Yes
#help-13
west dome
west dome
👍
west dome
Sure
midnight owl
kk gimme a sec
west dome
Ping me when you have itt
midnight owl
@west dome problem #3
I think I may have messed up on dz/dy
Shouldn't it be -2x+1 instead of 0?
west dome
At least write $\partial$ instead of d
wraith daggerBOT
Migillope
west dome
I get not typing it, but this is simply incorrect
You’ve actually messed up on all of them
dire geode
$\pa$
wraith daggerBOT
riemann
midnight owl
2x
wraith daggerBOT
Migillope
west dome
No
midnight owl
2xy
west dome
No
midnight owl
oh wait I need to use the chain rule don't I
wraith daggerBOT
Migillope
dire geode
Is this a package or base? That’s a nice shortcut
pinged you in #latex-testing
midnight owl
ah so 2y
west dome
Exactly
midnight owl
kk sec I'll redo with the correct notation
ignore the stuff above I'll redo that part
obv if I have the equations right I can plug in the numbers so didn't od that part
west dome
Yep
cedar kilnBOT
cedar kilnBOT
Available help channel!
safe yew
Hello how I do integral to (2x +1)/ root (x^2 +x-2)
cedar kilnBOT
Hello how I do integral to (2x +1)/ root (x^2 +x-2)
glad kestrel
what integration techniques have you learned
safe yew
What I know is I can do 2x+1 * (x^2+x-2)^-0.5
glad kestrel
wat
cosmic steppe
Hello how I do integral to (2x +1)/ root (x^2 +x-2)
Rhymes with Rule, starts with Quotient
safe yew
Now like this I guess ?
glad kestrel
Rhymes with Rule, starts with Quotient
??
cosmic steppe
Oh wait
safe yew
xd
glad kestrel
2x+1 is the derivative
you're sort of on the right track here... but i'm not sure you're 100% getting it
do you know of u substitution?
cosmic steppe
Hello how I do integral to (2x +1)/ root (x^2 +x-2)
Use u-sub
cosmic steppe
safe yew
But idk there some complicated stuff
safe yew
😅
cosmic steppe
But idk there some complicated stuff
Not really
Essentially you're changing the stuff you're integrating
It's like
safe yew
The complicated stuff is that I’m not that good at English xd
cosmic steppe
Oh I see
safe yew
Don’t understand the whole thingy
cosmic steppe
Yeah then it might be tough
pulsar chasm
Whats the best way to find the nth term?
cosmic steppe
Whats the best way to find the nth term?
What's the best way to read #❓how-to-get-help?
safe yew
xd
pulsar chasm
What's the best way to read <#488120190538743810>?
Idk was the first discord group
safe yew
Ok listen I watched some videos about sub u
cosmic steppe
Hint: this is not your help channel
cosmic steppe
Ok listen I watched some videos about sub u
Well you have $x^2 - x -2$ inside the square root right?
safe yew
With root or without ?
wraith daggerBOT
Umbraleviathan
safe yew
Yes
cosmic steppe
So set u = that
safe yew
With root
cosmic steppe
And take the derivative of both sides
safe yew
Why no xd
safe yew
Du/dx = u
cosmic steppe
You usually integrate arguments
safe yew
Just don't
Ok xd
cosmic steppe
So $u = x^2 - x - 2$
wraith daggerBOT
Umbraleviathan
cosmic steppe
Which means that
safe yew
Du/dx= 2x+1
cosmic steppe
$du = (2x + 1)dx$
safe yew
Yup
cosmic steppe
And notice how your function has a 2x-1 on the numerator
And that there is a dx at the end of the integral
safe yew
It’s +1 xd
safe yew
**Umbraleviathan**
And here + x
wraith daggerBOT
Umbraleviathan
safe yew
Yup
safe yew
So dx = du/ 2x+1
cosmic steppe
So you get $\int \frac{1}{\sqrt{u}} du$
wraith daggerBOT
Umbraleviathan
safe yew
Wait xd
cosmic steppe
Because the (2x + 1)dx got replaced by "du"
safe yew
How ?
cosmic steppe
The x^2 + x - 2 inside the square root was replaced by u
safe yew
Ah
cosmic steppe
But remember
After you find the antiderivative, PLUG THE STUFF BACK INTO U
Don't forget to do that
I gtg
safe yew
What xd ?
Ok cya xd
I’ll try to understand what happen and how I can complete that ;-;
Ok so
Idk how to complete after that I guess ;-;
Like what to do xd
<@&286206848099549185> sry but the guy who was helping me gtg xd
safe yew
Uhh
Ok lemme watch it rq
Oh damn first time I see math YT channel and have 5M subs xd
Here when he did integral u^3 became u^4/4
What happen to the du ?
I still don’t understand the sub u way
safe yew
**Umbraleviathan**
What I do with that ?
glad kestrel
that is the power rule of integration
...
you might want to start from the beginning
safe yew
I think I do
Listen
Since the 2x+1 is the derivative of x^2 +x-2 so the integral is 2 * root x^2 +x -2
Someone solving my question said that ;-;
glad kestrel
no
glad kestrel
no
glad kestrel
i have no idea what you want
if you don't want to learn integration, don't try integration problems
safe yew
I want xd
Ok I’ll try to understand how he did it or go understand how sub u work
Thx btw
.close
hidden sundial
whats the difference between a strong and weak skew to the right
is a weak skew to the right more varied, or less varied than a strong skew?
cedar kilnBOT
@hidden sundial Has your question been resolved?
hidden sundial
<@&286206848099549185> please someone
45 minutes now its a very simple question
whats the difference between a strong and weak skew to the right
is a weak skew to the right more varied, or less varied than a strong skew?
kindred storm
@hidden sundial That sounds like a statistics problem. If you don't get help here, try #probability-statistics or, if it's beyond the first course or two, #advanced-probability, which can be unlocked in #get-advanced-access.
hidden sundial
ok
cedar kilnBOT
@hidden sundial Has your question been resolved?
cedar kilnBOT
Available help channel!
cold briar
cedar kilnBOT
stiff zenith
i dont understand this
expand $(x+\frac {b}{2a})^2$
cold briar
a^2 + 2ab + b^2
wraith daggerBOT
Sus
cold briar
$a^2 + 2ab + b^2$
stiff zenith
they have done the reverse actually
wraith daggerBOT
MarveI
dusty hazel
yeah
stiff zenith
$(a+b)^2=a^2+b^2+2ab$
wraith daggerBOT
Sus
stiff zenith
here b/a is the 2ab
cold briar
oh ok i get it
stiff zenith
(b/2a)^2 is b^2
cold briar
and $b/a = 2(b/2a)$
wraith daggerBOT
MarveI
wraith daggerBOT
MarveI
valid bolt
We have $x_1(t) = 1$ and $x_2(t) = t^{\frac{1}{2}}$
cedar kilnBOT
We have $x_1(t) = 1$ and $x_2(t) = t^{\frac{1}{2}}$
wraith daggerBOT
Zim
valid bolt
They are linearly independent
When you take the wronskian, it gives us $w[x_1, x_2]=\frac{1}{2} t^{-\frac{1}{2}}$
According to the principle of superposition, $x = Ax_1(t) + Bx_2(t)$
wraith daggerBOT
Zim
valid bolt
Where x is the general solution
But this isn't the case for the differential equation I have...
And I have no idea why
Is is possibly because $x_1(t)$ is a constant?
valid bolt
Guys, I'm kinda going crazy. Cuz $x_1(t) = 1$ and $x_2(t) = t^{\frac{1}{2}}$ are a fundamental solution set, as they're linearly independent... So why isn't $x = A + Bt^{\frac{1}{2}}$ not the general solution? infact, it's not a solution at all... 😭
wraith daggerBOT
Zim
valid bolt
cerulean star
Please provide the complete problem statement.
dire geode
what ^ said
valid bolt
Ok
I have a theory, but would also like to know what you guys think
(Also, I have no answers from this. It's from a midterm archive with no solutions.) :^(
dire geode
this is why it's important to state the context of the whole problem first
you don't even have a linear ODE
the "results from class" is probably about second order linear differential equations
cedar kilnBOT
@valid bolt Has your question been resolved?
valid bolt
you don't even have a linear ODE
wallahi I still don't understand the relevance of this
I beg you enlighten me
The principle of superposition says we can combine two linearly independent solutions to form a general solution, but it doesn't say anything about the ODE's linearity
cedar kilnBOT
cedar kilnBOT
Available help channel!
craggy anchor
to factorise this expression i find 2 numbers and form groups but how do i find those 2 numbers
craggy anchor
is it just trial and error
cedar kilnBOT
@craggy anchor Has your question been resolved?
crimson sedge
try using the quadratic formula to factorise
like assume a as a variable and b as a constant and use the formula for roots
and then its factorized
cedar kilnBOT
@craggy anchor Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
languid sky
.open
cedar kilnBOT
cosmic steppe
$147 = x^2 + 4xh$
wraith daggerBOT
Umbraleviathan
wraith daggerBOT
Umbraleviathan
cosmic steppe
And leave it as that
Yeah
Np
I can't really do it in my head rn, I'm on a golf course lol
Just check using desmos
v(x) = whatever
And then do v'(x) and it'll automatically compute
And compare v'(x) to your V' to see if they're the same
obtuse basin
How do I solve parts A and B?
obtuse basin
<@&286206848099549185>
obtuse basin
I figured out part b!
If exactly 6 one's is 13C6, then at least 10 is 13C10 + 13C11 + 13C12 + 13C13
And for at least one, the inverse would be at most 0
But there's only one option that has all 0's
So we subtract the total amount of options, right?
But how do you calculate the total amount of options?
Each bit has 2 states, so wouldn't be 2**13 - 1?
Book says that is correct
But now moving on to these...
Erm...
55 isn't right for part A either
Oh wait, it's 45
I forgot to shift down by 1
I got this answer by simplifying the example down to 4 points
The first dot connects to 3 points
The second dot only connects to 2
The third connects to just one
And the last dot is already all connected
So the amount of straight lines determined by n points is just n - 1 + n - 2 + ... + 0
But now for checking how many of them pass through point A or have triangles?
loud anchor
a more meaningful and abstract question would be to ask for a combinatorical explanation for the identity $$\binom{n+1}{k+1} = \binom{n}{k} + \binom{n}{k+1}.$$
obtuse basin
Pfft
wraith daggerBOT
vin100
loud anchor
with this identity and part (a), you'd be able to solve part (b) with $n = 9$ and $k = 1$.
wraith daggerBOT
vin100
obtuse basin
Wait, why is that?
loud anchor
normal add. maths teacher/question writers would ask to you do prove this by induction.
but that's, IMHO, not a real induction problem
the inductive proof logically establishes its validity
obtuse basin
I'm confused
loud anchor
but that's not quite educational from my personal viewpoihnt
the combinatorical meaning of $\binom{n}{k}$ is "n choose k"
wraith daggerBOT
vin100
loud anchor
we have a new comer
in our combinatorical explantion, we don't need factorial
one min plz
i needa draw $\LaTeX$ figure
wraith daggerBOT
vin100
loud anchor
,,\underbrace{\underbrace{\square\cdots\square}{n \text{ objects}} \quad \underbrace{a}{\text{new object}}}_{n+1 \text{ objects}}
wraith daggerBOT
vin100
\begin{gather*}
\underbrace{\underbrace{\square\cdots\square}_{n \text{ objects}} \quad \underbrace{a}_{\text{new object}}}_{n+1 \text{ objects}}
\end{gather*}
loud anchor
oups typo
,,\underbrace{\underbrace{\square\cdots\square}{n \text{ objects}} \quad \underbrace{\Large\circ}{\text{new object}}}_{n+1 \text{ objects}}
wraith daggerBOT
vin100
crimson sedge
What this.
loud anchor
trying to explain a basic combinatorical identity $$\binom{n+1}{k+1} = \binom{n}{k} + \binom{n}{k+1}.$$
wraith daggerBOT
vin100
crimson sedge
Oh ok
loud anchor
LHS = no. of ways to choose k+1 objects from n+1 objects
obtuse basin
Hmmmmmmmm
reef venture
**vin100**
we could also prove this using the pascals triangle
loud anchor
term 1: new object circle not selected, so we select k objects from remaining n objects
term 2 : new object circle not selected
so we select k+1 objects from remaining n objects
these two cases cover all possibilities, so QEED
loud anchor
we could also prove this using the pascals triangle
that in line with what double felix thinks of the binom coeff: a fraction of factorials. that's numerical way to view this. combined with basic arithmetic operations, we get an algebraic proof for this. however, IMHO, that's less educational than the combinatorical explanation that i've just given.
obtuse basin
I don't see how that applies to this problem
I'm trying to find this formula in my book
loud anchor
suppose that you hav the solution for part (a)
obtuse basin
45
loud anchor
treat point $A$ as a "new comer"
wraith daggerBOT
vin100
loud anchor
you're trying to choose 2 points from the remaining 9 points
so you apply this formula with $n = 9$ and $k =1$
wraith daggerBOT
vin100
loud anchor
9C1 = 9 you dun needa caltor to do this
so 9C2 = 10C2-9C1
the first term is in part (a), the 2nd term is trivial
just substraction
no multiplication involveed
so it's slightly simpler to do
obtuse basin
Wait why do I need to choose 2 from the remaining 9?
Oh
2 points to make the line
9 points to choose from
loud anchor
the arithmetic operations are a bit simpler to do
2 points to make the line
that's in Euclid's Elements
obtuse basin
So I have 10C2 as the total number of lines
Which is 45
And then I subtract all the lines that are made with that one point
Which is 9C1
And for triangles, it's the same application but with 3 points chosen
loud anchor
books help you to understand principles, but you dun need a book if you've already got that
obtuse basin
So 10C3 is for triangles
And without A that's uhhh..
10C3 - 9C3?
Wait no
9C2?
loud anchor
yes, provided that no three points are collinear
obtuse basin
Okay, now I do choose but order matters
No repetition
Hey wait a minute
Book says to use P(n,r) if order matters, and tall parenthesis n / r if it doesn't
But it also says that P(n,r) is notation for that tall parenthesis thing
loud anchor
gimme one min to type out a simple case
obtuse basin
Oh wait
loud anchor
suppose that you hav to arrange {A,A,B,C}
i start from a simple case
then you generalise
loud anchor
here you've repetitions
obtuse basin
Oh I do
loud anchor
so you needa divide by some factorials
(A,A,B,C) and (A,A,B,C) "spells the same": AABC
so you needa divide it by 2!: 4!/2!
obtuse basin
So the factorial of the amount of elements divided by the factorial of the amount of elements that are equivalent
So MILLIMICRON
We have 3 I's, 2 L's, and 2 M's
So 39916800 possible combos
Divided by 3! divided by 2! divided by 2!?
Or 554400
That's not right
wraith daggerBOT
Result:
1.6632e+6
,calc 101
wraith daggerBOT
Result:
101
,calc 10!
wraith daggerBOT
Result:
3.6288e+6
What is 3!22?
loud anchor
i typed =calc 11!/(3!*2*2)
loud anchor
Book says to use P(n,r) if order matters, and tall parenthesis n / r if it doesn't
Your book puzzles me
loud anchor
just draw digrams to see
loud anchor
for me i dun even need a book
obtuse basin
I get it now
So 3! accounts for the options where the I's are in different spots
But we don't care if they're in different spots
And the 2 2! accounts for M and L
So now for this
It's the same procedure except it's just 9! / 3! * 2!
Right?
loud anchor
,,\underbrace{\underbrace{\square\cdots\square}{r \text{ chosen objects}} \quad \underbrace{\circ\cdots\circ}{n - r \text{ not chosen objects}}}_{n \text{ objects}}
wraith daggerBOT
vin100
obtuse basin
I don't get what this means
loud anchor
you can derive the numerical value of $nCr$ and $nPr$ from the basics
wraith daggerBOT
vin100
loud anchor
for combinations, arrangement doesn't matter, so you take $n!$ permutations
wraith daggerBOT
vin100
loud anchor
in the group of $n - r$ unchosen objects, their permutation doesn't matter, so you divide $n!$ by $(n-r)!$
wraith daggerBOT
vin100
loud anchor
the same goes on for the group of $r$ objects
wraith daggerBOT
vin100
loud anchor
so you have $$\binom{n}{r} = \frac{n!}{r! (n-r)!}.$$
wraith daggerBOT
vin100
loud anchor
for permutations, the permutation of the $r$ chosen objects matter, so you have
$$nPr = \frac{n!}{(n-r)!}$$
wraith daggerBOT
vin100
loud anchor
hope that helps you develop confidence in these two basic tools, so that the next time you need them you dun needa go chk ur book
obtuse basin
So then 9! / 3! * 2! should be right
Oh wait you need those parenthesis
That was my issue
It's 9! / (3! * 2!)
Why do they give different answers?
Order of operations for multiplication and division shouldn't matter
lyric jungle
in the group of $n - r$ unchosen objects, their permutation doesn't matter, so y...
I think this idea is better understood as simply choosing r objects from n things, so for your first choice you have n things to choose from, then n-1, then n-2... and lastly n-r+1 for a total of n(n-1)(n-2)...(n-r+1). This mathematically is the same as n!/(n-r)!
lyric jungle
(And to add, you remove the repetitions when you divide by r!)
obtuse basin
So P(n, r) gets the amount of ways you can take r objects from n with no replacement
lyric jungle
I think this idea is better understood as simply choosing r objects from n thing...
This is for nCr
obtuse basin
And you use nCr to do the same with replacement
loud anchor
I think this idea is better understood as simply choosing r objects from n thing...
that's easier to imagine for $nPr$ alone. i'm thinking about a general illustration (say, in double felix's problem with identical items).
wraith daggerBOT
vin100
loud anchor
more precisely, the use of \underbrace{...}_{...} for a more general situation
lyric jungle
that's easier to imagine for $nPr$ alone. i'm thinking about a general illustra...
And nCr! Since if you have r things, and order doesn't matter, then you have r! ways to rearrange those r objects. So you divide by r! to count an assortment only once.
lyric jungle
And you use `nCr` to do the same with replacement
I prefer to think of nCr as the number of ways to pick r things from n objects discounting order. While nPr is the number of ways you can do the same thing but including order.
obtuse basin
So those parenthesis is nCr, right?
wraith daggerBOT
castroploiin
obtuse basin
Yeah those
wraith daggerBOT
castroploiin
obtuse basin
Cool
I never thought I'd find combinations as confusing as inductive proofs
Man, I really don't like math
I just want to finish this course so I can be done
loud anchor
that's why i'm drawing figures
lyric jungle
that's why i'm drawing figures
This especially helps with realizing why Pascal's identity works
loud anchor
to capture the essential conditions with a minimum of words
i'm finding a way to draw/illustrate things that kill two birds with one stone
lyric jungle
I never thought I'd find combinations as confusing as inductive proofs
Induction isn't too bad. It's just a way of saying, "okay, I have this thing which I assume only works up to this limit. If I can prove it works for one plus that limit then I prove it for all cases since the limit can be anything."
loud anchor
to illustrate the value of using diagrams, try a a less well-known but useful and simple problem: "n choose k with repetition allowed.
obtuse basin
Then do nCr except substituite n with r + n - 1
loud anchor
Induction isn't too bad. It's just a way of saying, "okay, I have this thing whi...
it depends on who does the inductive thinking. if the question asker simply spoonfeeds the general terms, then in most cases, that's not real induction. that is, the inductive step doesn't provide novel arguments, and the proposition itself can be proved from well-known arguments without explicitly invoking induction. in that case, IMHO, i find inductive not so educational
you know stars and bars that's great
lyric jungle
it depends on who does the inductive thinking. if the question asker simply spo...
I do agree in that induction tends not to be preferable over other well known methods of proofs.
obtuse basin
So now I got this
In this case, CR act as one letter
And so ON
So it's the same calculation as the first one but with 2 less letters
so 9! / (6 * 2 * 2)
15120?
Problem says yes.
loud anchor
I do agree in that induction tends not to be preferable over other well known me...
with one single exception: sum of cubes = square of sum
obtuse basin
I tried that too
That's just 21 which wasn't right
Oh wait
So for the first element, you have 7 choices
Then 6 choices, then 5, all the way down to 3 choices
Then you stop because you have 5 elements
So it's just 7 * 6 * 5 * 4 * 3
obtuse basin
What does that notation mean
lyric jungle
Permutations
obtuse basin
nPr(7,5)?
wraith daggerBOT
castroploiin
obtuse basin
Oh
I see
I just didn't know what the extra symbols mean
So it's just 7P5
Oh I see
lyric jungle
Is your answer right?
obtuse basin
Yup!
🎉
2 problems left
This is just more of the same
Let me try this on my own
I got A
So there are 60C5 total ways to get a shipment
But 57C5 ways to get 5 non-defective chips
So it's 76%
Oh
Oh there we go
At least one chip is just total number of shipments minus the amount of shipments with no defects
And no defects is 57C5
Almost done!
An odd number + odd number = even
even + even = even
So it's only even if the parity of the chosen numbers are the same
So say we pick 2 as our first number
Then there are floor(101 / 2) other options to pick
So shouldn't it just be 100?
If we pick 1, then the other options are 3, 5, 7, ..., 101
Oh wait, it'd only be 98
That's not right either?
Let me try to rethink this
There are 51 odd numbers
And 50 even numbers
OHHH
And since they need to be either even or odd
Then we just pick 2 from each pool
And add them together
So 2500
Okay, final problem
What did I do wrong here?
loud anchor
it was in fact next to my laptp
obtuse basin
lol
loud anchor
silly me
wraith daggerBOT
vin100
loud anchor
but we have two chosen groups
obtuse basin
This illustration confuses me quite a bit tbh
loud anchor
sorry to spoonfeed you this
but i needa go out breath some fresh air
,,\underbrace{\underbrace{\square\cdots\square}{r_1 \text{ chosen objects}} \quad \underbrace{\triangle\cdots\triangle}{r_2 \text{ chosen objects}} \quad \underbrace{\circ\cdots\circ}{n - r_1 - r_2 \text{ not chosen objects}}}{n \text{ objects}}\
wraith daggerBOT
vin100
wraith daggerBOT
vin100
loud anchor
so permutations of mices without the same grp doesn't count
from this you easily see that the ans is indeed a multinomial coeff
,,\begin{pmatrix} n \ r_1, r_2 \end{pmatrix}
wraith daggerBOT
vin100
obtuse basin
I am not smart enough for this
I was just trying to write it out in terms of this formula they gave me
loud anchor
,,\begin{pmatrix} n \ r_1, r_2 \end{pmatrix} = \frac{n!}{r_1! r_2! (n-r_1-r_2)!}
wraith daggerBOT
vin100
obtuse basin
Oh
I got the problem wrong anyway
I just don't get it
Why am I in college
I hate math
loud anchor
obtuse basin
Thank you for your help
Sorry I'm so stupid
@lyric jungle Thank you as well
It's a good thing I'm done with this class soon because then I can stop torturing people with my stupidity
Sorry :/
.close
fiery flare
There is store that sells chocolate in an ask. The cashier knows how much the ask costs so he only weights the chocolate.
Oscar ask: 3,4 hg for 176 kr
Hannah ask:2,2 hg for 110 kr
A) How much does the chocolate cost per hg?
B) how much weights the empty ask
sinful geyser
What does hg and kr stand for
fiery flare
What does hg and kr stand for
Hg=Hectogram
Kr is Swedish money
fiery flare
Lol if you don't understand hg then use it as kg
glass oasis
hg is not the problem
fiery flare
What's the problem then
sinful geyser
What is 3,4 hg.
fiery flare
Listen
glass oasis
like a decimal?
fiery flare
Oscar bought 3,4 hg chocolate for 176 kr
sinful geyser
3 chocolates 4 hg's right?
glass oasis
is 3,4 a decimal?
sinful geyser
Damn
glass oasis
that's what we wanted to know
fiery flare
3 chocolates 4 hg's right?
No the weight of the chocolate is 3,4 hg
fiery flare
176/3,4 is wrong
Cause 3,4 is the weight of the chocolate and ask
Lol
Sorry for the misunderstanding
fiery flare
Cause 3,4 is the weight of the chocolate and ask
And we want the answer for only chocolate
fiery flare
Let the weight of ask be something.
Wdym
fiery flare
Yea but how do we get value of the ask
fiery flare
I don't understand lol
fiery flare
Yes
dusty hazel
Let's say the ask costs x.
So
Cost of ask + cost of 3.4hg = 176kr
Cost of ask + cost of 2.4hg = 110kr
Right?
fiery flare
No
sinful geyser
What is "cost of ask"
fiery flare
We don't know
sinful geyser
Waterdrop, what is the refference material of the question?
fiery flare
I swear idk lol
sinful geyser
Where did you get the question from?
fiery flare
Where did you get the question from?
It's an old exam question
dusty hazel
They probably used translator.
sinful geyser
I assume
sinful geyser
It's an old exam question
Is it written in Swedish?
fiery flare
Is it written in Swedish?
Yea
fiery flare
Omg sorry I thought they used ask in English as well
sinful geyser
You might have used a translator, and the translation is pretty bad
fiery flare
Anyways it means box
fiery flare
You might have used a translator, and the translation is pretty bad
Lmao I am the translator
dusty hazel
Anyways it means box
THAT IS WHAT I SAID
sinful geyser
Let's try it again
dusty hazel
sinful geyser
Hey waterdrop
fiery flare
Hoi
sinful geyser
Do you have the question with you?
fiery flare
Yea
fiery flare
Okay
sinful geyser
I'll try using google lens
fiery flare
sinful geyser
Little more clearer?
sinful geyser
Ok
dusty hazel
yeah, for real, haha.
fiery flare
And then?
sinful geyser
It is x+demanded weight
fiery flare
Huh
loud anchor
loud anchor
already solved
fiery flare
How
wraith daggerBOT
vin100
loud anchor
in reality just plot the data points (obtained from experiments) on a graph then do linear regression
fiery flare
Huh
loud anchor
i'm really not talking about this question but what reality shld b
fiery flare
I never used a graf calculator
So I don't i should use a graf calculator for this question
loud anchor
in theory, the price is a dependent variable. as hillbill mentioned, one part of that is constant (weight of the ask), and the other part is proportional to the weight
$$P = k + qw$$
wraith daggerBOT
vin100
fiery flare
I don't understand a shit
loud anchor
you've learnt Variation & Proportion ?
fiery flare
Is that with statistics?
loud anchor
i dun think so.
loud anchor
nvm understanding the concept is much more important than solving problems
fiery flare
Ok so what shall I do
loud anchor
We say that $y$ is directly proportional to $x$ if there's a constant $k$ such that $y = kx$. We denote this as $y \propto x$.
wraith daggerBOT
vin100
loud anchor
Let $P$ be the total price
wraith daggerBOT
vin100
loud anchor
$k$ be the cost of an empty ask.
wraith daggerBOT
vin100
fiery flare
Ok
loud anchor
$w$ be the weight of the chocolate taken by a customer
wraith daggerBOT
vin100
fiery flare
K
loud anchor
the more the chocolate taken, the higher the price
fiery flare
Yes ofc
loud anchor
so we would expect one part of the price to be directly proportional to the weight, and we use a fixed constant $q$ to represent that
wraith daggerBOT
vin100
loud anchor
so we get $$P = k + qw$$
wraith daggerBOT
vin100
loud anchor
on a ruff work sheet you might try drawing a data table for understanding, but that's optional
fiery flare
What's qw
loud anchor
here $w$ is the independent variable
wraith daggerBOT
vin100
loud anchor
$q$ times $w$
wraith daggerBOT
vin100
fiery flare
Ik but what is q
loud anchor
we're gonna set up a system of equations to find that out.
,,\begin{array}{c|c}
w & P \ \hline
0,8 & 33 \
1,6 & 77 \
2,2 & 110 \
3,4 & 176
\end{array}
wraith daggerBOT
vin100
fiery flare
Yea and then?
loud anchor
in reality you can input the data into the linear regression mode of your scientific calculator, and it would calculate the slope and the $y$-intercept of the best fit line
wraith daggerBOT
vin100
loud anchor
in this question, we learn from Steve Jobs
connect the dots
then calculate the slopes
wraith daggerBOT
fiery flare
It's not a homework
wraith daggerBOT
loud anchor
what's linear?
something related to a line
but that's irrelevant to the so-called solution to this idealistic question with correlation coefficient $r = 1$.
wraith daggerBOT
vin100
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fiery flare
I'm just 15 how can I know linear
loud anchor
fiery flare
Aren't there any other solutions
wraith daggerBOT
Result:
55
you do the rest
fiery flare
,calc (77-33)/(1.6-0.8)
Why did you do that
loud anchor
to calculate slopes
fiery flare
What do you mean with slope
loud anchor
we're trying to find the "best-fit line"
fiery flare
we're trying to find the "best-fit line"
And what's that
loud anchor
oops sorry i jumped too quick
actually the graph with data points is what i immediately visualize
fiery flare
What in the hell is this
fiery flare
How do we get the valur of the box
loud anchor
which box?
fiery flare
Box of chocolate
loud anchor
i'm explaining
fiery flare
The weight
loud anchor
our model is $$P = k + qw$$
wraith daggerBOT
vin100
loud anchor
$w$ is the weight of the chocolate
wraith daggerBOT
vin100
wraith daggerBOT
vin100
wraith daggerBOT
vin100
loud anchor
we're given some data points $(w_1,P_1), \dots$
wraith daggerBOT
vin100
loud anchor
and we're asked to find $k$ and $q$
wraith daggerBOT
vin100
loud anchor
$k$ is the weight of the ask, and $q$ is a coefficient of $w$ that partly determines the total price $P$.
wraith daggerBOT
vin100
loud anchor
you have
dep var = const + coeff * indep var
that's the form of a straight line
the coeff is the slope of the straight line
and the const is the $y$-intercept
wraith daggerBOT
vin100
fiery flare
Cant you explain on 9th grade solution?
loud anchor
Cant you explain on 9th grade solution?
finding the slope of a straight line in the Cartesian coordinate system should be in the 9th grade curriculum
http://www.ciclt.net/ul/negaresa/CoordAlgSW61.JPG
fiery flare
What the
loud anchor
on the left column 2nd circle it reads "use distance formula, slope"
p..s when i was in form 3 (equiv. to 9th grade), i already self-learnt everything in high sch calculus and linear algebra
fiery flare
Idk dude
loud anchor
my geography teacher saw me calculating integrals and he exclamed that that's the math that he didn't know
so sor9y i have a poor idea abt what's in the curriculum
nvm i'm here to explain concepts
fiery flare
I don't understand the concepts bro
wraith daggerBOT
vin100
loud anchor
$P$ takes the role of $y$
wraith daggerBOT
vin100
loud anchor
(dependent variable)
$m$ is the slope, and $b$ is the $y$-intercept (the value of $y$ when you substitute $x = 0$).
wraith daggerBOT
vin100
loud anchor
in textbooks you usually see $$y = mx + b$$
wraith daggerBOT
vin100
loud anchor
in your question it becomes $$P = k + qw,$$ but the form is the same
wraith daggerBOT
vin100
cedar kilnBOT
@fiery flare Has your question been resolved?
loud anchor
sor9y needa cook 4 dinner c u later
fiery flare
Ok
cedar kilnBOT
@fiery flare Has your question been resolved?
cedar kilnBOT
@fiery flare Has your question been resolved?
loud anchor
why not solved?
you just find out the slope $q$ by $$\frac{P_2-P_1}{w_2-w_1},$$ that's a short cut of
$$\begin{cases} k + qw_1 &= P_1 \ k + qw_2 &= P_2. \end{cases}$$
wraith daggerBOT
vin100
fiery flare
I don't understand what you mean
loud anchor
what do you don't understand?
fiery flare
Slope
cedar kilnBOT
@fiery flare Has your question been resolved?
loud anchor
.reopen
lethal veldt
Yo I would like to solve for Energy Vs. Time
cedar kilnBOT
Yo I would like to solve for Energy Vs. Time
lethal veldt
So Im not sure how to make an equation that would put these variables together neatly.
The goal is to tell after X amount of seconds what the laser energy is at. The max energy is clamped to the variable "Beam Energy" and can not go above it.
The best I got so far is the equation
End Energy = (( Beam Energy - ( Beam Energy * Energy % Per Shot)) + Recharge Rate)
This equation only covers the scenario " after 1 Shot worth of time" so the goal is to make it work on an sequential basis Like
EndEnergy1 --(1 Second)--> EndEnergy2 --(2 Second)--> EndEnergy3 and So on.
Help with this would be greatly appreciated, Thanks!
cedar kilnBOT
@lethal veldt Has your question been resolved?
cedar kilnBOT
@lethal veldt Has your question been resolved?
cedar kilnBOT
@lethal veldt Has your question been resolved?
jade cosmos
hi
proud spindle
Hi, does anybody have any experience with excel?
cedar kilnBOT
Hi, does anybody have any experience with excel?
@proud spindle Has your question been resolved?
dire geode
Hi, does anybody have any experience with excel?
Not really a software server. I'd just Google excel plus your question
crimson sedge
Hi
crimson sedge
cedar kilnBOT
@crimson sedge Has your question been resolved?
bold hinge
@crimson sedge is each term some constant factor times the previous one?
proven marlin
i'm currently studying discrete mathematics, and in one of the lecture slides, prof glosses over the fact that set theory and propositional logic are kind of the same thing under the "boolean algebra" umbrella.
proven marlin
can someone point me to where i can read further about this?
stuck needle
Hell pld
cedar kilnBOT
@proven marlin Has your question been resolved?
cedar kilnBOT
@proven marlin Has your question been resolved?
crimson sedge
Does anyone see a connection here??
cedar kilnBOT
Does anyone see a connection here??
whole ember
look at the difference
crimson sedge
look at the difference
7 - 12 = 5
12 - 19 = 7
19 - x = ?
39 - 52 = 13
lyric leaf
what could you say about the pattern of the differences
you arent given that many so the only 'sequential' pattern you really have is 7 and 12
lyric leaf
lets say you had 2, 4, ?, 8
crimson sedge
and 12 to 19 is 7
lyric leaf
could you find ? t here
lyric leaf
this is a very similar problem
but the difference is increasing
try doing what you did for 2 4 ? 8 with the differences youve found
5, 7, ?, 13
crimson sedge
would it increase to 9 then?
lyric leaf
yeah
lyric leaf
yeah
crimson sedge
Oh so 39 and 52 are just there to confuse?
slim tusk
it doesn't increase by 2
crimson sedge
Does that mean 39 to 52 is just there to confuse?
lyric jungle
9 -> 11 -> 13
lyric leaf
no
crimson sedge
I know
lyric leaf
39 to 52 makes sense too
crimson sedge
Oh I see it now,
lyric leaf
but you cant really do anything with it as it isnt your starting term
lyric leaf
yeah
crimson sedge
I'm so dumb sometimes jesus
lyric leaf
hope that helps, this sequence is called arithmetic sequence
crimson sedge
hope that helps, this sequence is called arithmetic sequence
Yeah helped alot, thanks man
.close
crimson sedge
@lyric leaf Quick question, I'm not sure, but am I right in saying that the answer of the following question is 3:9?
On a handball team there are 12 players. Three of them are left-handed.
Describe the ratio of left-handed to right-handed players.
3 : ?
lyric leaf
yes but remember you have to simplify ratios to their smallest form
lyric leaf
unless its asking for it in terms of 3 : 9
crimson sedge
like
lyric leaf
then its fine
idle urchin
I’m confused with this question
cedar kilnBOT
I’m confused with this question
lyric jungle
What is the length of the missing side?