jewel
Will it be better to show that in interval [-1,1], f(x) is defined in real numbers plane?
lyric fossil
i again don't quite understand your question
the important thing here is that f(x) is defined from -1 to 1
and if you plug in numbers outside of that
f(x) will give you numbers that are not real
so it's not defined for other numbers
for example, it's not defined for 2 or -2
tepid jewel
I mean 2 and -2 is not in the domain of f(x), so it doesnt continue there, so if i show first that f(x) domain exist at [-1,1] before proving its continue, will it be better? Or is it trivial for f(x) to be defined at [-1,1]?
lyric fossil
i see
in a general sense you'd need to show f(x) is defined on [-1,1] yes
but the question probably assumes you know that already
tepid jewel
Yeah, thats what i mean by hole before, what if the domain doesnt exist between -1 and 1
lyric fossil
(also, if you show the function is continuous on [-1,1] then it is certainly defined on the interval as well)
lyric fossil
Yeah, thats what i mean by hole before, what if the domain doesnt exist between ...
i see
the idea is that the proof assumes it is defined from -1 to 1
so a hole isn't in question
tepid jewel
Oh ok, i understand it better now, thanks a lot
tepid jewel
Dont mind it just adds up to my list to learn in the future
Ok thanks, gotta close this for others
.close
vocal sleetBOT
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midnight apex
Why is the first quartile 28 and not 27 (my TI calculated 28)
vocal sleetBOT
Why is the first quartile 28 and not 27 (my TI calculated 28)
midnight apex
I calculated 27 visually. The number of sample is 16. So 25% of the most left. Meaning 16, 23, 24, 27
So the first quartile is 27
sly sierra
i guess they're taking the midpoint of 27 and 29
since those are the 4th and 5th points
midnight apex
But that doesn't make it the first quartile then
sly sierra
similar to how if there's an even number of points, the median is the average of the two middle numbers
i'm not sure if that's the convention with quartiles as well
midnight apex
First quartile is also refered as "25th percentile"
Meaning by definition, all values are the same or less
Which makes sense for 27. I don't see that working for 28 though
sly sierra
well 25% of all values are also less than 28
outer warren
note that the median here splits your dataset in to two groups of 8
the first quartile will be the median of the first 8
sly sierra
yea that makes sense
midnight apex
wait, so in order to calculate the first quartile. I have to calculate in respect to the first 8 elements?
OH
Wait. So you're saying, since the median is 31.
We get the data
16 23 24 27 29 30 30 31
yeah no
I'm still confused.
outer warren
1 sec
16, 23, 24 , 27, 29, 30, 30, 31 | 31, 31, 31, 31, 31, 32, 32, 40
that's the median line of all your terms right?
midnight apex
yes
outer warren
the first quartile is the median of the first half, i.e. the median of
16, 23, 24 , 27, 29, 30, 30, 31
and for an even number of terms, you take the average of the two in the middle
midnight apex
wait wait wait, the first quartile is the median of the first half?
outer warren
yes
midnight apex
ok so whenever I'm calculating percentiles, I have to do it by first dividing the data set?
midnight apex
and for an even number of terms, you take the average of the two in the middle
so, it'll be 28
outer warren
yes
midnight apex
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vocal sleetBOT
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fading forum
Can you help me w this LU decomposition?
vocal sleetBOT
Can you help me w this LU decomposition?
twin meteorBOT
Ñøïr
fading forum
But none of the elements are -2
royal grove
vocal sleetBOT
royal grove
I was trying to prove it for all even n's first
this expression will have a factor of (n+1)
but how do i prove that it has a factor of n too
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autumn bear
Using double integrals, how do I start to find the volume of the solid bounded by the sphere x² + y² = 9, cylinder x² + y² = 4 and the hyperbolic paraboloid y² - x² = z?
vocal sleetBOT
Using double integrals, how do I start to find the volume of the solid bounded b...
@autumn bear Has your question been resolved?
empty frigate
...i don't think x^2 + y^2 = 9 is a sphere
jade oxide
why did the answer find x using dV^2/dx and not dV/dx
vocal sleetBOT
why did the answer find x using dV^2/dx and not dV/dx
errant briar
cursive fern
vocal sleetBOT
cursive fern
So I managed to get this far, but what is my function g(x)?
I need to take its partials but I don’t know the function
vocal sleetBOT
@cursive fern Has your question been resolved?
late sky
I’m having some difficulties with latex, I downloaded a png of a plot I made in python. Then I used the command \includegraohics{plot.png} but it gives an error saying no file found
vocal sleetBOT
I’m having some difficulties with latex, I downloaded a png of a plot I made in ...
vast shale
make sure the image is in the same folder as your tex file
paper depot
^
soft walrus
you can also change the path of the image (like the folder path)
late sky
How do I put both plots onto the same horizontal axis?
late sky
change their sizes
It only works when they’re super small
vast shale
(tho it would be easier to use subplots in matplotlib)
vast shale
It only works when they’re super small
can you send an image of what you have and what you want
late sky
I changed the width to 2.5cm
vast shale
use [width = .5 \linewidth]
late sky
What does this do? It comes up with an error
late sky
use `[width = .5 \linewidth]`
What does this do? It comes up with an error
late sky
What does this do? It comes up with an error
When I change the width to 4 or 5 cm it stacks the plots vertically which I don’t want
late sky
try textwidth then
It throws up an error, what am I doing wrong?
vast shale
dont put cm
vast shale
It throws up an error, what am I doing wrong?
put [width = .45 \textwidth] exactly
late sky
put `[width = .45 \textwidth]` exactly
It works now but still I don’t really like the size of the pictures, I tried it with width=.5 but it just goes back to stacking the plots below each one another
vast shale
what do you want then
late sky
You see how I have the grid option on
I ideally I want each plot on each side of the grid
vast shale
what does it look like rn?
late sky
put `[width = .45 \textwidth]` exactly
It’s better but still is leaving white space on the right side
Does this have to do with the size of the mini page?
vast shale
Does this have to do with the size of the mini page?
yes
also figures always look better in a centre
late sky
Yes I got rid of the mini page now
It looks better though I’m not sure if it’s centred, I can’t tell haha
vast shale
also figures always look better in a centre
.
\includegraphics....
\includegraphics....
\end{center}```Thanks!
vocal sleetBOT
@late sky Has your question been resolved?
analog pier
vocal sleetBOT
vast shale
what are you stuck on
analog pier
Should I do differntianon two times here?
analog pier
I just learnt the formulas now can u say me how to do it ?
This question was a weird one 😕
potent stirrup
@analog pier
analog pier
Yep
potent stirrup
Can you identify it as a composition of two functions?
analog pier
Ummm which two functions?
potent stirrup
think about it maybe?
shoot your guess
What do you know about composition of functions ?
analog pier
Just this
potent stirrup
I understood
potent stirrup
What do you know about composition of functions ?
^
analog pier
Umm I did not understand by the term "composition" and "function"
Like is that in my question
I just want to know the special chain rule before I go to bed
potent stirrup
Well
Its a composition of g(t)= t^2 and f(t)= 2t^2+4
The given function is g(f(t))
potent stirrup
chain rule is the method of differentiation for such functions
ie composition of functions are differentiated using Chain Rule
potent stirrup
Sure
analog pier
Maybe like this ??
potent stirrup
I’ll solve this
potent stirrup
Let me phrase what a chain rule is
Derivative of the outside function evaluated at the inside function times derivative of inside function
f’(x)= $2(2t^2+4)* (4t)$
twin meteorBOT
Dubleyou
potent stirrup
Notice, i identified the outer function as t^2, so it’s derivative it 2t, plug inside function into t
then multiply the derivatives of inside function
potent stirrup
If you are serious and want to know why chain rule looks like this
I can give you reading to develop intuition
It is sort of same as converting hours to second
pulsar scroll
vocal sleetBOT
pulsar scroll
a is obv 11!/2!2!2!
what do u get for part b
I split it into EXAM and INATION
8 total things
double repeats I and N
so 8!/2!2!
but mark scheme says I'm wrong
pulsar scroll
a is obv 11!/2!2!2!
what do u get for part b
I split it into EXAM and INATION
8 ...
apparently its not 8!/2!2!
over 11!/2!2!2!
lyric fossil
what is the question asking you for
pulsar scroll
what is the question asking you for
probability that EXAM appears in one of the arrangements
lyric fossil
right
and what does 8!/2!2! represent
is it a probability? or a number of combinations?
pulsar scroll
sry I wasn't clear, I meant to say apparently it's not 8!/2!2! over 11!/2!2!2!
lyric fossil
the issue is probably with the repeat A’s as well
pulsar scroll
I thought that wouldnt change anything tho
we are only moving around EXAM as a fixed block
and other letters
therefore the other A never comes into contact with that A in EXAM
right?
vocal sleetBOT
@pulsar scroll Has your question been resolved?
vocal sleetBOT
@pulsar scroll Has your question been resolved?
torpid knoll
therefore the other A never comes into contact with that A in EXAM
yes, that should work as now the entire block "exam" has to be together
which means before we had to find all arrangements of 'E','X','A','M','I','N','A','T','I','O','N'
now you have to find the # of arrangements of 'EXAM','I','N','A','T','I','O','N'
hopefully that helps a little
vocal sleetBOT
@pulsar scroll Has your question been resolved?
misty surge
vocal sleetBOT
misty surge
how do i go about solving this
do i add them all togther and make it one big fraction from there ot what?
pulsar scroll
I think it might be better to evaluate each term seperately
for the first term as n goes to infinity, what do you think the first term will tend towards
vast shale
^
misty surge
would it be 1?
vast shale
yes
misty surge
so would the 2nd one be 1 as well
vast shale
yes
misty surge
would that make my answer 2?
vast shale
well what is the last limit?
misty surge
1/3 but i thought if -1>r>1 and put to the power of infinity its 0
misty surge
omg thank you so much
cyan talon
do you know how to derive that formula ?
late current
well yeah i looked at the derivation but b4 i was just trying to come with it intuitively
did u understand what i did
late current
do you know how to derive that formula ?
like i know the dot product of 2 vectors simply give how much for example u is parallel to v, . and thats js a number cant i just multiply that by the unit vector of b
cyan talon
the thing is the dot prod also depends on the length of v
<u, v> = || u || || v || cos(theta) right
late current
the thing is the dot prod also depends on the length of v
yes i agree
late current
<u, v> = \|| u \|| \|| v \|| cos(theta) right
yes
cyan talon
now if you used the formula proj_v(u) = <u,v> v_hat
what happens if you scale up v by a factor of 2
your projection would also be scaled up
cyan talon
but like 2v is in the same direction as v
cyan talon
your projection should be the same
cyan talon
cheers
late current
.close
vocal sleetBOT
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Available help channel!
sour violet
The topic is evaluating functions I completely forgot how to work it
outer warren
simple substitution
substitute all x in the equation with 1,
(maintaining the order of operations)
night crown
help
flat whale
Draw a picture
indigo jay
to be more specific, draw three points: A, B, and C (the airport)
you should have a triangle, and you know two angles and one side length
flat whale
can u help me
Show your picture
vocal sleetBOT
@night crown Has your question been resolved?
wispy schooner
I have a question about these two questions. I was wondering how do I ser up the equations and for the graph how do find the vector equation and apply it to the t=-1?
vocal sleetBOT
I have a question about these two questions. I was wondering how do I ser up the...
@wispy schooner Has your question been resolved?
mild flower
derivative of a vector function is just the derivative of each component
wispy schooner
For which?
mild flower
for r'(t)
wispy schooner
So the equation for r’(t)=4,2t?
mild flower
you want to find equations that make r(0) = P and r(1) = Q
wispy schooner
you want to find equations that make **r**(0) = P and **r**(1) = Q
How do I set up that equation? Does it correlate to 3.5-1.8, .3+2.8, 2.1-2.1?
mild flower
well you'll need ts in there somewhere
do them one component at a time, so starting with x(t) = A + Bt -- you want x(0) = 3.5 and x(1) = 1.8
wispy schooner
do them one component at a time, so starting with x(t) = A + Bt -- you want x(0)...
So like (3.5+3.5-1.8) and continue on?
mild flower
you still need a t
wispy schooner
How would I start finding my t?
mild flower
that x(t) that I just posted with the A and the B? take that and figure out what values of A and B work
wispy schooner
With finding the t, I implemented the value for x(0)=3.5, x(1)=1.8, y(1)=-2.8, y(2)=.3, z(1)=2.1, z(2)=2.1, I just wanted to know what you meant by the equation, like which is A and B is that the x(0) and x(1)
mild flower
if you've already found the equations for x,y, and z then don't worry about the A and B. What are those equations you've found?
wispy schooner
It was the equation (x+(x2-x1)+(y+(y2-y1)+(z+(z2-z1) but i’m not sure if that’s right to use
mild flower
i think you've made some kind of transcription error there; let's go through how to get the formula for x(t) together
we know x(t) is going to look like x(t) = A + B*t, where A and B are just numbers (we don't know what those numbers are yet), and we know we want x(0) = 3.5 and x(1) = 1.8, because we want our x-component to start at 3.5 and go linearly to 1.8, does that make sense?
wispy schooner
Yes, kinda, are you saying it’s a linear formula but solely for the t?
mild flower
yes x(t) will be linear in t, it will look like the equation of a line but with t as the input variable and x as the output variable
wispy schooner
Is it possible you can provide an example?
twin meteorBOT
kitten.in.a.teacup
wispy schooner
Oh, so subtracting it
mild flower
sort of? let's plug t=0 and t=1 into our formula, remember we want x(0) = 3.5 and x(1) = 1.8
starting with $x(t) = A + Bt$, we get $x(0) = A + B*0 = A$
twin meteorBOT
kitten.in.a.teacup
mild flower
and we want x(0) to also equal 3.5, so we can see that A = 3.5
wispy schooner
Oh ok, i see that
mild flower
now we can do a similar thing with x(1), can you do that and figure out what B should be?
mild flower
go ahead and write out the equation like I did
start with x(t) = A + Bt and substitute in t=1
wispy schooner
3.5+1.8(1)=5.3 (unless it is still 3.5 because of the sub being 3.5)
mild flower
A is 3.5 yes, but we don't know B yet
starting with $x(t) = A + Bt$, we get $x(1) = A + B*1 = A+B$ and remember we wanted $x(1) = 1.8$ as well
twin meteorBOT
kitten.in.a.teacup
wispy schooner
3.5+b*1=1.8
wispy schooner
B=1.8/3.5
mild flower
division is incorrect here, 3.5 is being added not multiplied
mild flower
yep so now we can write the equation of x(t) using the actual numbers we just found instead of A and B
wispy schooner
So every number is going to be like that for the equation?
mild flower
yeah you'll get three of these equations, one for each of x, y, and z
it'll always be A = [something] and A+B = [something] though so you'll get pretty fast at it
we deliberately chose to work with t=0 and t=1 for that reason
wispy schooner
Ooh okay
So that means for this problem, we solved for 3.5 and 1.8, for -2.8 and .3, we do -2.8+b*2=.3
mild flower
where'd you get the *2 from?
wispy schooner
Because its the next value from the number
Like x(0)=3.5
I thought that the 2 is because -2.8 is *x2
mild flower
x(t) is done, dusted, we don't need to mess with it again; we're starting a brand new thing called y(t) with two new points y(0) = -2.8 and y(1) = 0.3
wispy schooner
Oh ok, so it’s the same as before, -2.8+y*1=.3
mild flower
yeah
mild flower
and the same will be true for z(t) although that one will have a neat property
wispy schooner
That would be 4.2 for z
mild flower
no it wouldn't
mild flower
actually can you write the equation for x(t) for me? like x(t) = ____ + ____t
wispy schooner
2.1+z*1=2.1
mild flower
So B equals to -1.7
let's back up to here
we're back on x(t) now, forget about y and z
we started with $x(t) = A + Bt$ and then we spent a bunch of time computing values for A and B, remember?
twin meteorBOT
kitten.in.a.teacup
wispy schooner
Yes
mild flower
so now we can substitute those values into that equation to get $x(t) = 3.5 - 1.7t$
twin meteorBOT
kitten.in.a.teacup
mild flower
so we write that down and do a similar thing for y(t) -- starting with y(0) = ___ and y(1) = ___
if it makes it easier you could say y(t) = C + Dt so that we're not reusing A and B
wispy schooner
Is the C and Dt the new values for y?
mild flower
i mean yes, but we don't know what C and D are yet; we have to figure them out using the points we're given
we know that $y(0) = -2.8$ and $y(1) = 0.3$
twin meteorBOT
kitten.in.a.teacup
mild flower
yep, z(t) = E + Ft and you'll compute numbers for E and F
wispy schooner
Y(0=2.1 and y(1)=2.1
mild flower
those are z
wispy schooner
Oh z, i mean