Oh yeah
#help-0
haughty fiber
next brook
(Correction to above: "thousands of constraints" is perhaps not exactly a small problem, now that I look up the state of the art ...)
haughty fiber
So I'm not crazy right Time and Shirts are the only constraints?
YEAH I THINK WE HAVE ALL THE CONSTRAINTS
WOOOOOOO
@next brook Ur da best
@next brook I'm getting an error
next brook
You might be supposed to write 0 <= a, a <= 50 instead of 0 <= a <= 50.
Or possibly leave out the Z = in the objective function.
It's not a very informative error message ...
next brook
Perhaps it wants e.g. 20*b instead of 20b. Otherwise I got nuthin.
haughty fiber
@next brook
Here's the format they had before
Idk what the _ is
oh maybe it wants
x_1 x_2
instead of a b
next brook
Looks like it wants trailing commas in all but the last box, too
next brook
Sorry.
next brook
Oh, it probably wants <= rather than =<.
next brook
Yeah, you had =< for some of the inequalities where it expects <=.
haughty fiber
LOL god I can't believe I messed that up
thanks so much dude I really appreciate all the help
you are a life saver
tacit arch
.close
lone heartBOT
alpine sable
Is it alright to say that there's a linear relationship between the degree of bernstein polynomials and their accuracy as they converge uniformly to f(x)?
alpine sable
Because it kinda means that the accuracy approaches 0 at a steady rate, so =linear rate?
Cause to me if $\varepsilon\to0$ uniformly, the the graph of $\varepsilon$ would be a straight decreasing line, no?
ocean sealBOT
Etienne
alpine sable
<@&286206848099549185>
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@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
junior panther
.open
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silent owl
How do i show the sequence is upper bound by 1
lone heartBOT
How do i show the sequence is upper bound by 1
silent owl
I have a_1 and a_2 which 13/16 and a_3 is something like 923/1045 and we are supposed to do it by hand so im kinda shying away from a_3
marsh rapids
you can prove it by induction
silent owl
how would i go about doing that
marsh rapids
do you know how proofs by induction work ?
silent owl
kinda but im very bad at them
marsh rapids
you already have the base case. You just need to show the actual induction property, i.e. if a_n <= 1, then a(n+1) <= 1
silent owl
then i would have to insert a_n+1 into the sequence right?
marsh rapids
you don't "insert", what would that mean ?
you prove that if for any n, a_n <= 1, then a_(n+1) <= 1. Then according to the principle of induction, this allows to conclude that a_n <= 1 for all n
silent owl
and i honestly have no idea how to do that besides using showing that 1/2<13/16
marsh rapids
actually think abstractly, use the only thing you know about a(n+1) that's linked to a_n. Don't limit yourself to the first values, proofs by example aren't proofs
silent owl
the only thing that is linking them that i can see is that they are both parts of the sequence
marsh rapids
use the definition of the sequence to prove it
silent owl
you want me to use the sequence to prove its limited by 1?
marsh rapids
yes
there are only 2 things you know : a_n <= 1 and a_(n+1) = (a_n² + 3)/4, so use them both
do you understand what you're trying to prove ?
and how this is approached/handled ?
silent owl
the only thing i can see, is using 1/2 to show that i get 13/16 but ive already done that and i feel like that would'nt suffice
marsh rapids
the only thing i can see, is using 1/2 to show that i get 13/16 but ive already ...
Congratulations, you proved the property for the first 2 natural numbers. Can you prove it the same way for all remaining integers ?
have you ever done a proof ?
silent owl
honestly ive avoided them like the plague most of the time
marsh rapids
why pursue math if you're not into proofs ? You're gonna eat them for years in a math career
silent owl
im not pursuing maths tho its a cs degree
marsh rapids
undergrad ?
silent owl
ye
marsh rapids
gotta work on these math skills though. I don't see how you'd do anything algorithmic if you can't understand how a sequence works
like recursive algorithms or even loops
silent owl
i am working on it tho
marsh rapids
how about we get back to that sequence ?
silent owl
that would be great
silent owl
i think i may do im looking at an example
marsh rapids
so you don't
otherwise you'd be confident
let's take a simpler example. Let a_0 = 0, a_(n+1) = a_n + 1. Can you show that for any n, a_n = n ?
silent owl
not really and im way to tired to continue tbh
thanks for the help ill read up on induction and try again tomorrow
.close
stark ravine
lone heartBOT
stark ravine
How would you solve this
Can someone show me something last time a
I waited a whole day with no reply and some one just closed my question without replying
lone heartBOT
@stark ravine Has your question been resolved?
kind pelican
Help, I'm sufferin in hell, does this ex have an answer?
lone heartBOT
Help, I'm sufferin in hell, does this ex have an answer?
kind pelican
<@&286206848099549185>
merry depot
Help, I'm sufferin in hell, does this ex have an answer?
what have you tried?
kind pelican
what have you tried?
everything
merry depot
have you set up the radius of each circle intersecting with that line segment?
merry depot
kind pelican
yes but I don't have enough information to find r
merry depot
you don't need to find r. You need to find the area
can you relate r and R together with an equation?
merry depot
yes but I don't have enough information to find r
hang on. starting over. You want to find the area of the red space. Can you write a formula for that area in terms of the radii r and R?
kind pelican
hang on. starting over. You want to find the area of the red space. Can you writ...
I'm genuinely confused
merry depot
I'm genuinely confused
If the larger radius is R, what is the area of the big circle?
kind pelican
If the larger radius is R, what is the area of the big circle?
I have no idea
merry depot
do you know the formula for area of a circle?
lone heartBOT
@kind pelican Has your question been resolved?
alpine sable
why does f(x) = x / x - 1 not have an extreme value on the interval [0, 5]
last ether
Because between those values lies no critical point
Basically where f'(x) ≠ 0 when x ε [0, 5]
alpine sable
how do u know when f' = 0?
cinder sorrel
how do u know when f' = 0?
Can you work out the derivative if x/x+1?
alpine sable
not sure tbh
cinder sorrel
Use the Quotient rule
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
idk what differentiation is
@still storm
we were learning aobut
completing the squares
and quadratical formula
and factoring
then she pulls up some big ass numbers like 1000
like where do you get that from
still storm
ok, so do you know how to completing the squares of this P(x)?
factorising it into the form of P(x)=±(x±a)*(x±b)
still storm
so P(x) is just the function of x, it is like y = x....., where in this case y is replaced by another function P
alpine sable
Alr
still storm
you can factorise P(x) into some square form for this question
still storm
@alpine sable P(x) = (2x-5)^2 if you completing the square.
open folio
Vertex?
-b/2a = x coordinate of the vertex
Since they are just asking about the about of items (x) then we only care about the x coordinate of the vertex
Which will be the maximum point on the parabola since it has a negative coefficient
open folio
I told you what you are looking for
...
Quit pinging all helpers
The maximum y point is the VERTEX, which the x coordinate is found using the formula -b/2a from the form ax^2 + bx + c
lone heartBOT
@alpine sable Has your question been resolved?
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@alpine sable Has your question been resolved?
copper thicket
you want to find the maximum of the given function,
derivative of the given function is -8x + 16
let this equal 0 for the vertex of the parabola
or as its a multi choice question just plug x = 1, 2, 3, 4 respectively into the equation and see which one is biggest
@alpine sable does that help?
copper thicket
the function given tells u the profit, for a given number of items x
hence plug in a value of x to get the profit
stark ravine
.reopen
native temple
helo
there we go
uhh
how do I solve this
I tried to use polar coornates
but solving for are didn't work
my x coordanate I found was 6
since 4 + 2 6
y was 8
since 5 + 3 = 8
grim delta
I tried to use polar coornates
youre working too hard
im pretty sure you can just solve it using basic trig
hell even pythagorean
native temple
youre working too hard
im pretty sure you can just solve it using basic trig
no I can't the x
isn't a right triangle
grim delta
you can make a bigger right triangle
with x as one of the sides
you have all of the side lengths you need to do that
grim delta
you have to combine some of the sides you are given
native temple
now how do I use polar coords
I did and I didn't get the point where the triangle was
when they said 5
grim delta
now how do I use polar coords
guarantee you you dont need that
native temple
norht did they mean north east
because 5 in the graph isn't a straight line
it's tited
sorry norht west
and not perfect north is techinically north west
grim delta
it's tited
it looks sketchy but according to the drawing its also a right angle
native temple
if it's like that
grim delta
and theres a right angle under it
native temple
so it's north then
grim delta
so it should technically be straight up
native temple
5+3 is 8
2+3 is 5
wait or my messed up
og my gosh
I got this
(r, 45
where I got 45 from is
alpine sable
.
native temple
the constant implication of north east
compass heading
N 90 degrees
east uhh 0
middle is 45
the direction the mouse headed is 45
does this make sense
native temple
I don't
alpine sable
is 2.20810850013585409e+17 220,810,850,013,585,409 as a decimal notation
grim delta
i think the drawing is throwing you off
because its weirdly drawn and not straight
but look at whats written
the two triangles are right, and the angle between them is also right
youve got the bottoms and sides of both
just combine them to make an a and a b and then find c
pythagorean theorem
$a^2 + b^2 = c^2$
ocean sealBOT
Dogecode
native temple
$$r = \frac{x}{cos(\theta)}$$
ocean sealBOT
Nerdy_Coder
native temple
come one texit
yes
x is 6
right
cos 45
that should be the anser yet it's wrong
so which part of the equation is wrong
grim delta
$\sqrt{(3+2)^2 + (5+4)^2} = \text{?}$
ocean sealBOT
Dogecode
native temple
$\sqrt{(3+2)^2 + (5+4)^2} = \text{?}$
wait that makes no sense
as they are 2 different right triangles
and also what was wron gwith my solution
what was wrong
where did I mess up
the answer I got was
$$r = \frac{5}{cos(\pi\div4)}$$
ocean sealBOT
Nerdy_Coder
grim delta
cos 45
the angle isnt necessarily 45
thats assuming you go an equal amount east and an equal amount north
which the mouse did not
native temple
okay
so I need to determine the angle then
wait
$$\sqrt{(5-4)^2+(2-3)^2} = distance$$
ocean sealBOT
Nerdy_Coder
grim delta
**Dogecode**
i literally already told you how to solve it
this is the drawing if it was drawn by a person who can draw correctly and wasnt trying to confuse you with their math problem 
β could and would be a 180 degree angle.
lone heartBOT
@native temple Has your question been resolved?
fickle lotus
lone heartBOT
fickle lotus
can someone please help me again?
short cobalt
Assuming your eq is good you can just plug 10 into t
Since t is number of years after 2015 and it is asking for a year 10 years after 2015.
somber hare
Is there a name for a relation between two semigroups A and B, with some g : A -> B -> B? I'm looking for a generalization of a vector space or a module.
oak perch
Can you show me the original text about this? Where you see this thing
somber hare
Can you show me the original text about this? Where you see this thing
I'm writing a program, and I want to name something, I'll fetch what I've written
data Errable p f a = Unqualified a
| Partial p a
| Fail f
instance Functor (Errable p f) where
map g (Unqualified a) = Unqualified (g a)
map g (Partial p a) = Partial p (g a)
map g (Fail f) = Fail f
instance Applicative (Errable p f) where
pure = Unqualified
fa <$> Unqualified g = map g fa
Unqualified a <$> Partial p g = Partial p (g a)
Partial p a <$> Partial q g = Partial (p <> q) (g a)
Fail f <$> Partial p g = Fail (scale p f)
I haven't finished it
But on the last line scale is the kind of morphism I'm talking about
Here, I have two different error types p and f
oak perch
So it’s a programming problem… I thought it was a math problem…
somber hare
Well, yeah it's a math problem. I'm asking if this structure has a name
oak perch
I see, someone else might help
last tendon
Do you mean AxB, not sure why the map would look like that
somber hare
Do you mean AxB, not sure why the map would look like that
Ah, that's currying. Yeah A×B -> B is isomorphic to that
somber hare
I don't know any R, but maybe
Basically g : A -> B -> B, then g a : B -> B (g called on a), and g a b : B (g called on a called on b), which is basically the same as starting with g : (A, B) -> B, and calling g (a, b)
There are utility functions uncurry : (a -> b -> c) -> (a, b) -> c and curry : ((a, b) -> c) -> a -> b -> c to go back and forth, should you need to.
last tendon
I believe this is just called an S-Act, which is short for semigroup action, but I kind of hate that name personally. Formally a (left or right) S-act maps AxB -> A or B by the action (a,b) -> ab. It also needs to satisfy an associativity property.
somber hare
I believe this is just called an S-Act, which is short for semigroup action, but...
Yeah...well that's much closer than anything I've found, and some name is better than no name. Thanks!
last tendon
I've never really been that interested in abstract algebra though so I'm not really the right person to talk to. I use a bit of it because some of the Calculus I use forms a normed semigroup, and I know a bit from linear algebra but that's about the extent of my interest
somber hare
I tried to ask in #category-theory , but apparently I can't send messages there. I figured that would've probably been the place though
last tendon
You can try flipping through here and see if it's defined in it, the pdf isn't well made for searching
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Available help channel!
oblique jewel
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oblique jewel
i know how to find <DBE but not knowing how to find DEF and AFC
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oblique jewel
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oblique jewel
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wicked wing
Just set up an arbitrary equilateral triangle with the following requirements and find the respective areas 💀
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obsidian forge
hybrid tinsel
you're welcome
oblique jewel
.close
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sonic cave
Not quite sure how to get the values using the exponential smoothing factor, any tips would be appreciated
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sonic cave
<@&286206848099549185>
Anyone?
The formula is: Fn+1 = Fn+ α(An–Fn)= αAn+ (1 –α) Fn
Ft+1 = αAt+(1- α)Ft
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tawny fable
Hi tehre
tawny fable
I need some help with a question in calculus
I need to compute this integral or prove that it doesnt converge
now
that is my process
idk how to continue from here
shadow tangle
are you familiar with gamma function?
shadow tangle
the function used to define the factorials of integers
nvm that, found another way
instead of using t=2x-1, use t^2=2x-1
from there you can substitute for t and then use integral by-parts
lone heartBOT
@tawny fable Has your question been resolved?
tawny fable
instead of using t=2x-1, use t^2=2x-1
from there you can substitute for t and th...
You got that right?
I get dt = -1/2sqrt(2x-1)
oh
then it dissapeares
oh wait
shadow tangle
See, taking t^2=2x-1
we get after differentiation, 2 t dt=2 dx
tawny fable
it doesnt
shadow tangle
then put value of dx in the new integral
shadow tangle
yeah exactly
lone heartBOT
@tawny fable Has your question been resolved?
tawny fable
yeah exactly
sorry for the delay
shadow tangle
idk how to continue from here
are you not familiar with integrals of products of two functions?
shadow tangle
sorry for the delay
issokay
lone heartBOT
@tawny fable Has your question been resolved?
tawny fable
It’s 1/e^t isn’t it?
solemn grove
yeh, like can you integrate (t^2)*(e^t)
yeah
lone heartBOT
@tawny fable Has your question been resolved?
lone heartBOT
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Available help channel!
solemn estuary
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solemn estuary
hi, thought i could just row reduce
fuck nvm
forgot to row reduce the 1
think i got it
.close
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Available help channel!
thin urchin
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thin urchin
-2/27 does not seem to be the correct critical number. But I've done this 3 times and got the same answer
drifting hull
how did you get -2/27?
thin urchin
i already found the critical number for when the numerator is zero so to find when the deritvative is undefined I have (3x^2 +1)^2 = 0
but now I am realizing that maybe 9x^4 + 6x^2 + 1 is not compatible with the quadratic formula
drifting hull
i already found the critical number for when the numerator is zero so to find wh...
you need to find values for which the numerator of the derivative is 0, right? So what is the derivative?
thin urchin
the derivative is (-1+x)/(3x^2 +1)^2
drifting hull
no
thin urchin
oh
(-3x^2-1)-(-x)(3x^2+1) is what I have for the numerator
which I thought would simplify to -1+ x
drifting hull
@thin urchin the quotient rule yields a numerator of (-1)(3x^2+1)-(-x)(6x)
split kraken
Suppose a spaceship is traveling through space on a path along a line given by x =
1 + t, y = 3 −4t, z = t + 1. Suppose there is a planet located at the point (5, 6, 1)
(assume for simplicity the planet is just a point and so has zero radius). What is the
shortest distance the spaceship will reach from this planet?
tacit arch
Suppose a spaceship is traveling through space on a path along a line given by x...
come up with a distance formula from point to line and then minimize it
equivalently, minimize the distance squared to make algebra easier
tacit arch
have you taken calculus?
tacit arch
yes minimum is a type of extrema
split kraken
come up with a distance formula from point to line and then minimize it
hm how would i come up with said distance formula
i apologize in advance for my lack of knowledge related to this question, because i was not taught about it properl
hello?
blissful temple
For a given time t, what is the distance between the spaceship and the planet?
split kraken
no clue
blissful temple
What do you know about the distance between two arbitrary vectors?
blissful temple
Ok, just apply it to the position of the spaceship and the planet
wary orbit
We're given x = 1 + t, y = 3 - 4t, z = t + 1 and a point (5, 6, 1)
I don't know what to do with this information to find the shortest distance
blissful temple
Write down the distance for some fixed time t first
wary orbit
I honestly don't know how to do that
My professor gave us these problems but we've never learned these equations
blissful temple
Well, it's just Pythagorean theorem
alpine sable
sqrt(x^2 + y^2 + z^2)?
blissful temple
Yes
alpine sable
Idk I think I saw it in the fast inverse sqrt video
wary orbit
so sqrt((1+t))^2 + (3-4t)^2 + (t+1)^2) and then what do I do from here
split kraken
@blissful temple
wary orbit
Sorry
wary orbit
It would be - 5 , -6, -1 right
blissful temple
We are interested in the distance, so you plug in the difference for x, y, z
split kraken
sqrt((1+t-5))^2 + (3-4t-6)^2 + (t+1)^2-1)
correct?
then we would find the minima?
minimum
wary orbit
How would we minimize that then?
split kraken
calc, 2nd derivative?
blissful temple
Now you have the distance as a function of the time
split kraken
yessir
blissful temple
You can compute the minimum of this function
split kraken
how exactly
wary orbit
Sorry how do I get the minimum of the function?
blissful temple
You consider its derivative
As mentioned before, you can also consider the derivative of the squared distance to make things easier
blissful temple
Yes (leave out sqrt to make it easier)
wary orbit
So nothing changes even if I leave out the square root?
blissful temple
Correct
wary orbit
Since it's asking for minimum distance, what is the format of the answer going to be?
blissful temple
The minimum distance
split kraken
its gonna be in units right
blissful temple
Solve for t to find out the time when the spaceship is gonna be closest to the planet
Since you already wrote down the distance as a function of the time, you can just plug in the value for t into the formula to get the minimum distance
split kraken
Solve for t to find out the time when the spaceship is gonna be closest to the p...
how exactly?
wary orbit
Is it fine if I verify my answer with you if you give me like 5 minutes
blissful temple
how exactly?
Find critical points of the distance function by differentiating it
A local extremum point x satisfies f'(x) = 0
blissful temple
-16/36 = t
Correct, now what is the minimum distance?
blissful temple
Yes
split kraken
so the minimum distance would be...
wary orbit
I got square root of 193 / 3
blissful temple
You mean sqrt(193)/3, right?
wary orbit
Yes sorry
blissful temple
That would be correct
blissful temple
Glad I could help
waxen arch
How would you do the 2nd part (ii) as I’m not too sure, is it sum of roots?
fervent timber
I think so
waxen arch
Do u know how to solve it?
Because the roots I got was pi/9 4pi/9 7pi/9
<@&286206848099549185>
fervent timber
Because the roots I got was pi/9 4pi/9 7pi/9
how did you get this?
fervent timber
and x = tan theta right?
fervent timber
hmm
well -tan(2π/9) is equal to tan(-2π/9)
maybe you have to use -2π/9 as one of the roots?
waxen arch
But I don’t know how to get that lol
fervent timber
how to get the sum?
waxen arch
No the root -2pi/9
fervent timber
how did you get the other roots?
fervent timber
hmm
well you can go the other way right
so 3 theta = -2π/3
and theta = -2π/9
also tan(-2π/9) = tan(7π/9) so they are the same root
since you can add π without changing the value
waxen arch
Oh ok, so how would u answer part ii tho like what do they mean by evaluate
fervent timber
I found this which is pretty interesting
so the sum of the roots of ax^3+bx^2+cx+d=0 is just -b/a
and since you are basically summing the 3 roots
you can just plug in b and a into -b/a
fervent timber
b=-3sqrt(3) and a=1
covert ferry
keep in mind the roots are tan(pi/9), -tan(2pi/9) and tan(4pi/9)
fervent timber
so -b/a is 3sqrt(3)
waxen arch
How do I evaluate that tho?
covert ferry
simplify as much as you can
fervent timber
I think evaluate just means to find the answer
I'm not sure if there's an alternative way, without knowing the sum of the roots of a cubic formula
because I didn't know about that formula before looking it up haha
covert ferry
what's the coefficient of pi in this second line
waxen arch
12
covert ferry
tangent doesn't distribute over addition, so you cannot add the angles together like that
fervent timber
you can't add tangents like that
yeah
I think the first line is the answer right
waxen arch
Yeh I thought so
fervent timber
just put tan(-2π/9) instead of tan(7π/9)
fervent timber
no problem!
waxen arch
Do I need to close this chat now?
swift shore
If you’re all set then yeah
waxen arch
Yep I’m all good
swift shore
Do .close
lone heartBOT
swift shore
Np
lone heartBOT
Available help channel!
median mauve
lone heartBOT
alpine sable
is ur topic geometry
median mauve
this is in review question
floral cairn
lone heartBOT
floral cairn
I know the question already have been solve, I just need work
wary stream
Find the volume of the coin
thorny bough
I know the question already have been solve, I just need work
get the formula for calculating a cylinder's volume
then multiply by density
wary stream
Then apply the density formula
thorny bough
tada
wary stream
Well, did you convert mm to cm first?
wary stream
Then that's the problem
wary stream
Or you can convert the measurements to cm first then find the volume
wary stream
Not exactly
floral cairn
convert your mm to cm
Do I multiply by 10?
floral cairn
So divide by 10
thorny bough
yh
wary stream
Yes
wary stream
convert your mm to cm
I literally stated this. You don't have to repeat what I said before
floral cairn
3.857
thorny bough
I literally stated this. You don't have to repeat what I said before
My bad, missed yours
floral cairn
Do I multiply that by 10.5?
wary stream
Yes
wary stream
But that is In gram
Yes, because the density is given in g/cm
floral cairn
Got it
Thanks
I have a helper doing this problem before
He’s clearly smarter than I am which cause difficulties when teaching me
I’m glad you guys understood my level
@wary stream @thorny bough I got one more problem
Can you guys help?
floral cairn
I need side but they give me idk if it radius
How do you find the area of a pentagon without side
wary stream
You can find the side by applying trig
floral cairn
I found
36 as inside angle
The blue arc equals 72
And the rest of the angle are 54
Green is 36
Yes?
wary stream
You have the radius and angle, find the side of that triangle
wary stream
Then multiply by 2 to get the side of the pentagon
floral cairn
Wait
Is it soh cah toa?
Cause isn’t that to find the acute angle
My brain have been fried, I couldn’t remember
wary stream
You use soh cah toa to find the side
ocean sealBOT
Fourfirehydra
wary stream
Not exactly tangent
floral cairn
Opposite over adjacent
wary stream
The radius of the pentagon is the hyp of the triangle
wary stream
I missed that, my bad
floral cairn
So I was right?
wary stream
Yes
wary stream
Find the side of the triangle
floral cairn
I just do tanger of 36 then multiply by 4?
wary stream
Yes
wary stream
Yes
wary stream
As what?
wary stream
Sure
wary stream
Does it show you the answer?
floral cairn
No
I can submit the homework and it’ll show me the answer
But that just cheating plus I need work to get credit
wary stream
What did you get as the side length?
wary stream
Then that's your problem
floral cairn
Should I not round?
wary stream
You round at the very end
ocean sealBOT
Result:
-20.523514680066
I did simply tang of 36
floral cairn
How do you know it radian?
wary stream
Because online calculator defaults to radians
floral cairn
Oh
I got 5.812340224 as side length
I simply put 5.8 and 6 as side and height in a volume calculator
wary stream
And as I stated, you round at the very end of the problem
floral cairn
Should I put in the whole number in the calculator?
wary stream
Yes
floral cairn
348.74 is the new answer
wary stream
And notice how the answer before, you were off by 1.5
floral cairn
Yeah
I hope this is correct
Imma summit the homework
Dang
Wrong again
By a lot
218.0
wary stream
I think I see now, the issue was it was tricking you with the 6 cm, by that's the height of the entire box, it mentions 1cm thick sides
wary stream
This one is tricky so I'm not too sure
next void
How can I solve this question to get the correct answer which is 22? I don't know what I need to do. I tried solving it and got it wrong.
last ether
Dear god the handwriting uh
last ether
You can't really guarantee something
7 days in a week
You need 4 people
You can have like 928493938494949494 people but some might never be born on Tuesday
What I'm thinking is this
Let's say you gather people each born on the days, so in a group of 7 you have a guy born on Sunday, a guy born on Monday, etc
With this, 3 groups of these 7 people will have 3 people born on each day
And then add another Sunday guy and now you have at least 4 people born on Sunday
Which is 21 + 1 = 22
lone heartBOT
@next void Has your question been resolved?
next void
thank you very much. Sorry about the bad handwritting.
I am not sure how to say the question is resolved
lone heartBOT
@next void Has your question been resolved?
placid wharf
lone heartBOT
placid wharf
why does this have no solution according to the solutions
last ether
Factor it
buoyant kayak
no real solutions
placid wharf
wdym?
buoyant kayak
i'd check the discriminant first
placid wharf
i havent done that stuff yet
i was just doing wuestions in texxtbooks above my grade
buoyant kayak
do you know what an imaginary number is?
placid wharf
no
placid wharf
but why when i completed the sqaure i still got an answer
like y = 1/2 +/- root - 7/4
buoyant kayak
you'll get an answer... it's not a real answer
placid wharf
oh ig ill learn it later
buoyant kayak
you cannot take the square root of a negative number and get a real answer
that's where imaginary numbers come into play
$i=\sqrt{-1}$
ocean sealBOT
a disappointing son
buoyant kayak
if you'd like to learn imaginary numbers, the introduction to them isn't really all that bad
so at your level you shouldn't have trouble with watching an intro youtube video on them or something
(if you want to know more, that is)
hexed magnet
Trying to take the definition of the shear transformation matrix as shown here and apply it to my transformation matrix with which I have already applied scale and rotation
hexed magnet
And then to confirm my results I'm checking it against skimage's affine transformation function... but can't seem to get the shearing right
Have the array here
np.array((
(c*1/.8, -s, 256),
(s*, c*1/.4, -256),
(0, 0, 1)
))```
Should be operations of rotation (`c` and `s` are sin and cos of the angle respectively), translation of 256, -256, and scale of .8, .4
Seems to work okay except I can't seem to figure out how to properly apply shear such that I get results equivalent with the affine transformation function.
`skimage.transform.AffineTransform(rotation=np.pi / 8, translation=(256, -256), scale=(1/0.8, 1/0.4), shear=np.pi / 6)`
Any pointers would be appreciated@hexed magnet Has your question been resolved?
cunning trout
How do I find the area of this base, I know it’s a triangle but I can’t identify the base and the height
cunning trout
Also I don’t know where the right angle even is here
naive valley
can you paste a screenshot without the red highlighting?
cunning trout
placid zinc
Or Heron's if you're crazy
placid zinc
The base is 10 what?
I just pointed out the side lengths of the base, that's all I know so far haha
cunning trout
Ok lol
I’m having the problem only with the base area
Like how would I find that
placid zinc
Can you get an angle in the base?
Once you do, you then have a height of the triangle, and can do A = 0.5bh
cunning trout
How though?
placid zinc
How to get an angle in a triangle with all sides known? Cosine law.
cunning trout
Ok
dusty flare
why would getting an angle get you a height?
vale wigeon
@placid zinc @cunning trout the base is an isosceles triangle 
no need to calculate any angles
cunning trout
Ok
Ok I got this
Can I get help with this question, thanks
So area of trapezium: A =1/2(a+b)h
But I don’t exactly know what to do with this
vale wigeon
no wonder, because this question gives insufficient info
first off, it's a little unclear if they mean reducing the area a hundredfold, or just taking off 1% from it
second, it's unclear whether the shape that remains afterward is a trapezoid at all, let alone what its sides are
cunning trout
Yh that’s true
vale wigeon
third, even if it is a trapezoid, there are many different ways you could reduce its area by 1% (or to 1% of the original), and those will give different side lengths
you're not being put at gunpoint to solve this particular problem, are you?
vale wigeon
yes
lone heartBOT
lone heartBOT
Available help channel!
light tusk
How do you get this?
lone heartBOT
How do you get this?
rare verge
alpine sable
Your boss asks you to find the cheapest way to link San Francisco (SF) with Dallas with fiber optic cable via Reno, Salt Lake City (SLC), and then Denver. There are 20 different companies that offer links from SF to Reno, 15 that offer links from Reno to SLC, and 30 that offer links from SLC to Dallas. How many distinct ways are there to link the cities. (A distinct way to link the cities is determined by the companies providing the links. You may assume all 65 companies are different.)
alpine sable
Can someone help please <@&286206848099549185>
it is permutation stuff
I got 9000 but idk if i am correct
covert ferry
looks right to me
covert ferry
20*15*30
alpine sable
ok thx I think i get it
covert ferry
np
alpine sable
.close
lone heartBOT
lone heartBOT
Available help channel!
haughty holly
does anyone know how to do this?
lone heartBOT
does anyone know how to do this?
tight locust
Please don't occupy multiple help channels.
lone heartBOT
@haughty holly Has your question been resolved?
haughty holly
<@906108821871689779> Has your question been resolved?
yeah
rich kestrel
react to the check when or use .close
use the fact that the interior angle sum of a triangle is 180 (looks like ur problem is resolved already tho)
split vector
a farmer picks 83 oranges and places them in barrels according to their size: small, medium, large and extra large. Find the value of x if at least one barrel has at least x oranges
lone heartBOT
a farmer picks 83 oranges and places them in barrels according to their size: sm...
@split vector Has your question been resolved?
lone heartBOT
lone heartBOT
@zinc cosmos Has your question been resolved?
lone heartBOT
@zinc cosmos Has your question been resolved?
lone heartBOT
@zinc cosmos Has your question been resolved?
lone rain
seems like combinations only
rotund plank
You’re asking people to read all of that, you should probably be more specific with parts of it
stiff hornet
What reasons r there an exponential growth model might not be realistic
rotund plank
What reasons r there an exponential growth model might not be realistic
You can often tie it specifically to the problem
stiff hornet
I’ll show u the problem
rotund plank
For example, for an increasing graph, say for population, it is unrealistic for the graph to grow indefinitely at increasing rate
Okay
stiff hornet
rotund plank
Lmao would you look at that
Yeah so my above reason stands since it’s population
It depends on infinite resources which is an unrealistic assumption
stiff hornet
Ok thanks
stiff hornet
It also assumes ceteris paribus
True
rotund plank
So like, there could be a war, natural disaster, people could move away, or it could grow faster than predicted for whatever reason
It’s usually good to look at the extreme for a reason for it being unrealistic, and then just making a general comment about basically any model like the ceteris paribus one
stiff hornet
Ok thanks mate
Could u check if my other working for the questions is correct?
Nm I think it’s fine
rotund plank
Yeah sure
Generally you should open another help channel
But you can still tag me
rotund plank
How do you find the normal to a curve?
stiff hornet
Negative reciprocal
rotund plank
Negative reciprocal of what?
stiff hornet
Gradient
rotund plank
Gradient of?
stiff hornet
Isn’t that my second line of working
rotund plank
Oh I didn’t see you actually had working I just read the question mb
stiff hornet
All good lol
rotund plank
Yeah you can but it’s probably easier to find the gradient of the curve, and then take the negative reciprocal
No reason to write $-\frac{1}{8x-6}$
stiff hornet
Oh
ocean sealBOT
dk.dkn
stiff hornet
So what would I do now?
rotund plank
What is the gradient of the curve at P?
stiff hornet
8x-6
rotund plank
You can do what you were saying btw that’s fine, this is just easier
Yes but specifically at P
That’s in general
stiff hornet
0.5
rotund plank
If an exam question asked you what the normal to a curve is, would you answer ‘negative reciprocal’?
Imagine I know nothing about normals
stiff hornet
I’d say the normal is the line that intercepts the original line at 90’
It is purpendicular
stiff hornet
It’s is y= 0.5x +c
ocean sealBOT
dk.dkn
rotund plank
Probably better
stiff hornet
C=1.75
rotund plank
Show me all the working you’re doing
stiff hornet
