their product = number of possible "one of each color" draws
#help-0
dire gale
Is 20C3 the total?
storm ridge
But idts it should be 20C3 in the denominator, since it says without replacement
Ok nvm
lone heartBOT
lone heartBOT
Available help channel!
earnest bane
I need help with this question.
lone heartBOT
I need help with this question.
earnest bane
I tried a(b+c-5)=b(a+c-5) but I can go two ways: a(c-5)=b(c-5) which makes a=b and then I find c, or I could get c(a-b)=5(a-b) which gets me c=5, so I can get a and b.
earnest bane
In the first one I get (a,b,c)=(5,5,7/5) and (-5,-5,43/5) and in the second one I get (7,-1,5) and (-7,1,5), (7,1,5) and (-7,-1,5)
earnest bane
are a, b and c supposed to be integers
It's not explicit in the question, but I assumed, so.
It's in the quadractics section of the book, but before the quadractic formula. I am suposed to solve this only with factoring polynomials.
My question is why can I go 2 ways in the first equation? If I isolate in different ways I get different results.
mortal trellis
well you are either assuming that c-5 is nonzero so you can divide by it or you are assuming a-b is nonzero so you can divide by it
earnest bane
Yeah, but they are not exclusive, are they? Can I assume both?
mortal trellis
well they each will lead to solutions and those solutions might be different
earnest bane
In the end the solutions they provide, if I'm right, checks out in the system.
Ok, so the "biffurcation" happens because I divide by a term that contains a variable that I don't know if the result equals 0, is that it?
mortal trellis
basically, yes
in the first scenario you precisely get that a=b, aka a-b=0. which is what you assume does not happen in the second scenario
earnest bane
Oh.
Ok, so how do I know if it's a solution or not? Because I tried pluging in in the system and it checks out.
earnest bane
OK, bear with me for a moment. I tried using symbolab.
And it gives only one solution, but during the solution steps it aknowledges all the possibilities.
BBut in the end, it gives only one solution. Why?
mortal trellis
well online calcs are sadly not always correct
mortal trellis
it might assume that everything has to be integers
which isnt the case in your first scenario
earnest bane
Ok, last thing: is there a name for this kinds of situation where different assumptions in solving an equation results in biffurcation?
earnest bane
I tried a(b+c-5)=b(a+c-5) but I can go two ways: a(c-5)=b(c-5) which makes a=b a...
I understand that quadractics have 2 solutions, but I'm surprised by the situation in this line.
mortal trellis
well this isnt just a quadratic
earnest bane
Yeah, I know. But is there a name for it?
mortal trellis
not a specific one that comes to mind
slow hedge
lone heartBOT
slow hedge
anyone wanting to do grade 9 Math question lol
slow hedge
the question is:
"write a in terms of /type b"
I mean this probably isnt the server to ask this but if anyone is interested in this they can try
hollow zephyr
slow hedge
theyre asking me to write a in terms of b
idk if the translatation I did is correct but
let a be 4
let b be 2
writing a in terms of b would be ---> 2b
noble notch
which q is it
slow hedge
i didnt understand
lone heartBOT
@slow hedge Has your question been resolved?
grave canopy
I need clarification on something
lone heartBOT
I need clarification on something
grave canopy
.close
lone heartBOT
alpine sable
What
lone heartBOT
Available help channel!
simple parrot
lone heartBOT
simple parrot
For a), where did they use the given impulse and velocities in the solution?
how dioes the soln even work
lone heartBOT
@simple parrot Has your question been resolved?
lean forge
If the restriction of a function f on R\Q is injective, show that f is injective
lean forge
I think I might need to use the sequencial characterization of a limit along with the density of R\Q in Q
But not sure how to get started
bruh that was actually stupid
.close
dusk granite
What undefined in math we have(like ∞^0 and other)? Can i get all undefined list?
off-top question: what bot use font for math symbols?
foggy pecan
yes, there are 7 such symbols i write them:
barren portal
what do you think, when we say 'undefined' ?
foggy pecan
$\frac{0}{0},\frac{\infty }{\infty },+\infty-\infty,0\cdot \infty,1^{\infty},\infty^{0},0^{0}$
ocean sealBOT
Joanna Angel
barren portal
Consider 0/0, we know its undefined (why?)
dusk granite
And it`s all? What about ⁿ√x?(n=0, i don`t have small zero in keyboard like ¹²³⁴)
foggy pecan
And it\`s all? What about ⁿ√x?(n=0, i don`t have small zero in keyboard like ¹²³...
i gave you undetermind symbols you can meet, when you calcuialte limits
these above refers to limits
because, you wanted them saying it in between the lines
barren portal
Consider 0/0, we know its undefined (why?)
because, if I let 0/0=x, this means 0*x =0. notice any x will make this statement true
foggy pecan
the other undefined symbols refgr to numerical meaning,
barren portal
and we cannot properly 'define'
dusk granite
Consider 0/0, we know its undefined (why?)
because 1*0=0 and 0/0=1, 2*0=0 0/0=2
barren portal
essentially, since any number times zero is zero
dusk granite
0/0=all numbers
barren portal
yes, we cannot define, as in uniqueness is lost
dusk granite
hmmm
barren portal
same reasoning goes for other cases
dusk granite
**Joanna Angel**
btw, what font is it?
dusk granite
.close
dapper talon
lone heartBOT
dapper talon
How do I start this? Do I convert the 10ft radius to inches?
vale wigeon
you convert all measurements into the same unit. which one you use is up to you.
converting the radius into inches is more convenient than the other option.
dapper talon
Ok then I'll have to convert it from cubic inches to cubic yards
vale wigeon
yes
welcome to the american measurement system
where these conversions are everywhere and also idiotic
cerulean garnet
lone heartBOT
cerulean garnet
no iudea what that means
X -> Y notation
is it asking me to translate the equations where x is = to y
instead of y = x
alpine sable
X is the domain of f and Y is the codomain
slate dawn
Do you have the answers?
exotic canopy
what is, in general, the difference between an n-valued function and a n-ary operator?
exotic canopy
like how would some function $f : S^2 \to S$ differ from $a*b=c$ where $a, b, c \in S$?
ocean sealBOT
artemetra
exotic canopy
where S is just some random set
can't we just rewrite all operators as functions, LISP-style?
frail grove
like how would some function $f : S^2 \to S$ differ from $a*b=c$ where $a, b, c ...
They're not the same, f could be the sum of (a,b) not multiplication
If that operator is multiplication xd
exotic canopy
binary meaning takes 2 things as input
there are unary operators like $\frac{d}{dx}$ that take only 1 input
ocean sealBOT
artemetra
exotic canopy
and binary operators like $+$ or $\cdot$
ocean sealBOT
artemetra
exotic canopy
don't have any good examples of higher order operators tbh
frail grove
The function could be f: (a,b) --> a²+b
exotic canopy
they are definitely separate terms though
i just fail to grasp the difference
ooooooooh i see the difference
actually no
i just see that operators are functions with both domain and codomain the same
(ignoring the arity)
but idk feels too vague
okay i used misnomer too
what i should be talking about is operations, not operators
those sre different
but still, can't we formulate all of them as just functions with some input and output?
tacit arch
what is, in general, the difference between an n-valued function and a n-ary ope...
n-valued is the dimension of the output, where as n-ary is the dimension of the input
tacit arch
exotic canopy
n-valued is the dimension of the output, where as n-ary is the dimension of the ...
what's the equivalent of n-ary for functions
also arity?
exotic canopy
https://en.m.wikipedia.org/wiki/Arity.
damn
okay i did some reading
would it be valid to say that given domain S^n and codomain S all possible operations with those domains and codomains are functions?
tacit arch
I suspect this is starting to be some category theory question
#category-theory maybe?
lone heartBOT
@exotic canopy Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
noble trail
With this triangle, i was asked to find the angle A and the length of AD.
I know the angle A is 15º, but i'm having some trouble to calculate the length of AD. I'm supposed to use law of sines, right? But how should i start solving the problem?
azure shuttle
Doesn't the "law of sines" relate angles and opposite edges.
Do you have an angle opposite the edge you need to know?
@noble trailStill interested?
noble trail
yes
tardy stag
are you sure angle A is 15º? that's not anywhere near the number i got
azure shuttle
Was the sin you used in degrees?
noble trail
are you sure angle A is 15º? that's not anywhere near the number i got
I did
A + 135^\circ + 30^\circ = 180^\circ \\
A = 180^\circ - 165^\circ \\
A = 15^\circ
persa
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
limpid turret
I did
```tex
A + 135^\circ + 30^\circ = 180^\circ \\
A = 180^\circ - 165...
You haven't proven EB and DC are parallel
azure shuttle
@tardy stag@limpid turretToo many cooks.
limpid turret
Also what hayley said
ocean panther
in the smaller triangle u know all the side lenghts
maybe try law of cosines?
@noble trail
ocean panther
wait me a bit ok?
limpid turret
@noble trail this problem is demonstrably erroneous
The measurements and angles make no sense
Using the givens provided angle BED would not be 135
!original
lone heartBOT
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.
noble trail
limpid turret
Tell your teacher the problem is impossible with the given input
It is contradictory information
noble trail
There was this concern on this questions, howeverthe answer was this:
the difference between those two (finding the angle AEB either by the angle DEB or by the side of triangle AEB) is not big. This is mostly due to the roundings. So you can assume that they are the same angle.
limpid turret
That's called a shit answer to a shit problem
But that's not your fault
And I don't blame you for having to suffer that
But your instructor I would definitely have choice words for...
noble trail
Thanks for lightning my mind 
I will talk with other students so we can talk with the instructor. I shall close this channel, thanks again and a happy Christmas!
.close
lone heartBOT
lone heartBOT
Available help channel!
sullen sky
lone heartBOT
sullen sky
need help to put this expression into complex form
remote heron
hmm its really not rice
try finding a form for e^i thats not miserable
well, use eulers
it still sucks
then you can split using exponent rules
get you something you can type in
foggy pecan
need help to put this expression into complex form
$exp\left( i \right)=\cos1+i\sin1\\exp\left( exp\left( i \right) \right)=exp\left( \cos1+i\sin1 \right)\text{ }\text{ etc}$
ocean sealBOT
Joanna Angel
last heart
I am practicing for a math competition and have a problem i need help with question 11
lone heartBOT
I am practicing for a math competition and have a problem i need help with quest...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
rustic coral
Step 1
Hint: Create a system of equations in terms of ||the width of an armrest and the width of a seater||
last heart
I dont understand is the 220cm the combined width of the 2 arm rests or just 1 armrest
empty moss
\section{Product Rule Derivation}
\subsection{Equation 1}
The product rule for derivatives is given by:
\begin{equation}
f'(x) \cdot g'(x) = \lim{{h \to 0}} \left( \frac{f(x+h) - f(x)}{h} \right) \cdot \lim{{h \to 0}} \left( \frac{g(x+h) - g(x)}{h} \right)
\end{equation}
Expanding Equation 1, we get:
\begin{align}
&\lim{{h \to 0}} \frac{f(x+h)g(x+h) - g(x)f(x+h)-f(x)g(x+h) + f(x)g(x)}{h^2} \nonumber
&= \lim{{h \to 0}} \frac{f(x+h)g(x+h) - g(x)f(x+h)-f(x)g(x+h) + f(x)g(x)}{h} \quad \text{(since as } h \to 0, h^2 \to 0 \text{)}
\end{align}
\subsection{Equation 2}
\begin{equation}
f'(x) \cdot g(x) = \lim{{h \to 0}} \frac{f(x+h)g(x) -f(x)g(x)}{h}
\end{equation}
\subsection{Equation 3}
\begin{equation}
g'(x) \cdot f(x) = \lim{{h \to 0}} \frac{g(x+h)f(x) - f(x)g(x)}{h}
\end{equation}
\subsection*{Sum of Equations 1, 2, and 3}
Adding Equations 1, 2, and 3, we get:
\begin{align}
&\lim{{h \to 0}} \frac{f(x+h)g(x+h) - g(x)f(x+h) + f(x+h)g(x) -f(x)g(x+h) + g(x+h)f(x) + f(x)g(x) - 2f(x)g(x)}{h} \nonumber
&= \lim{{h \to 0}} \frac{f(x+h)g(x+h) - f(x)g(x)}{h}
\end{align}
This is the definition of $(f(x)g(x))'$, and thus, the product rule is derived as:
\begin{equation}
(f(x)g(x))' = f'(x)g'(x) + f'(x)g(x) + g'(x)f(x)
\end{equation}
I was trying to prove the product rule myself and then ended up with a different version, which I know is false but I don't get the flaw in my math
ocean sealBOT
Don Bugito
lofty gorge
your issue is when you change the h^2 into an h in equation 1, as that's not how limits wok
empty moss
why not
lofty gorge
stupid example: the as limit of h^2/h^2 is 1 but the limit of h^2/h is 0 as h goes to 0
essentially h and h^2 as functions of h behave very differently near 0, as h^2 is a lot smaller
empty moss
I see, thanks.
Also for limits, when we plug in the limit value we have to plug it in for all values of that variable, right? We can't just plug in one of the places it appears?
lofty gorge
yes
it's actually the same idea here, in your work you're essentially substituting sqrt(h) for h in just the denominator but not the numerator
empty moss
alright thanks
real panther
Q94?
forest harness
!status
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@real panther
real panther
real panther
It's a parabola
real panther
forest harness
nice
ok now we need to find its mirror image with respect to y=x
try drawing y=x
forest harness
do you know what reflecting over y=x does to the x and y coordinates?
lone heartBOT
real panther
.reopen
lone heartBOT
✅
real panther
Don't know
forest harness
ok try imagining reflecting a point like (1,-1)
real panther
y=-x
forest harness
no if you reflect (1,-1) what does it become
real panther
(-1,1)
real panther
(0,1)
real panther
Thanks for your patience
forest harness
of course
real panther
Interchange the values of y and x
forest harness
exactly ⭐️
real panther
Next?
forest harness
ok so now if we do this for a whole graph, we can just swap x and y in its equation
real panther
Ok
forest harness
so what equation does y²=4x become?
real panther
x²=4y.
forest harness
yessir
real panther
Graph become up
forest harness
normally i would just use a little calculus
real panther
?
forest harness
taking the derivative gives you the slope of the tangent
forest harness
yeah y in terms of x
forest harness
sorry i was trying to think about the parametric solution
real panther
Of which?
forest harness
like how to find dy/dx for the equation 4y=x²
real panther
Ok
forest harness
so dy/dx=?
forest harness
yeah
real panther
dy/DX is slope
forest harness
yes
real panther
4 goes to that side.
real panther
ok actually i checked this and i think you just have the x and y flipped
Eq of tangent
But why x=2?
dy/DX =x/2
forest harness
yup
real panther
Then?
forest harness
so now you have a slope and a point so you can write the equation of the line
real panther
y=MX+c
Or
(y-y1)=m(x-x1)
forest harness
yeah second one is easier here
real panther
Oh I got it
forest harness
awesome
real panther
One minute
real panther
What I have learnt:
1)mirror image is flipping of x and y values
2)new parabola eq
3)for eq of tangent
4)we have to find slope by differentiate
5)then sub in one point- slope form to get eq
forest harness
nice! ⭐️
real panther
but yeah i think the parametric equation you had should be xt=y+at²
It's for x²=4y i think
forest harness
yeah
real panther
One minute
forest harness
so you can use that too
forest harness
yes
real panther
Yes
x²=4y
Eq of tangent
Yes
y-y1=m(x-x1)
When x = 2
Slope= 1
yes
(y-1)=1(x-2)
Eq of tangent
y-1=x-2
forest harness
for transparency, here's how i checked the tangent line formula
forest harness
yup that should be correct
real panther
I think parabola contains good no of questions
real panther
yup that should be correct
Yes that's correct i checked but thanks
forest harness
oh ok
real panther
Let's solve more questions
forest harness
did you try it?
real panther
Yes
forest harness
what did you try doing
real panther
I have a big doubt
Parabola is up
x²=4y like parabola
Then rectangle lies on x axis
forest harness
no not up this one is down
real panther
Like y²=4ax
forest harness
it might be helpful to think of it as y=-x²+12
forest harness
oh yeah you can do that
real panther
Yes
forest harness
no you still have a /12 with the y
forest harness
yup awesome
forest harness
we have to graph it
real panther
Down like arch
forest harness
yes
real panther
One minute
forest harness
oh not quite
real panther
Why?
forest harness
the general equation is (x-x₀)²=4a(y-y₀) and (x₀,y₀) is the vertex
real panther
In here the general eq,x²=-4ay for down
real panther
the general equation is (x-x₀)²=4a(y-y₀) and (x₀,y₀) is the vertex
Correct
forest harness
yup
real panther
Other all are correct?
forest harness
yes i think so
real panther
Next step?
forest harness
Next step?
now we need to find a formula for the area of the rectangle and maximize it
real panther
L*B
forest harness
that’s the way you find dy/dx when you’re dealing with parametric equations
unfortunately i couldn’t tell you why it holds
forest harness
is L horizontal or vertical? (we can do either way)
forest harness
ok
real panther
Horizontal length x2-x1
By distance formula
Vertical length y by distance formula
forest harness
yup
real panther
But l*b is (x2-x1)*y
tacit arch
!redir
lone heartBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
forest harness
But l*b is (x2-x1)*y
how are x2 and x1 related?
forest harness
They are equal
they have the same magnitude
but one is positive one is negative right
real panther
How?
forest harness
because of the symmetry of the parabola
real panther
but one is positive one is negative right
Ok
real panther
Distance from vertex are equal
real panther
then x₂-x₁=?
0
forest harness
no it shouldn’t be 0 remember x₂-x₁ is L
real panther
Distance between them is 2x is l
real panther
How
forest harness
how are y and x related?
real panther
2x=y
real panther
y²=4x
real panther
2x*(12-x²)
forest harness
great
forest harness
oh wait i wasn’t expecting a cubic umm
are you supposed to be able to use calculus?
maximization is another thing calculus is really good for
that’s probably the only way to do this without a calculator
real panther
How?
forest harness
when there’s a maximum, dy/dx=0
real panther
What is your answer?
real panther
when there’s a maximum, dy/dx=0
Which we have deferentiate
forest harness
oh not 8
real panther
6
forest harness
yup
real panther
Sorry
real panther
Root 3
forest harness
wait use the equation with 6
forest harness
yup! so that should be the x that makes the area the maximum
real panther
Now sub in 24x-2x³
Concepts learnt:
1)Draw a good graph
2)x2,x1 are equal distance from vetex
3)y in terms of x
4) multiplication l*b
5)when dy/dx is zero area is maximum
6)sub x in first eq
How you have this much problem solving skills.
forest harness
lmao thanks
real panther
Brilliant
forest harness
just experience
vagrant agate
how do i do b? am i supposed to create like simultaneous equations for all three?
elfin fiber
Maybe graph all three and see if they intersect at exactly one point
pliant cedar
find the intersection of the first two
if the third passes through the same point
they are concurrent
acoustic mango
i need help
lone heartBOT
i need help
foggy pecan
i need help
do you want to write your sum as logarithm? what exactly do you want to do with it?
raw stream
i need help
how can you represent
acoustic mango
as single log
raw stream
1 as log of base 2
acoustic mango
raw stream
how can you represent
answer this
acoustic mango
1 as log of base 2
can we represtne log as that?
acoustic mango
how can you represent
i want to reperets it as one logarithm
acoustic mango
ok
raw stream
else we cannont proceed
raw stream
try it rn
foggy pecan
you need to use followinfg school formulaes:
$\log_{a}a=1\\p\log_{a}b=\log_{a}b^{p}\\\log_{a}x+\log_{a}y=\log_{a}\left( xy \right)$
ocean sealBOT
Joanna Angel
acoustic mango
raw stream
wrong
acoustic mango
what exactly is wrong inher
acoustic mango
log 1 to base 2 ?
raw stream
**Joanna Angel**
this might help
acoustic mango
ohh
acoustic mango
need help
raw stream
represent 1 as log of base 4
acoustic mango
i know if the base is the same these can divide
acoustic mango
represent 1 as log of base 4
but noi have to represent 2
ocean sealBOT
jan Niku
raw stream
but noi have to represent 2
why?
acoustic mango
2-log 2 base 4
raw stream
2 = log base = 4 , 16
raw stream
acoustic mango
ok
go ti t
thanks
i havent done much log so yea
but thanks any way this is very helpful
.close
raw stream
lone heartBOT
raw stream
<@&286206848099549185>
exotic canopy
reading
hm
can you draw some examples?
moreover there's n! chords aren't there
raw stream
granite warren
Is the question about the maximum number of triangles whose vertices are within the circle over he set ways to draw chords such that no 3 share a point?
raw stream
yes
raw stream
i have to be honest, so far i don't have much idea
same
i believe it will form some recursion
idk how
@foggy pecan
Someone help me 💀
<@&286206848099549185>
granite warren
Oh!
each triangle corresponds to each unique way of choosing 6 points, so there should be at most n choose 6 triangles
oh but that overcounts since it allows more than 2 chords to intersect at the circumference, sorry
raw stream
ok
granite warren
Do you have that if P(n) is your maximum number of triangles for n vertices, that P(n) = P(n+1) for even n?
raw stream
Do you have that if P(n) is your maximum number of triangles for n vertices, tha...
how did u get P(n) = P(n+1)
for n = even
@granite warren
granite warren
So, all of the above are allowed configurations, since no 3 chords have a common point. But, the number of internal triangles is clearly maximal when no two chords have a common point on the circumference
granite warren
no, that's not specified in your problem
raw stream
read q
granite warren
the only specification is that no 3 chords share a common point
then we are asked to find the maximum number of internal triangles given that
raw stream
granite warren
it's asking you to count them, not specifying that the only intersections have to be inside
raw stream
but all the vertices have to be inside
granite warren
to see why P(n) = P(n+1), try to add another chord and vertex to a set of chords. Either you don't intersect an inside triangle so no new inside triangles are formed. Or, you do intersect an inside triangle in which case that triangle becomes a little triangle and a trapezoid
maybe a good conjecture to try to prove would be that by adding two points, you can reate at most 1 new triangle, i.e., P(n+2) = P(n) + 1
raw stream
to see why P(n) = P(n+1), try to add another chord and vertex to a set of chords...
Okay I got this
raw stream
maybe a good conjecture to try to prove would be that by adding two points, you ...
ok trying
granite warren
Good luck! I believe in you
raw stream
Good luck! I believe in you
P(10)
p(8)
cant see this relation work
@granite warren
granite warren
I agree
raw stream
@granite warren
i found this
7 new triangles have been added
and the diff forms arithmetic
sequence
granite warren
Nice!
granite warren
Are you counting interior regions or triangles though?
raw stream
Are you counting interior regions or triangles though?
triangles
granite warren
because for triangles, P(6)=1, P(8)=2, P(10)=5 by your drawings
raw stream
oh they don't have to be disjoint!
yes
granite warren
you can describe that compactly by (n/2) choose 3, the number of waysof picking 3 chords
raw stream
I need a recursive formula
topic was recursion
difference of difference is in ap
I will get a cubic equation
@granite warren
but
hmm something is wrong
granite warren
I think if you count carefully you will get P(10) = 10 , not 9
raw stream
oh yes
granite warren
each way of choosing 3 chords gives you a unique triangle. for n=10, there are 5 that are points of the star and 5 that include the central pentagon, like you drew earlier
raw stream
1,4,10,20
okay
could you provide me complete soln and expl?
from here
oh i got it
granite warren
By the same logic, P(12) should be 20
I think you will need to do two recursion cases, for even and odd n
tight locust
P(12) should be 20
raw stream
i can do odd even i am done with even
granite warren
@ocean seal we can build a recursive definition from P(2n) = \frac{n(n-1)(n-2)}{3!} for the even case
I am new and don't know how to format here, sorry
granite warren
it's (n/2) choose 3, the number of waysof picking 3 chords
granite warren
n is the number of vertices, each chord has 2 unique vertices
granite warren
crimson oar
lone heartBOT
crimson oar
for the first half of the question
im getting x <11/3
although in desmos that isnt the case
vale wigeon
show your work
crimson oar
could anyone explain the calculation
crimson oar
show your work
can i type it out?
vale wigeon
if you can make it comprehensible then sure
crimson oar
-2 < 1/2 - (3x+1)/4
-2 < (2 - 3x + 1)/4
-8 < 3 - 3x
-11 < -3x
x < 11/3
the answer says x < 3
crimson oar
ohh
so it becomes 1 - 3x?
wouldn't that just give 7/3?
the answer says x < 3
this would give x < 7/3
vale wigeon
how are you getting x < 7/3 now
are you sure you are not making another sign error further down the line
crimson oar
how are you getting x < 7/3 now
cause you get -2 < (2 - 3x - 1)/4
so -8 < 1 - 3x
then -7 < -3x
3 goes to the other side
vale wigeon
how do you go from -8 < 1 - 3x to -7 < -3x
golden arch
What does this notation mean:
lone heartBOT
What does this notation mean:
lament forge
it's product
like $\sum_{i=1}^k$ if you've seen that but with multiplication instead
ocean sealBOT
bee [it/its]
regal fox
How do I differentiate with respect to X using chain rule
lone heartBOT
How do I differentiate with respect to X using chain rule
regal fox
this should be the answer but this is what I got
carmine reef
Where is u coming from
regal fox
u is this part differentiated
carmine reef
Why though
regal fox
I'm using the chain rule to get x
carmine reef
To get x?
regal fox
so when I differentiate y and then multiply with u it should get x
i need the differentiated answer with respect to x
amber nymph
this should be the answer but this is what I got
The product rule is incorrectly used
amber nymph
Uhh
regal fox
tho I still can't seem to get it right
amber nymph
A faster approach would be writting denominator as 5x-3x^3
And then applying power rule + chain rule
Oh yeah
regal fox
where is the power of 3 coming from?
regal fox
opal jolt
you should start with the quotient rule
amber nymph
By multiplying x to 3x^2
regal fox
for now I've only learnt the chain rule and this question is to test that particular rule
amber nymph
Have you studied power rule?
regal fox
By multiplying x to 3x^2
opal jolt
$\frac{d}{dx}\frac{u}{v}=\frac{u'v-uv'}{v^2}$
regal fox
Have you studied power rule?
I'm pretty sure no? though would u explain what it is
ocean sealBOT
LordFelix
amber nymph
$\frac{d}{dx} x^n=nx^{n-1}$
ocean sealBOT
Ericsson
amber nymph
Power rule ^^
opal jolt
in this case, u=1, and v=x(5-3x^2)
regal fox
yea I've done that ofc
opal jolt
so you got -v'/v^2
amber nymph
in this case, u=1, and v=x(5-3x^2)
They can't use quotient rule for this question apparently
regal fox
^^
opal jolt
huh?
amber nymph
Okay watch, i don't know how to write multiple lines in latex but bear with me
opal jolt
.\newline
amber nymph
$\frac{d}{dx} (5x-3x^3)^{-1}=-(5x-3x^3)^{-2} \cdot \frac{d}{dx} (5x-3x^3)$
regal fox
also can someone acc explain what differentiation is? Ik that if we have a curve we get the gradient of said curve but at the same time I don't get it
ocean sealBOT
Ericsson
opal jolt
you got a function, let's say f.
You differentiate it.
You get a new function, let's say g.
g gives you the slope of f at every point
regal fox
so it's a fuction where when u plug in the value of x you get the gradient of said point
opal jolt
the gradient of the original function at said point
amber nymph
**Ericsson**
Do you understand this @regal fox
regal fox
I get that but in more broader aspect cuz later we needa differentiate 3d objects like a cube
opal jolt
or in other words. If you were to draw a tangent line on the original function at that point, g would give you the slope of said line
regal fox
Do you understand this <@569491990144614410>
yes that makes sense
OHHHHH MY GOD
I REALISE WHAT I WAS DOING WRONG LOL
amber nymph
this should be the answer but this is what I got
If you solve it further, you will get a similar answer
regal fox
ahhhhhhhhhhhhhh ok ok lemme quickly try to do it again
opal jolt
if you're in 3d, you can get the slope of a plane instead of a line
regal fox
if you're in 3d, you can get the slope of a ***plane*** instead of a line
how do i visualise that
opal jolt
with a lot of difficulty
regal fox
I can't picture 3d objects having a slope
amber nymph
Hold a sheet of paper and tilt it, voila a plane and a slope
regal fox
questions like this for example (next chapter)
amber nymph
Oh
opal jolt
amber nymph
You are not gonna differentiating that cube
opal jolt
questions like this for example (next chapter)
that's not differentiating the cube
i thought you meant having 2+ variables. You still only have one there
regal fox
oh I haven't done those yet but the chapter is titles further differentiation so I just assumed
opal jolt
you have a function with only one variable, x, that gives you the volume of the cube
amber nymph
That's application of differentiation. A real nice topic
opal jolt
a very useful topic
regal fox
yea i like differentiation just a tad bit confusing at first
oke lemme try to first sovle the question first and see if I can get it right
opal jolt
specifically, your problem 9.3.1 there would be L=3x=80m, A=x^2, maximize A
lone heartBOT
@regal fox Has your question been resolved?
regal fox
<@&286206848099549185>
lone heartBOT
@regal fox Has your question been resolved?
rustic lily
<@&286206848099549185>
hi~! what's your problem?
regal fox
hi~! what's your problem?
I can't get this question right
no matter what I do
this is the question
meant to use chain rule to solve it
thats my answer and thats the correct answer
rustic lily
I can't get this question right
Ok Let me think about your problem.
I want to know the entire question. could you show me or tell me the whole conditions and questions?
regal fox
this is the entire question
and the only condition is that I must use the chain rule in solving this question
rustic lily
this is the entire question
above your working course.. what is the u = -9x^2 + 10x?
I can't see that equation in your problem.
regal fox
above your working course.. what is the u = -9x^2 + 10x?
it's differentiatng U
for chain rule to find out x you do this
I've solved all question but it's just this one particular thats giving me a headache
rustic lily
it's differentiatng U
I understood,
this is my answer,
as you can see.. the formula of chain is like this. (x^n)' = nx^(n-1)x'
in this formula we often omit x' because we often differentiate f(x) with x.
So.. and then let's talk about your problem.
let's assume f(x) = x(5-3x^2) = X!
and then your problem is to differentiate the f(X) = X(-1) with x.
the working course like this.
f'(X) = -1(X^(-2))*X' = 9x^2 -5/(5x-3x^3)^2.
if you make sense with this. plz ping me.
regal fox
I understood,
this is my answer,
as you can see.. the formula of chain is like t...
I don't get this part sorry, besides that it makes sense but I'm confused about this particular part
rustic lily
your problem is to differentiate (x*(5-3*x^2))^(-1), right?
regal fox
I'm not entirely sure but I'm assuming so
this was my working
this has to be the issue right?
rustic lily
yeah I also think that is the issue in your working
regal fox
But I'm not sure why it's wrong or how to fix it ;-;
rustic lily
But I'm not sure why it's wrong or how to fix it ;-;
I got the point. you have seen the problem not correctly.
in your working course the y = 1/(x(5x-3*x^2)) is wrong.
the correct problem is the y = 1/(x(5-3x^2)).
Get it?
regal fox
omg ☠️
regal fox
I got the point. you have seen the problem not correctly.
in your working course...
It was a written mistake
I see now
so when we differente it it will be 9x^2 + 5 and the answer will be correct
thanks a lot 😭 I've been soo confused
rustic lily
you are welcome. that's the common mistake with mathematicians.
regal fox
I'll try to be careful next time and check it a few times
thanks alot and have a great day!
.close
teal violet
i tried evrything but i still cant find the solution can anyone help ?
lethal belfry
mind translating it?
alpine sable
translate?
teal violet
find the real a
raw stream
translate?
snow, isnt the answer to my q 2^k - 1
teal violet
and limite in - infini = 0
teal violet
i tried evrything but i still cant find the solution can anyone help ?
need to use asymptotic development to solve it
lone heartBOT
@teal violet Has your question been resolved?
teal violet
sadge
lone heartBOT
@teal violet Has your question been resolved?
alpine sable
@teal violet
teal violet
yes ?
alpine sable
I need help with trying to find a formula for a equation I made
ax³ + bx² + c = 0
I tried using quadratic with changes and I got something which would get answers off by decimals
Like 0.5 0.33 etc
teal violet
ax³ + bx² + c = 0
tbf i dont think that u can find an exact solution for this
lone heartBOT
@teal violet Has your question been resolved?
lone heartBOT
@teal violet Has your question been resolved?
wispy ibex
Ah un français @teal violet
lone heartBOT
@teal violet Has your question been resolved?
olive sundial
Ah un français <@669201202076057612>
doesnt that mean stupid or failure
vale lichen
You didnt translate the full question
My french isnt the best but the full question was find a real number a so that the limit of the function as x aproaches -inf is 0
foggy pecan
i tried evrything but i still cant find the solution can anyone help ?
$\text{To solve your limit problem,}\\text{you need to use the following method:}\\a+b=\frac{a^{6}-b^{6}}{\left( a^{3}-b^{3} \right)\left( a^{2}-ab+b^{2} \right)}$
ocean sealBOT
Joanna Angel
lone heartBOT
@teal violet Has your question been resolved?
teal violet
My french isnt the best but the full question was find a real number a so that ...
ye that is the question
teal violet
$\text{To solve your limit problem,}\\\text{you need to use the following method...
idk how i m going to fully use this
foggy pecan
idk how i m going to fully use this
i solved it but it takes soem place, and i got:
$\displaystyle\lim_{x \to -\infty}\left( \sqrt{x^{2}-x+1} +\sqrt[3]{x^{3}+ax^{2}+1}\right)=\left[ +\infty-\infty\right]=\\=\lim_{x \to -\infty}\frac{\left( x^{2}-x+1 \right)^{3}-\left( x^{3}+ax^{2}+1 \right)^{2}}{\left[ \left( \sqrt{x^{2}-x+1} \right)^{3}-\left( x^{3}+ax^{2}+1 \right) \right]\cdot \left[ x^{2}-x+1-\sqrt{x^{2}-x+1}\cdot \sqrt[3]{x^{3}+ax^{2}+1}+\left(\sqrt[3]{x^{3}+ax^{2}+1} \right)^{2} \right]}=\\=\lim_{x \to -\infty}\frac{\left( -2a-3 \right)x^{5}+\left(6-a^{2} \right)x^{4}-9x^{3}+\left( 6-2a \right)x^{2}-3x}{x^{3}\left[-\sqrt{1-\frac{1}{x}+\frac{1}{x^{2}}}-1-\frac{a}{x}-\frac{1}{x^{3}} \right]\cdot x^{2}\left[1-\frac{1}{x}+\frac{1}{x^{2}}+\sqrt{1-\frac{1}{x}+\frac{1}{x^{2}}}\cdot \sqrt[3]{1+\frac{a}{x}+\frac{1}{x^{3}}}+ \left( \sqrt[3]{1+\frac{a}{x}+\frac{1}{x^{3}}} \right)^{2}\right]}=0\\\Leftrightarrow -2a-3=0\Leftrightarrow a=-\frac{3}{2}$
ocean sealBOT
Joanna Angel
teal violet
ah
foggy pecan
but LaTex cut part of text,
teal violet
i cant use devloppement asomptotic ?
teal violet
analyse
foggy pecan
ok but we do not use such mehtod liek aysmtpotics
teal violet
i got the exercise from the analyse
foggy pecan
i got a nice value of a = -3/2
teal violet
ah