i think
#help-39
vestal tapir
dusk otter
yeah the question doesn't specify
it's not very specific
I just dk because what if the pole is not even like what if it is 7
vestal tapir
and it's maybe still right if you;re allowed to leave empty space
a(0) = 1
a(1) = 1
a(2) = 4
a(3) = 4
a(4) = 9+3+1
hm
so you have to fill it completely, because there's no option like that
so it's 3a(n−2)
dusk otter
Yeah i agree
pearl pondBOT
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molten carbon
pearl pondBOT
molten carbon
How To Solve This.
pearl pondBOT
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molten carbon
<@&286206848099549185>
narrow turtle
Ok I'm here
pearl pondBOT
@molten carbon Has your question been resolved?
molten carbon
How To Solve??
pearl pondBOT
@molten carbon Has your question been resolved?
hazy lotus
HII! Can anyone explain me or have some good resources about problem decidability and turing machines. Also how do I prove that F(loop) <= F(M1, M2), where F(M1,M2) = True if and only if M1[111] = True or M2[111] = True
pearl pondBOT
HII! Can anyone explain me or have some good resources about problem decidabilit...
@hazy lotus Has your question been resolved?
dire jewel
pearl pondBOT
dire jewel
i suppose youd have to differentiate this and say that the differntiated equation is larger than 0
but how would u get an inequality a out of it
spare lark
h'(x) >= 0
north talon
if a is between some values h'(x) < 0
spare lark
Positive so
north talon
h'(x) >= 0
h'(x) = 0 isnt increasing
tame jungle
What's the problem mate
dire jewel
9ax^2-2a+5>0
tame jungle
I'm here to cook maths
dire jewel
hod o we solve for a
spare lark
Factor by a
north talon
9ax^2-2a+5>0
ax^2 is always > 0
tame jungle
a>0 right
For the inequality to satisfy
a<0 isn't possible.
So
Use d≤0
We get
dire jewel
wtf is d
dire jewel
oh.
tame jungle
yep
dire jewel
so the detrminant has to be larger than 0
worn bear
dire jewel
ohhh
tame jungle
cause theres no x term
Huh
dire jewel
like
tame jungle
Right
dire jewel
if u expand it and derive it
i think u get 9ax^2-2a+5
cause the expansion is 3ax^3-2ax+5x
dire jewel
its pinned i thunk
spare lark
They saying to work out possible values of a such that h(x) is increasing as a is positive
tame jungle
Yep
So we take constant
Greater or equals zero
We get 0<x≤2.5
Here zero comes from 9ax²>0=> a>0
These are the possible values
@dire jewel any query?
dire jewel
uh
dire jewel
We get 0<x≤2.5
whats this from
tame jungle
We take constant greater or equals zero
What's the constant in the derived eq?
-2a+5≥0
a≥5/2
Which implies a≥2.5
dire jewel
i thought its
tame jungle
hmm?
dire jewel
-4 times the constant
times 9 a
cause i thought its the discriminant
has to b eless than 0
right
for 9ax^2-2a+5 to be always bigger than 0
tame jungle
Yep it has to be bigger
tame jungle
Okay take the discriminant
tame jungle
yep
tame jungle
wait what the actual
dire jewel
holup
pearl pondBOT
@dire jewel Has your question been resolved?
dire jewel
ok im back sorry the internet went out
so solving rhe inequality gives us
0<a<2.5???
is that right
pearl pondBOT
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junior vapor
all i got was that the dot product of PA and PB = 3a+b
pearl pondBOT
all i got was that the dot product of PA and PB = 3a+b
ionic harness
all i got was that the dot product of PA and PB = 3a+b
well, the answer is depending on u, which is not given. Some data are missing.
pearl pondBOT
@junior vapor Has your question been resolved?
junior vapor
well, the answer is depending on u, which is not given. Some data are missing.
u is the unit for the area, not a variable
ionic harness
u is the unit for the area, not a variable
then it is easy. As the area equals |3b-a|/2=10 and a^2+b^2=80. So you find a,b.
junior vapor
then it is easy. As the area equals |3b-a|/2=10 and a^2+b^2=80. So you find a,b.
how did you get |3b-a|/2=10?
<@&286206848099549185>
ionic harness
how did you get |3b-a|/2=10?
do you know about cross product of vectors?
ionic harness
pretty sure that isn't taught in my high school
Ok, what formulas for the area of a triangle do you know?
junior vapor
1/2 bh 1/2 absinc
ionic harness
1/2 bh 1/2 absinc
ok, do you know that dot product is a product of lengthes times cos ?
junior vapor
yes
ionic harness
so. if your unknown dot product is x then you can find this cos in terms of x.
then you find sin. And use this for the area 1/2 absinc
junior vapor
so. if your unknown dot product is x then you can find this cos in terms of x.
so do I let the dot product of PA and PB = x, which is meant to be |PA||PB|costheta?
ionic harness
so do I let the dot product of PA and PB = x, which is meant to be |PA||PB|costh...
yeah
junior vapor
do I need to find what x is as well?
ionic harness
That is exactly what they ask you to do in the problem 🙂
ionic harness
cus i got costheta=x/20 root 2
looks plausible
junior vapor
ohhh I see wat u mean now I just sub it into the area
ok I got it from here thank you
.close
pearl pondBOT
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midnight flicker
pearl pondBOT
pearl pondBOT
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
1
wraith river
Use angle multiple formula to expand the 3x terms
$sin(3x) = 3cos^2(x)sin(x) - sin^3(x)$ \ $cos(3x) = cos^3(x) - 3cos(x)sin^2(x)$
jolly parrotBOT
LooseEthics
wraith river
Then you get
$$cos^3(x) - 3cos(x)sin^2(x) - sin(x) = \sqrt{3}(cos(x) - 3cos^2(x)sin(x) + sin^3(x))$$
jolly parrotBOT
LooseEthics
cursive wraith
are you trying to solve for x or trying to show this is true for all x?
If you're trying to solve for x, there's a much easier way
put the terms in 3x together, and the terms in x together
$\cos(3x) + \sqrt 3 sin(3x) = \sqrt 3 cos(x) + sin(x)$
jolly parrotBOT
rafilou is not not born in 2003
midnight flicker
are you trying to solve for x or trying to show this is true for all x?
solve for x
wraith river
and recognize angle sum formulas
That's better, forget what I wrote
midnight flicker
divide both sides by 2
why
wraith river
$\frac{1}{2}$ and $\frac{\sqrt{3}}{2}$ are sin and cos of 30 degrees, respectively.
jolly parrotBOT
LooseEthics
wraith river
So
$$L = \frac{\cos(3x)}{2} + \frac{\sqrt 3 \sin(3x)}{2} = \cos(3x)\sin(30) + \cos(30)\sin(3x) = \sin(3x + 30) $$
jolly parrotBOT
LooseEthics
wraith river
Similarly for the other side.
And then you compare the args.
Of course don't forget the periodicity.
midnight flicker
thanks
pearl pondBOT
@midnight flicker Has your question been resolved?
random hinge
could someone help me on this question
pearl pondBOT
could someone help me on this question
random hinge
i'm not sure where the factorisation comes from
pseudo oxide
tried expanding?
glacial sequoia
It's probably roots of unity
pearl pondBOT
@random hinge Has your question been resolved?
fresh silo
hello need help
pearl pondBOT
hello need help
fresh silo
What is the minimum vertical distance between the parabolas y= x - x² and y=x² + 1
fresh silo
and if it was not the minimum how i would do
fresh silo
no
bronze coyote
then just find distance between two vertex
bronze coyote
no idea
fresh silo
idk too
green dew
do yk how to graph the two parabolas?
fresh silo
yeah
green dew
ok then i can use desmos
since vertically speaking
the red parabola is lower than the blue one
we need to find the y value of its vertex
then find its corresponding value using the blue parabola
the absolute value of their difference is the distance
fresh silo
mhmm
green dew
does that mean u didnt understand
fresh silo
i didnt not understand why we need to do the difference
green dew
its the distance formula
if u wanna calculate the distance between two points A and B on a graph such that A and B are parallel to the Y-axis
all u have to do is subtract their Y values only
cause they have the same X value
fresh silo
how they have same X value
green dew
its a rule
if u have the straight line AB parallel to the X axis
then the points A and B have the same x value
wait, by minimum distance
u mean the shortest distance between them vertically?
fresh silo
ys
fresh silo
idk
midnight haven
wouldnt that be 0
fr
midnight haven
the minimum distance between two points of a parabolas such that those two points when joined form a line parallel to the y -axis
“If I had an hour to solve a problem, I'd spend 55 minutes thinking about the problem and five minutes thinking about solutions.”
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hidden void
Sorry for this horrible diagram but if you know that triangle ABC and DCB are congruent, can u say angle DBC and ACB are congruent because of CPCTC?
cursive wraith
congruency of triangles = congruency of all angles
crisp saddle
^
cursive wraith
so if ABC and DCB are congruent because A corresponds to D, B corresponds to C and C corresponds to B
the angles correspond too
long valley
Hello,
I'm trying to understand how Euler's equation of nth order can be reduced to a linear differential equation with constant coefficients, can someone help me figure this out? Ive done some work already: I used the substitution t = ln(x) and so far i've been working on identifying how that transforms the derivatives y^(n) although i cant seem to figure out a general pattern that works. I know the goal is to end up with a linear differential equation with constant coefficients perhaps simply of the form 1/x^k in the derivatives d^iy/dt^i, i dont know what to do with my 'extra' terms tho. I'll send a picture of the results of my work in a second.
long valley
pearl pondBOT
@long valley Has your question been resolved?
long valley
Does my question make sense? Can i do anything to help it get answered?
<@&286206848099549185> I beg 🙏
random flume
Does my question make sense? Can i do anything to help it get answered?
yo
dm me
@long valley
$\ln{x} = \log_e{x}$
jolly parrotBOT
Daddy| |matr!x
jolly parrotBOT
Daddy| |matr!x
random flume
therefore, $\frac{dy}{dx} = e^x$
jolly parrotBOT
Daddy| |matr!x
long valley
I appreciate you trying to help but thats not what i was talking about. 😅
random flume
can you be more clear
long valley
Do u know what an Euler differential equation is?
long valley
Hello,
I'm trying to understand how Euler's equation of nth order can be reduce...
<@&286206848099549185> pls hihi
midnight haven
<@&286206848099549185> pls hihi
You need to find the initial, or final derivative, and write it down. That's the only solution, or possibly one that goes around, which will be your way of the solution.
The term is a general question, sometimes you don't need to write down a final answer, or in your case it could be the opposite, like dxt over dly as a final answer, or something along this order of lines.
But the solution to your question is already derived by your final answer, which is your question, so it is hidden there. This, what I wrote down could be one of the solutions, but you need to think about it your way of things.
Hope I helped, let me know, or if you need anything else.
Just write it down here, and ping, if you have any more questions.
pearl pondBOT
@long valley Has your question been resolved?
pearl pondBOT
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Available help channel!
lapis hatch
pearl pondBOT
lapis hatch
Trig with vectors but im slightly confused
west bluff
Trig with vectors but im slightly confused
What confuses you?
lapis hatch
So ive drawn out the triangle it forms
from origin to A and Origin to B with both values
lemme just draw it and show u
I think im not doing something right
pine jay
Where is the x-axis in relation to these?
west bluff
Recall AB=OB-OA
pine jay
It looks confusing
west bluff
Also, vectors are generally summed(and in consequence subtracted) according to the parallelogram rule
Never seen someone represent it as a triangle
lapis hatch
Never seen someone represent it as a triangle
my professor represents them using triangles ngl
when it comes to trigonemtry with vectors only
west bluff
my professor represents them using triangles ngl
That's certainly peculiar then
lapis hatch
Recall AB=OB-OA
so AB=(6i+2j)-(4i-j)
west bluff
so AB=(6i+2j)-(4i-j)
Essentially, yeah
lapis hatch
How will i find the angle it makes with the x axis then
west bluff
How will i find the angle it makes with the x axis then
Once you've got the vector, it will indeed form a triangle
Gimme a sec, imma graph it rq
lapis hatch
okay okay
west bluff
Alright, this is the vector that goes from the origin to some point
(any vector can be considered a vector of this form)
The red line is the vector itself
And the blue dot is the point where the vector ends
What can you say about that triangle?
lapis hatch
right angle triangle?
west bluff
right angle triangle?
Yup
And recall that in any right angles triangle you can apply the form of the trigonometric functions directly
Which values do you have in this triangle?
west bluff
so AB is the hypotenuese right?
Yup
west bluff
OA is the opposite
Not really
Look, im order to visualize this
Forget about the exercise for a moment
lapis hatch
okay
west bluff
And assume you've got a vector AB of the form(6,8)
What would the opposite and the adjacent be for the triangle it forms?
lapis hatch
6 and 8
lapis hatch
tan
lapis hatch
so then its
west bluff
Well, arctan to be more precise
lapis hatch
inverse function of tan
west bluff
But that's all you need to do
lapis hatch
would 6 be the adjacent?
west bluff
Yes
broken fossil
,tex .unit circle
jolly parrotBOT
Steel
west bluff
the answers wrong
I gave ya a random vector
lapis hatch
but it says its wrong
west bluff
You need to do this for your vector AB
lapis hatch
oh shit
im bugging
😭
sorry
2,3
are my values for AB
so then
this would be correct?
lapis hatch
2?
west bluff
If you've got a triangle with the point (2,3) at the top
lapis hatch
the angle is facing toward the x axis
west bluff
And another one of its vertices at (0,0)
lapis hatch
opposite would be 3
west bluff
opposite would be 3
Yup
I think you can go on from here, the answer should be correct now
pearl pondBOT
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Available help channel!
dire jewel
pearl pondBOT
worthy lance
!show
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
dire jewel
Ok according to product rule of counting
we should have3 options for the first integer
and 4 options for the 2nd
wait
wait no 3
but im confused as to what to fill in the blakns cause they kinda overlap
dire jewel
7 8 9 right
worthy lance
Yes, and how many options are there for the last digit?
dire jewel
like 4
worthy lance
Why 4?
dire jewel
it has to be odd so u can have 1 7 8 and 9 as the last digit
worthy lance
Which digits?
worthy lance
So when the first digit is 7, the last digits can be…
dire jewel
1 8 or 9
worthy lance
Why do you still think 8 is an odd number?
worthy lance
define odd
Go back here
worthy lance
So when the first digit is 7, the last digits can be…
.
dire jewel
1 7 9
worthy lance
(3 cases) and if first digit is 9, the last digits can be…
worthy lance
A total of (7 cases)
In the middle of each case you have 3 digits
In how many ways can you rearrange them?
dire jewel
we have choice of 3 for first digit
times choice of 2 for second digit
times.1 choice
so 6??
worthy lance
So we have
Case 1: 7 x y z 1 = 6 ways
You have 7 cases
What would be the total then?
dire jewel
ahh
so each first and last digit case
has 3 remaingi digits left
so like 6 subcases for each of the 7 cases
worthy lance
To rearrange in 6 different ways
worthy lance
Correcto
worthy lance
You are welcome
dire jewel
but i'm still cooked for product rule for counting cause idk how u would even think to approach it like that 😭
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
dire jewel
.close
round pollen
pearl pondBOT
round pollen
How do I find the derivative of this function? I need it to find the critical points in order to determine where the function is increasing and decreasing.
wet swallow
|u|=$\sqrt{u^2}$
jolly parrotBOT
David
queen ice
how would u do 2a?
pearl pondBOT
how would u do 2a?
queen ice
am i correct?
midnight haven
am i correct?
Yep
midnight haven
is final velocity 150 or initial?
What do you think?
manic sparrow
how would u do 2a?
is it constant acceleration
queen ice
yes
midnight haven
probably final
It's final
Initially the plane is at rest which makes the initially velocity 0
And the final velocity is measured the moment when the plane takes off which is when it has obtained enough ground speed of 150m/s
pearl pondBOT
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round pollen
Why is this the answer? Isn't -1 not in the domain of h, meaning it cannot be a critical point?
hard kite
it's an open interval, -1 is not included
At -1, its not defined*, but for any value greater than -1, it is increasing
,w graph (x + 5)/(x + 1)
jolly parrotBOT
round pollen
Hold on, the way I thought of it is -5 is a critical point. I set up a number line and determined an interval for which its increasing or decreasing
So like this pretty much
hard kite
nvm i misread
round pollen
.close
pearl pondBOT
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halcyon karma
Hi, do you know how y was isolated here?
pearl pondBOT
Hi, do you know how y was isolated here?
halcyon karma
summer imp
There's a sign error I think
halcyon karma
that's what I thought but when I try to use my isolation I don't get the right answer
summer imp
You divide both sides of the equation by 2 and then bring the x's on the other side
You'll need to factor x out of those terms
And then you're pretty much all set
Do you have a picture of your work?
halcyon karma
i scribbled it all out sorry, i'll try your method out right now though
I'm getting:
8 = 1/4pix + y + 1/2
8- 1/4pix - 1/2x = y
halcyon karma
x * (-1/4pi - 1/2) ?
summer imp
yes
halcyon karma
thanks i'll try it out
pearl pondBOT
@halcyon karma Has your question been resolved?
halcyon karma
I'm supposed to get a positive answer for x but I don't know where I'm messing up
i'll just skip over this since online resources tell me that our y answer is correct
.close
pearl pondBOT
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Available help channel!
midnight haven
Require help with the (b) part of this question
pearl pondBOT
Require help with the (b) part of this question
midnight haven
I have thought of drawing a perpendicular on the y-axis
to form PM
now sin theta = OP/(AP)
sin beta = (PM)/(OP)
sin phi = (PM)/(AP)
.close
pearl pondBOT
midnight haven
got the answer lol
pearl pondBOT
Available help channel!
sharp smelt
pearl pondBOT
sharp smelt
I'm kind of confused
Let's assume for the sake of contradiction that range(T)=null(T) is possible.
We now choice $a$; $a \leqq 5$ linearly indepndetly vector in each set
jolly parrotBOT
A dense set
sharp smelt
We thus have $2a=5$, but it's evident that this would mean the dimension of the subspace would be 2.5, which is absurd. Thus, we can only conclude that such a transfromation, where range(T)=null(T) isn't possible
jolly parrotBOT
A dense set
sharp smelt
Is this fine?
<@&286206848099549185>
It isn't injective as it doesn't have the null mapping , $T : V \to {0}$
jolly parrotBOT
A dense set
sharp smelt
oops
misread it
Let T(v), Q(v) be two non-injective functions from $V \to W$. We then have T(v)= T(u) for some $v,u$. We also have $Q(r) =Q(s) for some $r,s$
jolly parrotBOT
A dense set
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sharp smelt
I basically want to show it isn't closed under addition
In other words, I want to show that the sum of two non-injective linear maps, can be injective
Let $w_1,\dots, w_m $ be a set of linearly dependent vector in $W$, let $v \in V$., where none of the vectors $v_i,w_i$ are zero
\
Consider the following linear maps $T(v) = \sum_{i=1}^{m} a_iw_i$; $Q(v) = -\sum_{i-=1}^{m-1} a_{i}w_i$.
\
It then follows that $T(v) + Q(v) = a_mw_m$
\
$a_mw_m$ is a linearly independent
\
It also follows that $Q(v)+T(v)$ is injective as $a_mw_m-a_lw_m =0 \implies w_m(a_m-a_l) \implies a_m +l$
\
Thus ${T \in \mathcal{L}(V,W) : T \text { is not injective }}$ is not a subspace of $\mathcal{L}(V,W)$
jolly parrotBOT
A dense set
sharp smelt
How does this look?
pearl pondBOT
@sharp smelt Has your question been resolved?
sharp smelt
<@&286206848099549185>
signal atlas
We now choice $a$; $a \leqq 5$ linearly indepndetly vector in each set
what does this mean? The idea looks correct though (getting a dimension of 2.5)
sharp smelt
We chose $a$ linearly indepndent vectors in$\R^5$
jolly parrotBOT
A dense set
sharp smelt
dim(range(T))+ dim(null(T))
signal atlas
Probably should mention you used the fundamental theorem of linear maps or whatever its called in there
but yeah thats good
sharp smelt
okie
sharp smelt
**A dense set**
How does this look?
It's still missing some detali I feel
I shoudl probably mention that such that removing $w_m$ doesn't make the set linearly indepndent
jolly parrotBOT
A dense set
signal atlas
I gtg for a bit but I think it would be easier to just find a counter example
sharp smelt
That's what I've done
but thanks!
Let $w_1,\dots, w_m $ be a set of linearly dependent vector in $W$, let $v \in V$., where none of the vectors $v_i,w_i$ are zero. We chose $w_m$ such that removing it from the list , doesn't make the list linearly indepndent
\
Consider the following linear maps $T(v) = \sum_{i=1}^{m} a_iw_i$; $Q(v) = -\sum_{i-=1}^{m-1} a_{i}w_i$.
\
It then follows that $T(v) + Q(v) = a_mw_m$
\
$a_mw_m$ is a linearly independent
\
It also follows that $Q(v)+T(v)$ is injective as $a_mw_m-a_lw_m =0 \implies w_m(a_m-a_l) \implies a_m +l$
\
Thus ${T \in \mathcal{L}(V,W) : T \text { is not injective }}$ is not a subspace of $\mathcal{L}(V,W)$
jolly parrotBOT
A dense set
sharp smelt
Let's assume to the contrary. that $T(v_1),\dots, T(v_n)$ isn't linearly independent.That would mean for some $a_i$ all, not equal to zero $\sum_{i=1}^{n} T_i(v_i)=0$. We thus have $T(\sum_{i=1}^{n} a_iv_i)=0$ where $\sum_{i=1}^{n} a_iv_i \neq 0$. However, T is injective, and the only vector mapping to $0$ in an injective function, is the zero vector itself, thus we;ve arrived at a contradiction, and the set ${T_iv_i}$ must be linearly indepndent
jolly parrotBOT
A dense set
sharp smelt
pearl pondBOT
@sharp smelt Has your question been resolved?
sharp smelt
We know that $T: V \to W$. Thus every vector in the range of $T(v)$ has a pre-image in V. It thus follows that ${T ( \sum_{i=1}^{n} \alpha_{i}v_i})$ spans $range(T)$ . But $T(\sum_{i=1}^{n} \alpha_{i} v_{i}) = \sum_{i=1}^{n} \alpha_iT(v_i)$ by linearity. Thus $T(v_1),T(v_2) \dots , T(v_n)$ span $range (T)$
jolly parrotBOT
A dense set
pearl pondBOT
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Available help channel!
upbeat wigeon
how to do this? i have found the area of the triangle first but not the trapezium. I was thinking we find the area of the triangle and trapezium and subtract them but we dont have h.
upbeat wigeon
pls help and lmk if i was on the right track
green dew
ur gonna have to use the other formula of finding the area of triangles which is
bronze coyote
use sin area formula
green dew
A = 1/2 absin(α)
bronze coyote
find the big one first
green dew
then whats the issue
bronze coyote
and then use the big one minus the small one
upbeat wigeon
then whats the issue
how u find the orange cz i find the unshaded first
bronze coyote
its a big triangle
and the unshaded one is a small triangle within the big triangle
upbeat wigeon
yea
bronze coyote
so find the area of the big triangle
upbeat wigeon
OHHHHHH
bronze coyote
and minus the unshaded area from it
thick swallow
how to do this? i have found the area of the triangle first but not the trapeziu...
1/2 ab sinc bigger one - 1/2 absinc smaller one
upbeat wigeon
1/2 ab sinc bigger one - 1/2 absinc smaller one
yea that makes sense lol i overcomplicated it
thanks alot
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pearl pondBOT
thick swallow
😀
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gilded dew
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midnight haven
What is method of difference?
"The method of differences solves the series that are not AP or GP series. This method finds a sequence in series by subtracting the values of the series term." => https://unacademy.com/content/jee/study-material/mathematics/the-method-of-differences/ ; I think that's what you're trying to figure out.
midnight haven
And it's casted onto the equation, or at least you're trying to do that, in the sum of cube formula.
valid kettle
Help with problem 1 please
hint: start with $n^3-(n-1)^3$
jolly parrotBOT
@valid kettle
sleek junco
pearl pondBOT
pearl pondBOT
@sleek junco Has your question been resolved?
sleek junco
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sterile star
Hi guys
dapper kraken
How do I solve it?
use power of point to find OF, since OD and OE are radius of the circle, they are equal, use power of point again to find x
sterile star
use power of point to find OF, since OD and OE are radius of the circle, they ar...
Yo dude
I tried that but somehow it is 7x4 = 2(2r -2) instead of 7x4 = 2(FO), explain why?
dapper kraken
I tried that but somehow it is 7x4 = 2(2r -2) instead of 7x4 = 2(FO), explain wh...
i was thinking of 7x4=2(2OF+2) bit the first one also works
oh wait
sterile star
why is 2 getting added?
dapper kraken
power of point is from edge to edge, not really sure what its called
like it intersects the circle
OF is just to the center
sterile star
so 7x4 = 2x(OF)!
OOH
ok now I unerstand
so like 2(OF)!
I still have no idea where the extra +2 game from
Oh wait that is to make the other sie
dapper kraken
yeah
sterile star
Thanks bro and after OF is found we found radius an then do the same for x?
north talon
"Projectiles, a,b, are shot up with the same angle and starting velocity from points A,B respectively. If A, B are l apart, find the delay of launching b such that a,b hit midair"
chilly sand
"Projectiles, a,b, are shot up with the same angle and starting velocity from po...
Same angle?
So the horizontal distance and maximum height will be same
What's their initial velocity
chilly sand
Okay
iron basin
"Projectiles, a,b, are shot up with the same angle and starting velocity from po...
👍
you dont need to check for vertical as both uy and ay are the same
pearl pondBOT
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inland ingot
I need help asap
pearl pondBOT
I need help asap
north talon
I need help asap
well, for part A the total price is (price of mugs) + shipping, so if theres no mugs its just shipping
inland ingot
well, for part A the total price is (price of mugs) + shipping, so if theres no ...
huh
Elaborate Please?
oh shi
WAIT OH
oh
mb
inland ingot
well, for part A the total price is (price of mugs) + shipping, so if theres no ...
and Part B?
<@&286206848099549185>
ay where df the helpers at
north talon
just look at the definition of slope
pearl pondBOT
@inland ingot Has your question been resolved?
pearl pondBOT
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stoic siren
i need a trig function that connects the blue and red graph together including their derivative
regal herald
if only i knew what the functions were
pearl pondBOT
@stoic siren Has your question been resolved?
stoic siren
if only i knew what the functions were
also this is gonna sound weird but the derivative of the trig function has to decrease
not increase
so it starts at blue function and ends at red function by decreasing
not increasing
regal herald
w(x)=Acos(Bx+C)+D
w(8)=Acos(8B+C)+D=f(8)
w(8)=Acos(13.5B+C)+D=h(13.5)
w'(x)=-ABsin(Bx+C)
w'(8)=-ABsin(8x+C)=f'(8)
w'(13.5)=-ABsin(13.5x+C)=h'(8)
so this is the foundation, and also that
w''(x)=-AB^2cos(Bx+C)<0
w'(x)>0
you can probably do some fun stuff with all that but im too tired to
river lodge
pearl pondBOT
river lodge
can someone tell me what i did wrong here
dusty flame
Why do u think u’re wrong
river lodge
nvm i figured it out
pearl pondBOT
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light breach
How can I find an equivalent of a sequence u(n) where u(n+1) = 3/2.u(n) + o(1) ? I know it will be C.(3/2)^n but I can’t prove it
woeful crescent
How can I find an equivalent of a sequence u(n) where u(n+1) = 3/2.u(n) + o(1) ?...
is O(1) supposed to be U(1)?
and should it be (3/2)U(n) or 3/(2.U(n))
light breach
o(1) is a sequence that has 0 as limit
And it is (3/2).u(n)
woeful crescent
is it of the form -----> A(n+1) = rA(n) + C
light breach
In my exercise o(1) = ln(1+exp(u(n)))
It is not a constant so I don’t have direct formula
woeful crescent
a base case must be given for this recursion
light breach
Just u(0) > 0
I don’t have to find explicit formula but just an equivalent
I can’t formalize the proof that u(n)~C.(3/2)^n
woeful crescent
So it's this?
woeful crescent
if we take it to the power of e maybe itll simplify
We try to solve this recursion on k then take its log for a
this recursion looks hella tough tho
light breach
Yay it seems really horrible to solve
And i’m supposed to find k(n) ~ C^((3/2)^n)
I’ve tried to copy proof for geometrical recursion formula and then work on the other term but that don’t really help either
woeful crescent
is it a proving question? @light breach
light breach
I don’t understand what you mean
woeful crescent
whats the statement of the question
Find the expression for so and so
or
Prove that this recursion has the form so and so
light breach
Oh yeah of course it is « find an equivalent of u(n) such as… »
With only the recursion formula
By passing the equality under the ln it give something interesting
I just have to prove that the right term tend to 0
But I don’t think it is true 😭
woeful crescent
wait how did you get that n out of that ln. and how did you get that product can you show ur working
light breach
I’m using « télescopage » summation
I don’t know how to translate it
<@&286206848099549185>
plush bramble
,rccw
jolly parrotBOT
sweet radish
What are mathematical ways to model this? And then make predictions using the model?
sweet radish
So far I have come up with:
- Sinosudial model
- Lagrange interpolation (but then I can't really use that to make predictions)
I need at least 3 solid models, what else could I do?
snow sail
this is all the data?
snow sail
What are mathematical ways to model this? And then make predictions using the mo...
how about a fourier
which is basically sine
but who is counting
pearl pondBOT
@sweet radish Has your question been resolved?
sweet radish
this is all the data?
I am using two year data
sweet radish
how about a fourier
Do you know about a good tutorial for that :/
snow sail
Do you know about a good tutorial for that :/
look at any tutorial on fft
matlab has a command fft for it
but there are free libraries too
pearl pondBOT
@sweet radish Has your question been resolved?
midnight flicker
pearl pondBOT
pearl pondBOT
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
1
versed mica
double angle identity
cursive wraith
just use the double angle identities in reverse
versed mica
$\sin(2x) = 2\sin(x)\cos(x)$
cursive wraith
to get sin(...) = cos(...) for example
jolly parrotBOT
knief
versed mica
$\cos(2x) = 2\cos^2(x) - 1$
jolly parrotBOT
knief
wet swallow
midnight flicker
wet swallow
Not too sure LHS=RHS
versed mica
$-\cos(2x) = \sin(2x)$
jolly parrotBOT
knief
versed mica
Not too sure LHS=RHS
you’re solving for the values of x that make it true
no one said it was true for all x
wet swallow
you’re solving for the values of x that make it true
Oh ok I thought it was one of those: prove the identity questions
versed mica
nope
midnight flicker
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pearl grove
does anyone know wtf im looking at? cause i dont
pearl pondBOT
does anyone know wtf im looking at? cause i dont
willow chasm
something is missing
dreamy shoal
I’m stuck on this since yesterday it’s the last problem on my hw please help;-;
dreamy shoal
I don’t understand it people tried to explain but I just don’t
No idea how to do or what to do
pearl pondBOT
@dreamy shoal Has your question been resolved?
pearl pondBOT
merry carbon
No idea how to do or what to do
.[Do you know what a point of inflection is? Note they allow you to compute the slope of the graph by moving the slider]
pearl pondBOT
Available help channel!
upbeat wigeon
how do yk when u have to use cosine rule or sine rule
pearl pondBOT
how do yk when u have to use cosine rule or sine rule
tall flint
you've hopefully heard the mnemonic "soh cah toa"? That's how
upbeat wigeon
you've hopefully heard the mnemonic "soh cah toa"? That's how
im actually restarded
tysm
ive been doing so much cosine/sine rule and non right angled trig i forgot how to do normal stuff 
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pearl pondBOT
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orchid cobalt
pearl pondBOT
midnight haven
plug it back in
orchid cobalt
pearl pondBOT
rough forge
-sigh- i dont even know how to start this.
what have you tried?
orchid cobalt
ok lemme snap a photo!!
rough forge
(2x)² ?
orchid cobalt
OH MB 4x^2
rough forge
yup
jolly parrotBOT
bacc (unhelpful)
orchid cobalt
okok!!
jolly parrotBOT
bacc (unhelpful)
rough forge
Now it's stinky normal quadratic equation
rough forge
how did you get that
orchid cobalt
uhh
jolly parrotBOT
bacc (unhelpful)
heady finch
you have -4x on the right hand side instead of +4x
rough forge
yup
orchid cobalt
tysssm!!
rough forge
nuit
orchid cobalt
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river lodge
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river lodge
how do i determine the equation of this graph
ik x ints r on the top and va's are on bottom
but how do i account for the oblique asympotote
hasty citrus
whats the function?
cosmic raptor
that’s what you have to figure out
river lodge
whats the function?
thats what we need to find
hasty citrus
ah well
river lodge
@regal herald can i see what u wrote
pearl pondBOT
@river lodge Has your question been resolved?
fathom mauve
how do i determine the equation of this graph
ik x ints r on the top and va's ar...
are all 3 lines the same graph
or just one
river lodge
are all 3 lines the same graph
same graph
pearl pondBOT
@river lodge Has your question been resolved?
haughty hamlet
im confused about part b because i got701/729 but its nothingg close to 3√9
plush bramble
im confused about part b because i got701/729 but its nothingg close to 3√9
Show your work
haughty hamlet
well for a =i just expanded the equatio which gave me
1-(1/3)x -(1/9)x^2
then i just did x=1/9 into the expanded equatin
simplufued, and.i got 701/729
plush bramble
well for a =i just expanded the equatio which gave me
1-(1/3)x -(1/9)x^2
How did you get this expansion
haughty hamlet
through the binomial formula?
haughty hamlet
plush bramble
I see
haughty hamlet
yea
plush bramble
,calc 701/729
jolly parrotBOT
Result:
0.96159122085048
,calc 9^(1/3)
jolly parrotBOT
Result:
2.0800838230519
Oh
1-1/9 = 8/9
So you're supposed to do something with the 8
Factor it out of the cube root yea
haughty hamlet
what do you mean by that?
pearl pondBOT
Available help channel!
astral pebble
pearl pondBOT
astral pebble
7(III) I don't understand where I'm messing up in my differenatation
atomic ferry
lol
astral pebble
atomic ferry
this one amath ah
astral pebble
astral pebble
this one amath ah
Yea
atomic ferry
look like the textbook
astral pebble
Sg?
atomic ferry
jc
astral pebble
Damn
astral pebble
Oh
atomic ferry
leave it out its a constant
astral pebble
But I don't rlly understand from that part where I factor out 1/6 what rule am I supposed to use if I use product rule it's troublesome
atomic ferry
use quotient rule
astral pebble
Can I just use the quotient rule for the partial fractions and ignore the constant?
atomic ferry
no
astral pebble
Oh?
astral pebble
Ohhh ok
Oh so when I differentiate I can js differentiate one part only and ignore the others?
atomic ferry
ya if its a constant
pearl pondBOT
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pearl pondBOT
glacial sequoia
wdym by the left
2, 3, 4?
what do you think about 2?
what even is the difference between 2 and 3
what's the subscript notation mean
I see
cosmic garnet
what's the subscript notation mean
- for a bit left and + for a bit right
like 0+ and 0-