So I just use
#help-23
brittle raptor
Wolfram alpha
Input the percentile and I'll get my answer..
OKAY, I THINK THAT'S ALL
THANK YOU SO MUCH SOUTH!
Have a wonderful day!
.close
safe radishBOT
safe radishBOT
Available help channel!
leaden glade
safe radishBOT
leaden glade
i just want someone to confirm part b) for me
is the reason for it because d(x) is not a factor of p(x) and therefore cannot share a common zero?
long oracle
Intuitively yes, since if they shared a root, the "remainder" polynomial would be zero too.
Which I assume u didnt get in a)?
This fact is due to the factor theorem (for polynomials)
leaden glade
This fact is due to the factor theorem (for polynomials)
okok
could i have some help w part a)
im a bit confused
what does it mean use long divison
what am i dividing by?
long oracle
Have you not used the long divion algo. before?
long oracle
Right, so notice that the equation in a) is solved for k, and if you compare with the equation given there's now a missing x. This confirms our suspicion because the expression on the right of k in a) has one degree lower than the one given..
What do you think we need to divide by now?
leaden glade
wait um what does 1 degree lower mean?
like as in what does it show for polynomials
long oracle
Do you know what the degree of a polynomial represents?
long oracle
Odd or even in what sense?
long oracle
So it's just the highest exponent in the expression (for the x terms in this case)
leaden glade
yes
long oracle
So they say cubic, and we see that x^3 is the highest one
leaden glade
Right, so notice that the equation in a) is solved for k, and if you compare wit...
how does that link to here?
i might be a bit slow
i think its dvided by x correct?
but probably smth more like x-2 or smth?
long oracle
So dividing a polynomial by another polynomial with degree 1 like ax + b for example lowers the degree of the "highest exponet by 1"
Right!
long oracle
So solve for k and make sure thats what you have to divide by
leaden glade
wait um
long oracle
in the equation given
leaden glade
so do i just divide by
x?
is that all?
cos what if its lke x-2 or x-3
or smth
long oracle
Not quite, it seems you might have some leftover constants too
leaden glade
yeah
long oracle
When solving for k
leaden glade
how do i find the constant?
like
thats my biggest quesiton
i understnad dividing by x now cos it lowers the power by 1
long oracle
So while solving for k you'll notice that you have to divide by an expression; it will arrive naturally you dont really to figure out how it'll look as long as you do the algebra right. You'll most definitely get somethhing of degree 1 however like we noted above.
leaden glade
wait so im a little confused now
how do i solve for k then?
do i just do
divided by x?
long oracle
Try to move the terms without the k coeffient and see if you can maybe factor out a k and then divide by whatever you have to solve for k
And when we do this we'll have to use long division which is why that was hinted at
leaden glade
im sorry im so lost 😭
if u have the itme
could u like write out the working out and send it to me
OH WIAT
DO U MEAN
make k the subject?
and thennn use long division
long oracle
It's perfectly fine to feel that way, but its worth thinking it trhough
Yes exactly!
long oracle
Ur welcome you managed to get it by yourself!
leaden glade
wait soryr
im not stuck on part 2
😭
ive maanged to prove k
how would i find this
long oracle
Since they're using the word "Hence" it makes it seem like the calculation done in part a) makes b) easier now.
Some first thoughts of mine:
Since k and x>0 are integers and x^2 + x + 1 in such case also must be an integer (mult. and addition of integers is an integer).
Then the only concern is 12/(x-1) which has to be an integer since LHS must = RHS, so x -1 must only be positive divisors of 12.
Hopefully this is enough for you to start!
long oracle
Ur welcome!
leaden glade
wait when the quesiton says
the equation has one postive integer solution for x
does that mean x>0
is that the point of that line
long oracle
Yes and note however that they say at least one, meaning you might have more such x's that give the same k integer if that makes sense
leaden glade
ohhh
long oracle
But its not important
leaden glade
so does
so basically if i see
the euqatoin has at least one positive integer solution for x
long oracle
As long as you find what x's and theyre integers and positive its fine, now you know all k
leaden glade
that means the x has to above zero
long oracle
Yeah
long oracle
positive meaning strictly above 0
leaden glade
like
why does one positive integer solution for x mean x has to be positive
i thought it mean that only k had to be positive or msth
oh does solution kind of mean like
find the values of x where it is a positve integer, and k will also be a integer?
long oracle
Yes! just that the equation is valid. We can find any such x's and k's but while the equation is not actually LHS = RHS.
Also I think it might help to think of this akin to equations such as x - y = 0.
Solving for y we just get y = x where the solution can be interpreted as all the points that lie on the line y = x, the solution of which are the infinite pairs (x, x). And even if x and y here was integers we would still have infinite solutions.
In our case however the restriction is quite important and makes it possible to concretely express all solutions to the equation. Maybe a shift of perspective that helps.
safe radishBOT
@leaden glade Has your question been resolved?
wide obsidian
need some help proving this question
safe radishBOT
need some help proving this question
wide obsidian
I know A* = A+ y and A+ = (At A)^-1 At
but how A*A = I can prove this
<@&286206848099549185>
safe radishBOT
@wide obsidian Has your question been resolved?
safe radishBOT
@wide obsidian Has your question been resolved?
glossy cedar
Yo
peak estuary
are you gonna post a question?
limpid light
glossy cedar
Yo
safe radishBOT
@glossy cedar Has your question been resolved?
fossil nimbus
I've read some explanations but still don't really understand
safe radishBOT
I've read some explanations but still don't really understand
fossil nimbus
pls give me a detail one
safe radishBOT
@fossil nimbus Has your question been resolved?
narrow vault
how is this the magnitude?
safe radishBOT
how is this the magnitude?
hoary wind
You can factorise what's inside the square root, so as far as I can see it's the same answer just in a different form
narrow vault
I dont get how to factorize this and get rid of the square root
hoary wind
It's a quadratic in $v^2$, $\sqrt{(v^2 + 2u^2)^2} = (v^2+2u^2)$
flat frigateBOT
TayBee
safe radishBOT
safe radishBOT
Available help channel!
haughty pewter
How do I get the bounds for phi (I got less than pi/3) but idk if it’s right
safe radishBOT
How do I get the bounds for phi (I got less than pi/3) but idk if it’s right
@haughty pewter Has your question been resolved?
wind echo
Is linear algebra worth taking after multivariable?
safe radishBOT
Is linear algebra worth taking after multivariable?
wind echo
maybe topology instead?
peak estuary
just take both
linear algebra is pretty important. you should have noticed that during multivariable calc
safe radishBOT
@wind echo Has your question been resolved?
craggy trout
How many different ways can you seat 11 men and 8 women around a circular table? Only relative positions in the circle can be distinguished
I'm not entirely sure what this is asking? At least the part about relative positions. Can someone point me in the right direction?
safe radishBOT
`How many different ways can you seat 11 men and 8 women around a circular table...
@craggy trout Has your question been resolved?
chilly lance
Relative positions means it's relative to each other and not their absolute positions.
craggy trout
Right I am maybe not understanding how that would affect the problem?
craggy trout
Relative positions means it's relative to each other and not their absolute posi...
Like does that mean there are only 11+8 ways that can be distinguished?
safe radishBOT
@craggy trout Has your question been resolved?
signal cove
helolo
inner parrot
what alpha value does a 90 percent confidence interval correspond to?
inner parrot
alright so $\alpha = \frac{1-C}{2}$
flat frigateBOT
y0shi
inner parrot
where C is the confidence level
that table doesn’t contain the confidence level but rather the alpha value, so we have to use this equation
signal cove
what is the thing that looks like a
inner parrot
alpha
signal cove
what does it represnt
inner parrot
the cut off value that we use for hypothesis testing, or the tail probability at a certain level of confidence
you don’t really need to know what that is for this
but the table is using this number instead of the confidence level
signal cove
so (1 -0.90)/2
signal cove
0.05
signal cove
i dont know why please explain please
inner parrot
well a t distribution as the degrees of freedom (the numbers on the left most column) goes to infinity approaches a normal distribution
since we are doing a one proportion z interval
we need to use the z score and not the t score
in simpler words, the infinity row shows all the z scores
signal cove
is that why we dont look at this page instead
inner parrot
you definitely can
but you would have to find 0.05 as the area
and get the z score that way
it’s just more convenient to use the other table
signal cove
that makes sense thank you very much
inner parrot
ywyw!
safe radishBOT
safe radishBOT
Available help channel!
pastel sinew
braindead rn,
how do i prove that a product of cyclotomic polynomials of orders d|n is x^n-1?
pastel sinew
that is, $\prod\limits_{d\vert n} \Phi_d(x) = x^n-1$
flat frigateBOT
🇵🇸Mína🔆
pastel sinew
well, the way i define a cyclotomic polynomial is $\Phi_n(x)=\prod\limits_{\substack{k=0\ \gcd(n,k)=1}}^{n-1} (x-\zeta_n^k)$ where $\zeta_n^k=e^{\frac{2k\cdoti\cdot\pi}{n}}$
halcyon flame
that is, $\prod\limits_{d\vert n} \Phi_d(x) = x^n-1$
Before anything this should be:
$\prod\limits_{d\vert n} \Phi_d(x) = x^n-1$
flat frigateBOT
🇵🇸Mína🔆
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pastel sinew
correct, thank you
flat frigateBOT
Daddy_314
pastel sinew
i know that in $\mathbb{C}\ x^n-1$ has $n$ nth rooths of unity, thus
$x^n-1=\prod_{k=0}^{n-1}(x-\zeta_n^k)$
flat frigateBOT
🇵🇸Mína🔆
pastel sinew
**Daddy\_314**
ok, i wanna get the same product from that, as from this
$\prod_{d\vert n}\Phi_d(x) = \prod_{d\vert n}\prod_{\substack{k=0\ \gcd(k,n)=1}}(x-\zeta_d^k)$
flat frigateBOT
🇵🇸Mína🔆
halcyon flame
braindead rn,
how do i prove that a product of cyclotomic polynomials of order...
It's not about being braindead, it's actually not that trivial without some group theory
Do you know the group of roots of unity
pastel sinew
It's not about being braindead, it's actually not that trivial without some grou...
yeah i am, is because this is my thesis which i've let to rot for 3 months xd
getting back on track has not been easy
pastel sinew
Do you know the group of roots of unity
Yes, they form a subgroup of the multiplicative group of the field over which the polynomial x^n-1 splits into linear binomials
halcyon flame
And usually utilizes some results
flat frigateBOT
🇵🇸Mína🔆
pastel sinew
there is $\varphi(n)$ different primitive nth rooths of unity
flat frigateBOT
🇵🇸Mína🔆
halcyon flame
**🇵🇸Mína🔆**
This one is easier to prove, or are you wanting to deduce this from the above
What are you trying to do...
pastel sinew
trying to prove this
pastel sinew
i can't click through the replies to a bot
halcyon flame
In an easy way
pastel sinew
can you give me a concrete thing please
halcyon flame
**🇵🇸Mína🔆**
I was trying to understand what you were going for and then you sent this
Which has nothing to do here
It's either a result you proved or a result you deduce after
pastel sinew
safe radishBOT
@pastel sinew Has your question been resolved?
pastel sinew
let's denote the group of n-th roots of unity $G_n$ and the set of primitive n-th roots of unity $\Omega_n$.
If $a\in G_n$, there exists some $d\vert n$ such that $a\in\Omega_d$ and on the other hand, for all $d\vert n$ if $a\in\Omega_d$ that means that $a\in G_n$. From that it should follow that $G_n$ is a disjoint set union $\bigcup\limits_{d\vert n}\Omega_d$ but I don't immediately see how that should be disjoint.
flat frigateBOT
🇵🇸Mína🔆
pastel sinew
<@&286206848099549185>
safe radishBOT
@pastel sinew Has your question been resolved?
safe radishBOT
@pastel sinew Has your question been resolved?
plain spear
How do we solve fraction equations to solve for a variable in grade 9 algebra. Like an example is -11/5 = -2 + n
safe radishBOT
How do we solve fraction equations to solve for a variable in grade 9 algebra. L...
acoustic kestrel
Ideally you'd keep n on the side that keeps it positive. That just makes it simpler to think about.
acoustic kestrel
No, you never move the equals sign
plain spear
oh
plain spear
ohhhhhhh
yea yeah
mb
right
where did the 2/1 come from
wait wait
so
u did
-11/5 = -22/10
and then
2/1 = -22/10
wait no
BRO IM SO LOST HOLY FCK
wait
OH RIGHT
RIGH
yeah cause
ok
ok
yeah
right
-1/5
so thatsd the answer?
ok ok ok
thanks g
safe radishBOT
If you are done with this channel, please mark your problem as solved by typing .close
plain spear
.close
safe radishBOT
safe radishBOT
Available help channel!
lean otter
I don't know how to approach this question
safe radishBOT
I don't know how to approach this question
hoary wind
What do you understand by the phrase 'comes to rest'?
safe radishBOT
@lean otter Has your question been resolved?
fickle rapids
safe radishBOT
fickle rapids
how to get area of rectangle
safe radishBOT
@fickle rapids Has your question been resolved?
fickle rapids
<@&286206848099549185>
bright bramble
try sine theorem
fickle rapids
try sine theorem
how
bright bramble
I'm just Grade 9
I only know this method may help you
I don't know how to apply it on radians
safe radishBOT
@fickle rapids Has your question been resolved?
fickle rapids
<@&286206848099549185>
proud vessel
Trace or graph the¿alture?
I don't know the name of It in this language but basically graph the line with is perpendicular to QS
Starting from the Vertex R
With that you can do realize the length of QS in terms of x (the angle you put)
safe radishBOT
@fickle rapids Has your question been resolved?
leaden glade
safe radishBOT
icy lance
winged flare
do you know the factor theorem?
leaden glade
yes i do
winged flare
if x - a is a factor of f(x), then f(a) = 0
leaden glade
but it has p inside it
winged flare
then here if you substitute p, it should evaluate to 0
leaden glade
so would i just keep testing values basically?
winged flare
just here a = p
leaden glade
is that all?
winged flare
yep
winged flare
4p^3 - (10p - 1)p^2 + (6p^2 - 5)p + 6 = 0
leaden glade
i thought normally for x-1
winged flare
like its on the other side of the equation
doesnt matter
leaden glade
oh
winged flare
4p^3 - (10p - 1)p^2 + (6p^2 - 5)p + 6 = 0
youd get this
winged flare
wdym keep testing
leaden glade
wait
so
can u explain
what i would have to do again>
?
do i just set the whole thing has to equal zero ?
and then solve for p?
leaden glade
4p^3 - (10p - 1)p^2 + (6p^2 - 5)p + 6 = 0
wait how come x becomes p?
winged flare
wait how come x becomes p?
because f(p) = 0
so i substitute p for x and set the equation to 0
safe radishBOT
@leaden glade Has your question been resolved?
leaden glade
spice furnace
You have made no attempt
leaden glade
.close
honest sequoia
Hi all
desert pasture
honest sequoia
Thanks !
desert pasture
ask, if anyone can help, they will
light shoal
no trolling in the doubt channels
honest sequoia
This question came in the exam man
light shoal
what exam
honest sequoia
My final term exam
light shoal
and how did you clear the doubt on that exam
light shoal
what do you think the answer should be
flat frigateBOT
ren
honest sequoia
Yes\
rose plume
is 10
frozen marlin
fr fr
honest sequoia
Bruh
light shoal
if it was stated as 8/2(2+2) then that's not the right interpretation
frozen marlin
ik
light shoal
would be (8/2)(2+2) under the usual rules of precedence
frozen marlin
?
honest sequoia
@light shoal you are right I agree
light shoal
but it's also a standard meme/troll style question
honest sequoia
No man I am not used to trolling people
frozen marlin
"not used to trolling ppl" 
honest sequoia
I actually hate trolling
rose plume
.close
light shoal
No man I am not used to trolling people
no i'm not saying you are, but this type of question shows up in memes all the time
honest sequoia
Oh
light shoal
the answer is that it's ambiguous
rose plume
im helpful the asnswer is 10
frozen marlin
anyway, back to the question
frozen marlin
im helpful the asnswer is 10
shhhhh
honest sequoia
BRO MAYBE MY TEACHER IS TROLLIN ME IN THE EXAM
safe radishBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
honest sequoia
WTH
frozen marlin
Please show the original problem, **exactly as it was stated to you**, with the ...
do this please
trail otter
$(1+x)\sum^{\infty}{k=0}(-1)^k\frac{x^k}{k!}-(1-x)\sum^{\infty}{k=0}\frac{x^k}{k!}=\sum^{\infty}{k=0}((-1)^k-1)\frac{x^k}{k!}-\sum^{\infty}{k=0}((-1)^k+1)\frac{x^{k+1}}{k!}$\\
how come these two are equal?
safe radishBOT
$(1+x)\sum^{\infty}_{k=0}(-1)^k\frac{x^k}{k!}-(1-x)\sum^{\infty}_{k=0}\frac{x^k}...
flat frigateBOT
Slowaq
safe radishBOT
@trail otter Has your question been resolved?
trail otter
<@&286206848099549185>
safe radishBOT
@trail otter Has your question been resolved?
mental needle
safe radishBOT
@trail otter Has your question been resolved?
safe radishBOT
@trail otter Has your question been resolved?
fair steppe
Yo
fair steppe
I need help with this
lean otter
?
fair steppe
I dont get it
I want someome to do an example or 2 for me and explain along the way
lean otter
I want someome to do an example or 2 for me and explain along the way
ok b4 i help
fair steppe
k
lean otter
do you understand a domain and a range?
vagrant ice
Do you understand what the domain and range are
lean otter
Do you understand what the domain and range are
...
fair steppe
do you understand a domain and a range?
Yes
steep kite
Domain is all possible values of x and range is all possible values of y
lean otter
ok @fair steppe look
Domain is the set of all x-coordinates like (1,1) (2,1) (3,1) etc
Range is the set of all y-coordinates (1,2) (1,3) and so on
vagrant ice
I have it on my notes
Fair enough, just trying to make sure we're all on the same page
vagrant ice
ok <@796031192037326888> look
Domain is the set of all x-coordinates like (1,1) ...
That's not quite right actually
lean otter
That's not quite right actually
it is .....
fair steppe
Fair enough, just trying to make sure we're all on the same page
Yea I understand
vagrant ice
The domain would just be {-3, 1, 1, 3, 5}
steep kite
That's not quite right actually
Yeah you wrote both coordinates
vagrant ice
The domain can't be a set of coordinates
fair steppe
ok <@796031192037326888> look
Domain is the set of all x-coordinates like (1,1) ...
Is the 1 always on the right side for domain?
lean otter
Is the 1 always on the right side for domain?
depends on the coordinates
fair steppe
The domain would just be {-3, 1, 1, 3, 5}
Here's the thing is it always those numbers?
vagrant ice
Here's the thing is it always those numbers?
No
fair steppe
Ok
steep kite
Is the 1 always on the right side for domain?
No
vagrant ice
It of course depends on the function
lean otter
Here's the thing is it always those numbers?
nope
fair steppe
Alr
vagrant ice
So when you have points, the domain and range are just a collection of numbers
But when your function is continuous
fair steppe
I see
flat frigateBOT
south
vagrant ice
Or you can have the real numbers as your domain
Most of the time, the domain will be the real numbers, so all possible x
fair steppe
Yep I learned about the real numbers today
vagrant ice
You will also have functions like $\frac{1}{x}$ where the domain is just all real $x$ except $x = 0$
flat frigateBOT
south
vagrant ice
Yep I learned about the real numbers today
Nice
fair steppe
Alr
vagrant ice
And there's functions like y = ln(x) where the domain is x > 0 for real x
vagrant ice
And there's functions like y = ln(x) where the domain is x > 0 for real x
(ln(x) is the mirror image of y = e^x across the line y = x cause it's the inverse function, you might get to that one later)
vagrant ice
Alr
So in summary, for a table or for when the graph has isolated points, just look at the possible x-values (domain) and y-values (range) for the points
For a continuous function you do the same thing, but you have infinitely many points, so your domain and range will be inequalities
fair steppe
(ln(x) is the mirror image of y = e^x across the line y = x cause it's the inver...
Yeah I don't get that exactly
steep kite
Here is an example of continuous curve, shape of curve doesn't matter
vagrant ice
For a continuous function you can imagine trying to draw a rectangle around your function
vagrant ice
Yeah I don't get that exactly
You'll come to it if you haven't studied logs and exponential functions yet
fair steppe
Here is an example of continuous curve, shape of curve doesn't matter
Oh so the shape doesn't matter?
vagrant ice
For a continuous function you can imagine trying to draw a rectangle around your...
The smallest rectangle actually
fair steppe
You'll come to it if you haven't studied logs and exponential functions yet
Yeah I haven't yet
steep kite
Oh so the shape doesn't matter?
If it is continuous
fair steppe
I see
vagrant ice
And then the range of x and y values of the rectangle is your domain and range
fair steppe
What about one that isn't?
vagrant ice
What about one that isn't?
So the ones with dots aren't continuous
Anything you can't draw without your pen leaving the paper isn't continuous
steep kite
Then you have to write seperate domain and ranges and use AUB if there are multiple curves
fair steppe
AUB?
steep kite
You know set theory right?
fair steppe
Idk that
steep kite
Oh you'll study that later
fair steppe
Alr hopefully
My teacher is ass
4 out of 31 students are passing with 50s
Highest mark is a 70 and the student is cheating 😭
Anyways I appreciate your guys help
Ima also ask a teacher for help during lunch in a bit
fair steppe
Yeah ima watch them
vagrant ice
Cool
fair steppe
I got them saved to watch later
lean otter
im doing combinatorics and im stuck on why Σ(j=0 to infinity):[n k]*t^k= 1/(1-t)^n where [n k] = (n+k-1 choose k) nεN
safe radishBOT
im doing combinatorics and im stuck on why Σ(j=0 to infinity):[n k]*t^k= 1/(1-t)...
vagrant ice
im doing combinatorics and im stuck on why Σ(j=0 to infinity):[n k]*t^k= 1/(1-t)...
Please use proper formatting, LaTeX / MathJax etc
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
lean otter
Please use proper formatting, LaTeX / MathJax etc
idk how to do that
safe radishBOT
Available help channel!
fair crane
is this wrong
safe radishBOT
is this wrong
steel stag
I don't think I believe the djvj to dj^2 step
it'd probably be an inequality there I'm guessing
yea it's this, called cauchy-schwarz inequality
although if you're maxing it I guess it is equals and fine?
guess it's all true
fair crane
yea it's this, called cauchy-schwarz inequality
it isnt the whole thing squared though is it? its just (uivi)^2?
steel stag
oh true I wonder what that's called
steel stag
like for n=2 this isn't always true right
fluid escarp
Hi can some one solve this?
safe radishBOT
Hi can some one solve this?
median vigil
do you know what kind of series this is?
safe radishBOT
@fluid escarp Has your question been resolved?
eternal carbon
do you know what kind of series this is?
@fluid escarp ?
fluid escarp
do you know what kind of series this is?
Geomerric?
fluid escarp
<@1063039177693855814> ?
Geometric?
median vigil
there is a formula for geometric series
safe radishBOT
@fluid escarp Has your question been resolved?
fluid escarp
there is a formula for geometric series
Yes
But how it solvea with it
safe radishBOT
@fluid escarp Has your question been resolved?
fluid escarp
find what is a and what is r, then apply the formula
Ok but it didnt worked
jolly shard
Ok but it didnt worked
What did you get?
fluid escarp
What did you get?
1-(1/4)^infinity
Over
1-1/4
jolly shard
1-(1/4)^infinity
Over
1-1/4
Two mistakes, what is a, and why do you have infinity in your answer?
fluid escarp
Two mistakes, what is a, and why do you have infinity in your answer?
Oh ok i find my mistake
I use this formula:
fluid escarp
Two mistakes, what is a, and why do you have infinity in your answer?
It should be 4/3 right?
jolly shard
It should be 4/3 right?
No, what is r?
safe radishBOT
@fluid escarp Has your question been resolved?
wispy portal
Then multiply 3
The answer is 4 right?
That is correct
safe radishBOT
safe radishBOT
Available help channel!
obsidian fractal
idk where to start w/ this question
safe radishBOT
idk where to start w/ this question
lost forum
Hey khat!
I’d start as follows:
The question is asking you “how to do something” so that profit is maximized. Therefore I should be able to calculate profit (no matter what the something is, I’m gonna need to be able to calculate profit to deal with it)
So, how would you calculate profit?
Say the profit of the company if they make 60 cars per month and sell them at 800+fp where fp is the factory price
The profit would then be 800*60
Per month
So say that they mark up by 20c where we are trying to find c
fathom pine
find the direction in which the Uf of f(x,y)=ye^-xy at (0,2) has value of 1
lost forum
find the direction in which the Uf of f(x,y)=ye^-xy at (0,2) has value of 1
Or do that…
obsidian fractal
The profit would then be 800*60
isnt it (800+fp)*60
lost forum
But you have paid fp to make the car!
So your clear profit is only the 800
That’s why they don’t specify the value of fp
You can think of it like this:
To make a car you pay fp and you get 800+fp so that the profit would be (800+fp-fp)60
safe radishBOT
@obsidian fractal Has your question been resolved?
obsidian fractal
im still confused
maybe im js not reading something properly or im just tired af but i dont rly get either explanation for why u dont add fp or how u get the equation from the question
exotic cypress
thw question is asking about how much profit you get
like if you buy something for $5 and sell it for $15 (geez how much did you rip someone off), your profit is $15-$5 ($5 is your 'fp'), which is $10, not $15 that you sold it
oh texit never needed u here bro i was just talking about money
obsidian fractal
why did the other dude even mention it then
exotic cypress
s/he didn't need to but just telling you what profit meant
cuz if you didn't know the definition of profit or how to work it out you can't understand the question
obsidian fractal
well thats one thing
but i also dont get how i make the equation with the stuff given
exotic cypress
so the profit would you gain from 1 car is 800, where you sell 60 cars per month, right? then, every extra $20 you make from 1 car will decrease the total sales by 1 car
thats all the information you need to make the equation from
obsidian fractal
ok i have the equatio
n
(60-1x)(800+20x)
how do i find x so profit is maximized
exotic cypress
(60-1x)(800+20x)
good thats ur 1st step
now its hard to explain but you can see that for exery extra $20 you lose 1 car so the money difference = +20(60) and -1(800+20x) or -1(800) + 20*(59)
so like u find a point where when u take away 1 car and times it by 800+20x is the same as the cost of 1 car (sry im bad at explaining this
)
obsidian fractal
❓
obsidian fractal
<@&286206848099549185>
storm sleet
?
ionic lark
?
storm sleet
yes
ionic lark
but why did you ping when someone else is helping you?
oh wait, that's 15 mins ago
Makes sense
proper spindle
obsidian fractal
.close
safe radishBOT
safe radishBOT
Available help channel!
crisp gyro
How would I do this q? I did u=ln(x) and then I got intergral of u/x du but idk if I did anything wrong
safe radishBOT
How would I do this q? I did u=ln(x) and then I got intergral of u/x du but idk ...
eternal carbon
How would I do this q? I did u=ln(x) and then I got intergral of u/x du but idk ...
are you familiar with integration by parts
crisp gyro
are you familiar with integration by parts
I've done it before but I wouldn't say I'm too good at it
eternal carbon
so that is recommended method of solving integral such as this
flat frigateBOT
tall bough
Okay nvm I can't do derivaives anymorw
split fulcrum
I've done it before but I wouldn't say I'm too good at it
You know the formula uv - integral vdu?
crisp gyro
You know the formula uv - integral vdu?
Ngl I need to go over this again
split fulcrum
Ngl I need to go over this again
Okay, do you still need help with the problem or do you just want to take time and learn IBP urself
crisp gyro
Okay, do you still need help with the problem or do you just want to take time a...
I'll redo the chapter
split fulcrum
Alright 👍
safe radishBOT
@crisp gyro Has your question been resolved?
versed wave
How would I do this q? I did u=ln(x) and then I got intergral of u/x du but idk ...
either you can do IBP, or IBS
me personally i prefer IBP
split fulcrum
what’s IBS
versed wave
int by sub
split fulcrum
oh I’ve only ever seen people call it u sub
untold oyster
could someone explain the step made in red?
safe radishBOT
could someone explain the step made in red?
cloud citrus
Expanding (2m+1)!
(2m+1)!=(2m+1)(2m)(2m-1)(2m-2)(2m-3)...(2)(1)
We can notice that (2m-2)(2m-3)...(2)(1) is actually (2m-2)!
safe radishBOT
safe radishBOT
Available help channel!
empty marten
there are 2 boys and 4 girls, they will be in groups of 3, what is the chance of the 2 boys being together in a group
safe radishBOT
there are 2 boys and 4 girls, they will be in groups of 3, what is the chance of...
lime dust
What did you try?
lime dust
Now calculate the number of groups that contains 2 boys
empty marten
4C1 = 4?
empty marten
4/20?
empty marten
but answer is 0.4
lime dust
Rly? Let me check
empty marten
what did you get?
empty marten
it was an instagram post lol
lime dust
Maybe i am getting braindead but i get 20%
lime dust
You count the two boys as 1
empty marten
ye it isnt permutation
lime dust
Maybe he forgot about that
empty marten
i consider one group only
oh
wait
total number of groups might be 10
because there are 2 of them
its repeated
imagine ABC, DEF
lime dust
Oh we treated differently in both scenarios
empty marten
DEF is already counted
empty marten
Oh we treated differently in both scenarios
what do you mean?
empty marten
thanks, i havent learnt about combinations yet but im interested in it
lime dust
I tricked myself xd
empty marten
i watched many youtube videos but they are all about letters
lean otter
- Idk where to start
Do you know the Quadratic formula?
Yep
Do I use that?
You can
thin bridge
using the discriminant component is enough
lean otter
Yeah
lean otter
using the discriminant component is enough
Idk that one
So, if the general solution of this equation is $\frac{-b (+-) \sqrt{b^2-4ac}}{2a}$
flat frigateBOT
Palahoo
lean otter
i.e. the
b^2 - 4ac
So I can only use this instead?
lean otter
So I can only use this instead?
It's the same thing
The discriminant (D) is equal to b²-4ac
So, as the equation has only one solution, the discriminant needs to be equal to zero
So (k)^2-4(4)(9)?
Yes
It needs to be equal to zero
k^2-144=0?
Yes
Notice that k has two solutions
So if I factor it’s gonna be (k-72)(k-72)=0
12
Oh
(k-12)(k+12)
It has the solutions 12 and -12
Can I find the roots dividing it by 2?
And i got 72
Is there another way
To find roots
With big numbers like that
lean otter
Can I find the roots dividing it by 2?
You mean dividing (k-12)(k+12) by 2 and get (k-72)(k+72)
?
No like 144
How do I factor this fast
Cuz I divided it by 2
To find the factor
Remarkable products
(a+b)(a-b)=a²-b²
Oh idk that maybe I should study that first
Ohhh
So (k-144)(k+144)=k^2+144^2?
To find the root of 144?
lean otter
So (k-144)(k+144)=k^2+144^2?
-144²
Not plus
But -(-144)
Since its k^2-144=0
?
No
How?
(a+b)(a-b)=a²-b², so we can conclude that a²=k² and b²=144
?
Oh
(-144)^2= -(144)=-144
(k+12)(k-12)=k²+12k-12k-12.(+12)=k²-144
No
Like how do u find the root
Of 144
That fast
That’s just expansion
Yes
?
No I’m talking abt 144
lean otter
Of 144
When you get used with numbers, you find the things faster
Then what were all those
😭😭
lean otter
When you get used with numbers, you find the things faster
So that’s the only way?
Ok helper is gone
.close
safe radishBOT
safe radishBOT
Available help channel!
tight scroll
How to do this?
safe radishBOT
How to do this?
patent flame
Let y=vx
tight scroll
I don't understand
tepid walrus
They‘re suggesting a substitution
tight scroll
Substitute what?
tepid walrus
y/x = v
tight scroll
Ohh
tepid walrus
So you get a more manageable form
tepid walrus
you shouldn‘t have dy/dx, it should be something with dv no? Unless I‘m missing something
tepid walrus
Well, I don‘t have much experience with differential equations, but I think you‘d want to have a dv/dx there?
Then you should be able to integrate both sides
But I may be wrong, so I‘ll go ask in the helper channel if someone wants to fact check this and help you :)
tight scroll
Okay
placid oak
the result should be separable once you rearrange everything
tepid walrus
Okay so I wasn‘t just blurting out random crap. Thanks Desync
tight scroll
the result should be separable once you rearrange everything
Ohh kkay
Thank you
.close
safe radishBOT
safe radishBOT
Available help channel!
reef flax
Help anyone? I've been trying to desperately find what this equation even is like i've searched youtube and google, some modules and there's NONE. Does anyone know what type this is? Example problem: If sin β = - 3/5 and tan β > 0, what is the exact value of cos² β-sin² β?
safe radishBOT
Help anyone? I've been trying to desperately find what this equation even is lik...
rich shuttle
Hmmm
reef flax
also the next step for the solution to that problem is like sin β = - 3/5 cos β = - 4/5 but where did they get the 4?
oops wrong numbers fixed
rich shuttle
Oh
hoary wind
also the next step for the solution to that problem is like sin β = - 3/5 cos ...
Pythagoras
placid oak
by drawing a 3-4-5 right triangle
reef flax
Pythagoras
wait i'll check
rich shuttle
so like
reef flax
i'm sorry i'm slow but what do you mean by drawing a right triangle, like literal? cause it was just numbers
rich shuttle
yes
placid oak
trig functions relate angles to the sides of triangles
rich shuttle
draw right angle triangle
abc
with b as the right angle
hpy is 5
and opp of angle beta is -3
by Pythagorus
we get 4
not -4
hm
reef flax
wait let me type in the solution, It doesn't say to make a triangle, its so confusing. Give me a few seconds please
reef flax
here
sin β = - 3/5 cos β = - 4/5
cos² β - sin² β = (- 4/5)² - ( - 3/5 )²
= 16/25 = 9/25 = 7/25
= 7/25
I kind of do get it but can't comprehend where the 4 was taken
is it pythagoras?
rich shuttle
yes
see If we take AC to be the larger side
AC^2=AB^2+BC^2
you can move AC and other sides
reef flax
I'm sorry but what does that mean, what AC?
rich shuttle
the sides let me send a pic
reef flax
okay
reef flax
/yes?
reef flax
you mean the overall answer would be 34?
reef flax
but the choices were either a.) - 1/5 b.) 7/25 c.) 1 d.) -1 (By the way I am not cheating this is a reviewer with already provided answers)
reef flax
wait
I can't make an over but its like negative 3/5
like both?
let me write it i'll send a picture
rich shuttle
ok send
reef flax
like that negative
help someone, I'm losing my minddd
how did 4 get there when and why
graceful forge
We have sin(x) to be negative, which means x cannot be in the first or second quadrant , also tan(x) is positive means x must exist in the third quadrant only .
And in the third quadrant cosine(x) is negative.
So cos²(x)=1-sin²x
=16/25
=>cos(x)=4/5 or -4/5 .
But we know cosine(x) is negative. So cos(x)=-4/5
graceful forge
7/25 is the correct answer ...
safe radishBOT
@reef flax Has your question been resolved?
safe radishBOT
reef flax
We have sin(x) to be negative, which means x cannot be in the first or second qu...
sorry can you explain it again? I really can't understand i'm bad at math
safe radishBOT
Available help channel!
reef flax
what did you mean by the x?
safe radishBOT
what did you mean by the x?
reef flax
I didn't get the 4
graceful forge
what did you mean by the x?
Well x is just β , we can write anything, writing x is faster than writing β
graceful forge
I didn't get the 4
Do you know about sin²x+cos²x=1??
reef flax
No
graceful forge
No
Well then can you tell me exactly how much trigonometry you know ? Because, these are very basic things.
reef flax
I actually don't know any, I'm in a strand that removed math and I'm trying to know all these equations for a try in scholarship
I don't even know why they removed it, its literally so important
graceful forge
Do you know what sine of an angle is ? Like it is opposite over hypotenuse that much ?
graceful forge
not really no, i'm sorry
I would recommend you pick up any book on trigonometry and read the first few pages .. the. You can have a solid idea .
If they will be asking questions on the scholarship test , it is best to skip the parts you are weak in like trigonometry, and focus on your strong areas .
reef flax
its more like a written test
graceful forge
wait so the equation isn't pythagoras?
Trigonometry is based entirely on Pythagoras, but for that you have to know what basic definitions of sin(x) , cos(x) , tan(x) are
reef flax
won't I fail though? math is like a major subject especially if the ones they accept are pretty much stem students
graceful forge
won't I fail though? math is like a major subject especially if the ones they ac...
What topics in math are you strong in then ? Otherwise your chances to get the scholarship are dim .
reef flax
well I'm going to be honest, I don't really excel at math and I focus on English more but I'll try searching trigonometry, calculus and such, the other problems here I'm so not sure what equation they even are though
graceful forge
well I'm going to be honest, I don't really excel at math and I focus on English...
Yeah in any examination, it is the best strategy to excel in your strong points , and maybe ditch the parts you are weak in , myself I have given multiple exams in STEM that's why I know this .
graceful forge
well I'm going to be honest, I don't really excel at math and I focus on English...
I will give you a brief preface of what's going on , but here's your strategy if you want to do something with math :
- get past math questions from the test
- identify which topics they ask the most
- pick up a book (download pdf) and read the basics of that particular topic and practice a few questions
reef flax
oh, I'll try that but usually whenever I read through a book and they give a few solutions, the practice problem always comes out different? Example is the equation I gave earlier, its gonna say cos β (sample number) and sin β < 0 and so on, are they supposed to have the same solution format? if that makes any sense (sorry not my native language)
it like, switched it up, is it supposed to be different?
graceful forge
oh, I'll try that but usually whenever I read through a book and they give a few...
Yeah sin and cos can switch up definitions based on the β they take in ..
reef flax
happens to every single module I come up with
vagrant ice
For trig you definitely need to know the unit circle in all four quadrants
graceful forge
happens to every single module I come up with
You have to know what sin and cos really are . There are some tutorials on YouTube which you can follow , like Khan academy is good for basics
vagrant ice
cos theta is the x-coordinate of a point with angle theta, and sin theta is the y-coordinate
reef flax
but is their solution format the same? but how do I know which is which? for example the other person that said about a triangle with A, B, and C. Lets say they 2 numbers are on A and B as the problem with solution was given, the next problem they make me solve is through B and C, its confusing (not accurate just example)
reef flax
You have to know what sin and cos really are . There are some tutorials on YouTu...
Oh thanks, I'll look into their content
graceful forge
Oh thanks, I'll look into their content
Just watch the first few videos on trigonometry, they will clear all your doubts on what trigonometry is , you won't have any doubts with solution formats anymore .
vagrant ice
So yeah, you can break down your study approach into:
- Unit circle: signs of sin, cos, and tan for all 4 quadrants (and these are the same signs of csc, sec, and cot as the reciprocal 1/x doesn't change the sign of a number)
- Using trig identities: Pythagorean identity cos^2 x + sin^2 x = 1, double-angle identities, and sin(A + B) and cos(A + B) if you have time
- Solving trig equations such as sin x = sqrt(3)/2: group sin and cos together cause their period is 2pi, and do tan separately cause its period is pi
safe radishBOT
Available help channel!
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
frozen marlin
*algebra
one sec, lemme just scan this rq
what have you tried
...?
what do you mean it's a test
<@&268886789983436800>
bro
we can't help with tests
im sorry
why would it be
no
we want to help others learn
simple oak
frozen marlin
we aren't here to do your homework for you or hand out free marks
well, my guy, then use your learnt material to do the test
ionic lark
Then come with the same question after school
frozen marlin
i'm afraid we cannot, and will not, aid you in this task
goodbye
yea exactly
you're worried abt marks not abt the actual question
quasi plume
.close
safe radishBOT
vagrant ice
we can't help with tests
Brooooo
safe radishBOT
Available help channel!
ember finch
I think i'm stupid
safe radishBOT
I think i'm stupid
vagrant ice
I knew how to do this before but i forgot
Solve y'' + 3y' + 2y = 0 first
Then your particular solution is going to be in the form $y_p = ax^2 + bx + c$
flat frigateBOT
south
vagrant ice
A quadratic double-differentiates down to a constant
ember finch
Then your particular solution is going to be in the form $y_p = ax^2 + bx + c$
how do you know this
vagrant ice
Sub the particular solution in and compare coefficients to find a, b, c
ember finch
is that always the case when the right side is a constant?
vagrant ice
is that always the case when the right side is a constant?
Yeah, it's going to be another polynomial for sure if the RHS is a polynomial