ohhh!
i see! ty!
#help-28
rare otter
swift shore
and the same thing for the y^2
rare otter
now lets see if itll accept that (the program)
okay it did! tysm! i was so confused lol
.close
viral oriole
hey guys, while calculating a limit near 0 if i have 0 in the numerator and denominator can for example (a+x)/x can i transform it to (a/x) +1 ?
swift shore
yes
candid ice
yes you can. limits only care about the function's behaviour around a point, and do not care what actually happens at the point
viral oriole
hey guys, i've got my finals next week! I would like some tips on how to make my demonstration more clear and understandable , as i always lose points because " i was not clear enough, or it was not properly written despite the primary idea being correct"
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hey guys, i've got my finals next week! I would like some tips on how to make my...
@viral oriole Has your question been resolved?
ivory cairn
make sure your notation is correct, make sure you continue to use notation while it is relevant, use sentences if you have to
use parenthesis when needed
solar hollow
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solar hollow
Why is this wrong?
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solar hollow
Thanks
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vapid barn
how can you use the tschirnhaus transformation to remove the linear term of a quadratic
vapid barn
$$x^2 + bx + c = 0$$
$$(x-x_1)(x-x_2) = 0$$
$$x^2 - (x_1 + x_2)x + x_1x_2 = 0$$
glossy valveBOT
EndTimes
vapid barn
$$-(x_1 + x_2) = b$$
$$x_1x_2 = c$$
glossy valveBOT
EndTimes
vapid barn
Let $$x = y + f(b,c)$$
$$y^2 + 2f(b,c)y + f(b,c)^2 + by + bf(b,c) + c$$
$$y^2 + (b+2f(b,c)) y + (c + 2f(b,c)^2 + bf(b,c))$$
$$(b+2f(b,c)) = 0$$
$$f(b,c) = - \frac{b}{2}$$
glossy valveBOT
EndTimes
vapid barn
Then we have:
$$y^2 + (c + \frac{b^2}{2} - \frac{b^2}{2})$$
vapid barn
wait nvm i figured it out
yeah just made a typo
it's supposed to be:
$$y^2 + (b + 2f)y + (c + f^2 + bf)$$
glossy valveBOT
EndTimes
vapid barn
when f = -b/2 we get:
y^2 + (c + b^2/4 - b^2/2) =
y^2 + (c - b^2/4)
which is exactly the same as completing the square
neat!
,w (x - b/2)^2 + (c - b^2/4) = x^2 + bx + c
glossy valveBOT
vapid barn
,w is (x - b/2)^2 + (c - b^2/4) = x^2 + bx + c always true
glossy valveBOT
Requested by EndTimes#8053
grizzled lance
,w is (x - b/2)^2 + (c - b^2/4) = x^2 + bx + c
glossy valveBOT
vapid barn
tf
no that has to be true
oh wait
i defined y = (x+b/2)
,w is (x + b/2)^2 + (c - b^2/4) = x^2 + bx + c
glossy valveBOT
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earnest tendon
is there anybody who could help me?
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is there anybody who could help me?
earnest tendon
hello?
cold saddle
please read #❓how-to-get-help
scenic reef
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rose nest
can anyone help me with this problem?
8x + 3y = 13
3x + 2y = 11
Here is what I did so far:
I moved the 2y from 3x + 2y = 11 to the other side, so:
3x = 11 - 2y
then I divided both sides by 3 so:
3x/3 = 11/3 - 2y/3
I then got x= 11/3 -2y/3
I then substituted my answer for X in the 8x + 3y = 13 equation and got:
8(11/3 - 2/3y) + 3y = 13
after distributing 8 through the parenthesis I got:
88/3 - 16/3y + 3y = 13
here is where I got stuck. After searching online I realized I was supposed to calculate the sum of 88/3 - 16/3y + 3y, which is supposedly 88/3 - 7/3y = 13, how do you get 7/3??
and how do you continue from that point? (I know the question is probs rlly easy but I’m stuck lol)
burnt pendant
can anyone help me with this problem?
8x + 3y = 13
3x + 2y = 11
Here is what ...
-16y/3 + 3y = (-16/3 + 3)y
sharp creek
Factor in y
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twin perch
how would i know to use the ratio test for this one?
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how would i know to use the ratio test for this one?
twin perch
we're trying to determine whether it converges or diverges
spice orchid
If you have something like $\frac{n^a}{b^n}$ then you're probably going to want to use the ratio test
glossy valveBOT
iCaird
spice orchid
Because the ratio simplifies somewhat nicely
wispy tusk
Number 16, answer key shows the answer is 17.09m but I’m not sure how to get that
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Number 16, answer key shows the answer is 17.09m but I’m not sure how to get tha...
@wispy tusk Has your question been resolved?
neon raft
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neon raft
how can I get rid of this product?
x, mu and sigma are all 3 vectors of the same size n
spice orchid
How do we simplify $e^ae^b$?
glossy valveBOT
iCaird
neon raft
that's e^{a+b}
I know it's gonna be a single exponential but how do I write it in vector form?
spice orchid
Vector form?
neon raft
yes. x, mu and sigma are vectors of size 1 x n
spice orchid
Right
spice orchid
that's e^{a+b}
Well use this
But you have n things instead of 2
The product goes away and instead you have a sum up top
neon raft
yeah and how do I get rid of the sum
$exp(\sum_{i=1}^n \frac{1}{2}(\frac{x_i - \mu_i}{\sigma_i})^2)$
this doesn'T looks very pretty
glossy valveBOT
Vertox
spice orchid
Well what's your end goal what are you trying to do
neon raft
this is what I'm trying to do
simplifying the last term
I got this now
here it's nice with the covariance matrix but that's from the joint probability density
now I have a single probability density so I can't use that covariance matrix
maybe I can just diagonalize sigma and then do the same?
like this but with 1 instead of 0
or should it be 0
well I'll play around with that idea
yep should work
.close
hoary basin
how do i find the solutions and the general solution of:
x^2y'' -x(x+2)y' + (x+2)y = 0
i made a post earlier but didnt end up getting an answer.. any help would be much appreciated, i dont know how to do these questions:)
plush egret
i always say power series solutions
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@hoary basin Has your question been resolved?
plush egret
i do think theres a less general method of doing these
hoary basin
i always say power series solutions
ive not learnt that at all so probably not? what would that working out look like?
hoary basin
i forget what power series is now lmao we havent learnt that in this course, its in some other course
plush egret
its a little bit of a hammer but it tends to shift the work from ODE into index fuddling and investigative work
ah
lemme see, i remember there being a nice way to do these i can just never recall it
hoary basin
okay thanks sm
cloud shore
how do i find the solutions and the general solution of:
x^2y'' -x(x+2)y' + (x...
Try a polynomial solution
knotty path
My bad
hoary basin
i think its a reduction of order question
although i forget how to do these questions even though i knew like a month ago
this is what i have currently
the I normally comes out to be a more normal number so thats why im unsure if i did something wrong
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median hemlock
should be 2u'x^2 instead of u'x^2
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torn jolt
How do I get the 1+cos out of the demoninator? I can find any identies to replace it with
light sonnet
Then you did that wrong
torn jolt
1-cos^2?
torn jolt
Ah ok ok ty
light sonnet
Then do you see what happens next?
light sonnet
What's cos/sin?
torn jolt
ohh you can separate them?
light sonnet
Yes because it's multiplication
light sonnet
What's cos/sin?
light sonnet
And cot is equal to?
torn jolt
1/tan
light sonnet
Ta da
torn jolt
Wth youre a magician
light sonnet
No I'm not
It's just realizing that you needed to start with doing (1 - cos) /(1 - cos)
torn jolt
Hmm wait so when multipling by the conjugate
1+cos and 1-cos will always equal 1-cos^2?
torn jolt
A little
light sonnet
That’s what you just applied
light sonnet
Too much to memorize in math sigh
That’s a very common concept, difference of squares
torn jolt
It terrorized me in gr 9
Factoring wasn't my think back then
So for the proof
Since tan is on the bottom we just multiply 1 by the 1-cos? to get final?
torn jolt
K
One last question
Did i do this proof right? I have a feeling something is off
With the ^4
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still mesa
Linear Algebra help about transition matrix
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Linear Algebra help about transition matrix
dawn torrent
be more specific
still mesa
How to find the transition matrix from one orded basis to another
lemme just grab a photo
How do I find the transition matrix from C to B
spice orchid
Assuming you've also been given a linear transformation, you need to apply the transformation to the basis C, and then write the result in terms of B, those will be the columns of your matrix
still mesa
I haven't been given a linear transformation
still mesa
How do I write C in terns of B
spice orchid
Or maybe it's the other way round, check your notes
still mesa
Or maybe it's the other way round, check your notes
Still a bit confused
dawn torrent
How do I write C in terns of B
for example $(x-1) = 1 \cdot 1 - 1\cdot x$
glossy valveBOT
Enoo58
dawn torrent
do it for (x-1)^2
still mesa
I have no idea 🥲
dawn torrent
first multiply everything out
still mesa
x^2 -2x +1
dawn torrent
yes now see how dou you express it in terms of B
dont overthink it you already have it
dawn torrent
here it is just reading it from the expression
if its more complicated you might need to solve a linear equation
still mesa
do i read it as a column vector ?
dawn torrent
you could
still mesa
so could it be [1 -2 1]
dawn torrent
exactly
still mesa
rightt
dawn torrent
do it for all three and they are your columns of your matrix
still mesa
okay what about if i was to go the other way
dawn torrent
this is where you might need to solve a linear equation
or if you already know if you have the Transformation from B to C, the one from C to B is just the inverse of the matrix
still mesa
That inverse sounds easy enough
dawn torrent
and you can always check by pluggin in one basis vector you should always get another one. So for example if T is our transformation from C to B you can check by:
T(1)=[1,0,0]= 1
T(x-1)=[-1,1,0] = x-1
T((x-1)^2)=[1-2,1] = x^2-2x+1
dawn torrent
T(X)=[1,1,0], because 1 + (x-1) = x
still mesa
where does the 1 come from
still mesa
so what would x^2 be
dawn torrent
you try it
still mesa
is it 1 + 2(x-1) + (x-1)^2 = x^2
dawn torrent
that would be x^2-x+1
its a bit tricky, try first getting rid of -2x and then see what happens with the 1
dawn torrent
correct
dawn torrent
thats good
still mesa
Thanks so much for your help! No doubt I will be back here soon
dawn torrent
no problem good luck studying
still mesa
.close
brittle monolith
e^(2x)=0 is not valid because e can't be equal to zero or negative right?
void wedge
e is a constant which is approximately equal to 2.718
that equation doesn't have real solutions yes
viral nexus
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viral nexus
can someone help me with this?
im seeing contradicting answers..
for a) , I believe the ans should be 21+2=23 bits
and im not sure what word addressable is anymore
.close
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lone flower
Hi i need help with question ii
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Hi i need help with question ii
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lone flower
<@&286206848099549185>
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hybrid fossil
whats this formula called
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whats this formula called
spice orchid
standard deviation formula for a sample of size n
hybrid fossil
thanks!
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harsh meteor
Hey, I'm stuck on this one
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Hey, I'm stuck on this one
harsh meteor
Not sure what to do next and I don't understand the solution
I'm not sure about that
spice orchid
line 3 to line 4 why did you put x^2+1 back in?
harsh meteor
I just don't know what to do next
I usually do it when I solve this kind of integration
glossy valveBOT
iCaird
harsh meteor
this part doesn't make sense
spice orchid
thats the power rule for integration
harsh meteor
ah right
spice orchid
add one to the power and divide by the new power
harsh meteor
I'm just not used to see it in that way
I just do it without thinking of it
writing the answer
I will try to do it now
Thank you so much iCaird!
spice orchid
You're welcome
proud dagger
I already asked how to solve sin x + cos x = 1.2
I was told to use the compound angle formula but i dont know how this is going to help me because i end up with sin x + cos x = 1.2 somehow
spice orchid
gritty rose
$R\cos(\alpha) = a$ translates to $\sqrt{2}\cos(\alpha) = 1$. Solve for $\alpha$
glossy valveBOT
riemann
proud dagger
thx
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cold kernel
Hey, I have a really long list of empty cells in which I can store numbers. I can do 5 operations:
>move to the right by one cell<move to the left by one cell-subtract 1 from the number in the current cell+add 1 to the number in the current cell."print" number from the current cell
Using this set of moves i need to produce these numbers:
84 101 99 104 110 105 107 32 105 110 102 111 114 109 97 116 121 107
what 3 starting numbers will require the shortest amount of moves to generate these numbers?
cold kernel
Or maybe someone could tell me on which channel i could ask?
wild sleet
moves or operations?
and you have to start with three numbers fit together or they can be spaced apart?
i guess there's no point in spacing them
cold kernel
moves or operations?
operations yeah
cold kernel
i guess there's no point in spacing them
yup
cuz that will just require more moves
(moves and operations mean the same thing)
cold kernel
polish
wild sleet
ok
i don't know how to do it, although you probably start with 32
essentially only use 2 cells
cold kernel
<<.<<-----.--.+++++.>.<+.<-.<.>>.>.<---.>+.+++.<<++.>-----.>++.+++++.<<--. thats my solution so far but with 5 numbers
32 108 106 110 84
also, lets ignore this limit what 3 starting numbers
wild sleet
without the limit you do .>.>.>.>.>.>.>.>.>.>.>.>.>.>.>.>.>.
cold kernel
but then i need to find a way to generate starting numbers
do you know brainfuck by any chance?
cold kernel
oke
neat bay
@cold kernel I don’t understand, don’t you need more than 3 starting numbers?
Why can’t you just choose
84 101 99 104 110 105 107 32 105 110 102 111 114 109 97 116 121 107
as the starting numbers?
wild sleet
they actually start with no numbers and they make some numbers at the cost of more moves
for some reason they separated it into 2 tasks
cold kernel
yeah cuz generating starting numbers is more complicated
+[+[<++>--->>+>-<<<]>--] thats how i generate my 5 starting numbers
it requires loops
wild sleet
yeah it makes sense
cold kernel
i just wanted to simplify my problem for ya
cold kernel
honestly, i just bruteforced maaaany loops
wild sleet
yeah i see
cold kernel
and this one had the best starting numbers
wild sleet
so you actually have an impressive solution
cold kernel
yep
it is not bad
but i was wondering if there is some mathematicall way
to find best numbers
wild sleet
right
cold kernel
or maybe some correlations between them
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marble atlas
Help pls
static leaf
marble atlas
Wait I can show proof it's done
here's 55
I finished it awhile ago people said the answer is 11 although I don't know why
In all honesty I just wanna know how to answer the things I didn't know about
Like 23 and 24 I don't even undersatnd it
<@&286206848099549185>
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marble atlas
I think this is a and d
but I'm still not sure of the rest
<@&286206848099549185>
hollow spire
How many lines are there from/to each of the vertices
marble atlas
How many lines are there from/to each of the vertices
for the eucler I'm not so sure?
The only thing I'm sure of is that a and d is odd
hollow spire
For this, you just want to count how many edges touch each vertice
marble atlas
Yah I understood that already, took a while for me to get it
hollow spire
So how many odd nodes are there?
hollow spire
And can you make a path if you have two odd nodes?
marble atlas
uhhh, I don't even know what you mean by path
hollow spire
A path is just a series of nodes that are connected to each other, so a path like a b e c d would make a z shape. A Euler path is a path that does through all of the edges.
Does that make sense?
hollow spire
No, that is just one vertex, the Euler path is a path.
marble atlas
ah so eabdc?
hollow spire
Not quite, since it doesnt go through the edge from d to e, for example. You are allowed to repeat vertices, just not edges.
marble atlas
eacdb
hollow spire
How many edges are there?
marble atlas
8?
hollow spire
Almost.
marble atlas
10?
hollow spire
Yes. So if you have a Euler path, it has to go through all 10 edges. The paths you have said only go through 4.
marble atlas
eacdbeceba?
hollow spire
How many edges does that do through?
marble atlas
10 I think I hit all of them circling around the image
hollow spire
how many edges are in the path ab?
hollow spire
So there are two vertices, but one edge. So if you have 10 vertices, how many edges do you go through?
hollow spire
Not quite, what about the path abe, how many edges does that go through?
marble atlas
4?
hollow spire
Can you explain why?
hollow spire
that would be abea, not abe
but for abea, what is the difference between the number of vertices and the number of edges
marble atlas
but then aren't I moving in the parameters of abe
hollow spire
what do you mean by that?
marble atlas
like I still move in a b and e like I never left
I kinda don't understand why that became abea
hollow spire
I think you are thinking of a circuit, which is a path that ends at the same place it starts. That isnt true in general for paths.
If you go from a to b, then to e, then back to a, the order you visit the vertices is abea
So that is the name of that path
marble atlas
oh
hollow spire
So it has 4 vertices and 3 edges, right?
marble atlas
yes?
hollow spire
So what do you have to do to get from the number of vertices to the number of edges?
marble atlas
I have to hit the vertices once
hollow spire
So its:
2 vertices to 1 edge
4 vertices to 3 edges
what do you think the pattern is?
hollow spire
You just have to subtract one from the number of vertices, right?
marble atlas
uhhh
torn jolt
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torn jolt
Proving this is hard
I did
Trigonometry identities
This ^^ addition/subtraction identities but I can’t think after
On what to do next
dim wolf
I have done it
I can help
So the first step you did is right
Then what i did was foil it out
@torn jolt
torn jolt
Ohh
dim wolf
Try it from there
torn jolt
I will wait
@dim wolf will it be squared when foiling it
Or will it cancel
Cause when I foiled it
torn jolt
Oh yeah
What do you do next
I’m just confused on what’s next
That’s all
(Just a clue / hint is fine)
dim wolf
Yeah
torn jolt
but I got it right
dim wolf
Distribute
torn jolt
dim wolf
Yup
torn jolt
THANK YOUU!!
dim wolf
👍
stray oak
Hey guys
stray oak
I am not sure where to draw the tangent exactly and sketch the circles making an isosceles triangle. Can someone be able to explain it to me please?
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stray oak
<@&286206848099549185>
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astral field
say that a trigonometric function: y = a sin ( b ( x - c ) ) + d is designed to model the cyclic pattern of tide levels in a real world situation. In that case, what would the variables a,b,c, and d represent in real-life context?
can I simply answer that a + d is equal to the high tide, d - a is the low tide, 2 pi / b shows the time it takes to complete one cycle of the change in tide levels? in that case, I'm confused what variable c would represent.
or are do the four variables literally represent something in a real world context?
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say that a trigonometric function: y = a sin ( b ( x - c ) ) + d is designed to ...
@astral field Has your question been resolved?
astral field
<@&286206848099549185> it says after 15 minutes passes, you're allowed to ping the helpers.. so here it goes
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velvet marlin
say that a trigonometric function: y = a sin ( b ( x - c ) ) + d is designed to ...
a +d is the highest a tide can go, d - a is hte lowest, 2pi/b indeed shows the tide. Now, the c simply is the starting value. So for example, if it started at high tide, you can't let it just be y = asin(bx) + d. X is time, so at time t = 0, y should be a +d , but instead it's 0. So we put a c value to fix that
astral field
a +d is the highest a tide can go, d - a is hte lowest, 2pi/b indeed shows the t...
so in either real-world scenarios or mathematical contexts, C is always just the phase shift. and no other meaning?
velvet marlin
so in either real-world scenarios or mathematical contexts, C is always just the...
👍
velvet marlin
tysm that was clear.
Don't forget to close 🙂
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vapid barn
Prove that the cross product is linear and distributes
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Prove that the cross product is linear and distributes
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rugged harbor
Hi! I have a homographic function (equation not given). I have a point ∈ (Homographic curve) and the center. How do I mirror a point to get it to the "other side" of the homographic equation?
rugged harbor
Something like this
With A(0, 1) and C(2, 1) how do I find A'?
Ok, so I understood that I don't need A' to be on the other side of the curve, it just has to be another point ∈ (Homographic curve)
So I can mirror with axis of symmetry: y - yA = (x - xP)
But still, I don't know how to do it
<@&286206848099549185>
lean copper
find out the symmetry of the whole curve, which is the symmetry of the set of all points ∈ (Homographic curve)
Now obviously it is symmetrical about the center, then the point on one side must be symmetrical to the other side through the center
rugged harbor
Yes, the problem is that I don't know how to mirror a point with respect to an inclined line
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round wadi
quadratic with x intercept 2 and -4 and y intercept 4 whats the range
restive kelp
did you figure out the EQN itself?
round wadi
did you figure out the EQN itself?
the what?
round wadi
quadratic with x intercept 2 and -4 and y intercept 4 whats the range
nah the question is just like this idk how to solve it
restive kelp
well xd
restive kelp
did you figure out the EQN itself?
start with this then
round wadi
start with this then
how
restive kelp
you know the roots
round wadi
yes 2 and -4
restive kelp
so you know the factors for the quadratic, right?
round wadi
(x-2)(x+4)?
round wadi
so its (x-2)(x+4)+4?
restive kelp
no
restive kelp
?
restive kelp
With quadratics (x + 1)(x - 1) = 0 bro
and ist not even true
hollow wigeon
In quadratics it is
restive kelp
only you havent seen any other type yet
restive kelp
pls dont troll the channel, im asking you again
restive kelp
Just trying to help jeez
to whom?
hollow wigeon
Not all help has to be portrayed in a serious matter
Who do you think?
You?
He said quadratic so I’m just inputting some knowledge
Freedom of speech
restive kelp
@round wadi so you have (x-2)(x+4) but the y intercept will be incorrect yet, so u have to transform it, but be careful to not change the roots
round wadi
<@845959241432956928> so you have (x-2)(x+4) but the y intercept will be incorre...
how do i do that
and how can i do that fast since in my exam u have about 1 min/question
restive kelp
multiply it
when we are done look at the steps and memorize them, and thats how you will be able to do it in 60 seconds too
restive kelp
<@845959241432956928> so you have (x-2)(x+4) but the y intercept will be incorre...
first, calculate the y intercept in this form
and then write: a(x-2)(x+4)
round wadi
x^2+4x-2x-8
restive kelp
so the y intercept will be...?
round wadi
-8?
round wadi
add 12 to the whole thing?
restive kelp
so what will 'a' be?
no, with that you make ur roots change
because if you substitute in 2 you will get 12
restive kelp
and then write: a(x-2)(x+4)
thats why i wrote it like this
round wadi
A=2?
round wadi
-1/2(x^2+2x-8)
round wadi
4.5
restive kelp
note that the parabola is symmetric
round wadi
-0.5x^2-x+4
?
round wadi
f(x) less than or equal to 4.5?
restive kelp
yw
round wadi
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feral holly
if I have 16 IR codes which are 100001 to 111111 and there are 8 emitters and one receiver. Each emitter gets to send two codes for example emitter a has 100001 and 100011. The codes have to be arranged in a way that if all the emitters emit and some codes overlap at least one code from each emitter is received.take for example that there are two emitters and 1 represents code being sent and 0 represents code not being sent then for the two to emit and for at least one code to be received the order of emission and not emission for the first emitter should be 1001 and for the second 0110. if the first two ones overlap then the second two are recieved and vice versa. how to find the order of emission for all 8 emitters?
torn jolt
if I have 16 IR codes which are 100001 to 111111 and there are 8 emitters and on...
uhmm
can you clarify your example? @feral holly
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feral holly
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safe saddle
hey, how would i solve this? $e^3 = 3$
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hey, how would i solve this? $e^3 = 3$
glossy valveBOT
killua
tidal citrus
Check your laws of logs/exponents
This has to do with the inverse nature of logs and exponents with the same base
This is an easy problem once you find it.
echo lance
hey, how would i solve this? $e^3 = 3$
did you mean $e^x = 3$?
glossy valveBOT
Doggo
echo lance
$e^3$ is about 20 but 3 is just 3
glossy valveBOT
Doggo
echo lance
take natural log of both sides then
glossy valveBOT
killua
sleek apex
yes
And using property of logs you can turn lne^x
Into xlne
And lne is one
so that means x=ln3
fast sleet
could i use a random variable $X$ with $X~Bin(n,\frac{1}{c})$, being the total number of types found ?
fathom saddle
X isn't binomial, no. These aren't independent trials
glossy valveBOT
Rœmer
fast sleet
oh yeah of course, the probability changes if i find a new type of coupon
fathom saddle
The distribution for the number of coupons in n draws is difficult
However, the expected number of draws to find them all is well known!
fast sleet
is that $(c-1)!$ ?
glossy valveBOT
Rœmer
glass crystal
start simple and call (Xk)k>=1 the coupon you draw at step k, then try to build the event: i got all coupons at step n
think i would introduce : $p_{n,k}$ the probability of having k coupons at step n and try to find recurrence relations between those
glossy valveBOT
Benjamin
fathom saddle
I'm personally thinking about counting the number of ways to do n draws from k types of coupons, and not find them all
fast sleet
can't i just consider the amount of draws i need separately for each coupon type that i don't have yet?
so like a geometric distribution for all types separately
then find an expected value for that and then add up all expected values ?
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latent breach
im on the right track I think
the series from
1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 ... 1/10
wat I failed to realize last time due to my lack of concentration is that it stops at a certain point
$\frac{7381}{2520}$
glossy valveBOT
jpjthunder
latent breach
it says it is wrong
glass crystal
it doesnt stop in this case though
latent breach
wdym
glass crystal
well the sum goes to infinity
latent breach
it keeps adding on to infinity yes but after the first number reaches 1/11
it just starts cancelling out right?
latent breach
alright makes sense just trying to figure out why it doesnt add up to that number
Oh
I forgot ot multiply it by 1/5
I think
I got it
ty for u help honestly
latent breach
oh dang
I will need to practice some sigma notation algebra
but for now
doing this one now
I think I could just idk
glass crystal
just the first term is left
latent breach
oh I read it wrong that is why I got the wrong answer
@glass crystal is it really not 4?
glass crystal
consider only the partial summ
you have the term in N left
and the term in 1
and then you take the limit to know the sum
usually the term in N goes to 0
so only the term in 1 is left
but here that's not the case
latent breach
trying understand this sum notation like I understand why N+1
glass crystal
you wanna go on a voice call so i can explain it?
latent breach
yea sure
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magic roost
Course: Logic and proofs
Why is this function injective?:
h:Q-->P(Q)
x|-->{x}
Example: Wouldn't h(3/4) and h(75/100) share the same image which would prevent this function from being injective?
glass crystal
to prove injectivity in general:
for all x and y in your starting set
such that f(x)=f(y)
then x=y
magic roost
Just different ways of writing it
I understand that part, but wouldn't x=3/4 and x=75/100 both result in {3/4}?
cloud shore
I understand that part, but wouldn't x=3/4 and x=75/100 both result in {3/4}?
What's h(75/100)?
magic roost
But they are the same number, so injectivity isn't broken
Ok, that's what I needed to know. Thanks.
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loud sun
j
hasty tundra
so you have the normal vector n
hasty tundra
your k is wrong I think
loud sun
oh how come
loud sun
j
hasty tundra
and you plug in the point P
loud sun
yes
hasty tundra
yes
hasty tundra
yes
hasty tundra
for which you have the dot product
so is valid if you could do the calculation
for matrix multiplication, you have to have the columns of the first matrix equals the rows of the second
loud sun
for matrix multiplication, you have to have the columns of the first matrix equa...
for the first option we have column = rowj
j
yT x?
they also have column = rowj
j
hasty tundra
that valid thing is for the first question
for b you also have to check it's dot product
y^Tx is a dot product
loud sun
j
hasty tundra
so dot product
if you have two vectors
a = (a1, a2, ... , an)
b= (b1, ...., bn)
the dot product is a1b1 + a2b2 + .... + an*bn
first it will be two vectors of the same size.
second the product will be 1by1 (a constant)
so the vectors are in the form of (1 by n) * (n by 1)
hasty tundra
xd
loud sun
j
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fossil frigate
Hi, does anyone know what kind of equation it is if the second difference of my sequence has a ratio
fossil frigate
I thought it was just ratio to the power of n but I think that only works if the first difference has a ratio
hot herald
wdym by "has a ratio"
fossil frigate
So the second difference is like, 3, 9, 27, etc
So because the ratio is 3 since you multiply the previous number by 3
I thought it was exponential like 3^n
But that didn’t work for my sequence
My sequence is 13,74,435,2596,15557
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vast cove
Hi there
vast cove
I am on my way to prove the Ratio Theorem. (That is how we call it, idk if it is the same everywhere)
onyx glen
ratio test
vast cove
lol
I was looking at another theorem all this time instead of the right one...
which is the ratio test
anyways
thanks
lol
cya later 😛
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ocean narwhal
Hello everyone
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Hello everyone
ocean narwhal
I am new here
I have a problem
Could anyone help me? Much appreciate!!
I stuck here... don't know how to take the limit from here
quaint gyro
is this mulivariable calc? @ocean narwhal
ocean narwhal
Yes.
quaint gyro
maybe ask in #multivariable-calculus
you're more likely to get a quicker and better response there
storm olive
Can someone check if my work is correct? The question is on the second file
fathom saddle
What is A: E1, E4 supposed to mean, lol
Don't copy their terrible notation
Yeah that looks good
100% likely to get any event in Ac U B
torn jolt
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torn jolt
How do i solve his question?
Theres 6 sides but im not sure where a and b is soposed to be
magic harbor
yo
torn jolt
yo
magic harbor
have u draw it out
torn jolt
Forgive me drawing skills
The dots at the top was there to help with drawing since I keep drawing an octagon
magic harbor
ru sure b is not O->B rather than A->B
torn jolt
No idea
All i know is A and B both have their own position vectors
im not sure where a or b goes or which one it belongs too
magic harbor
ye so b is 0->B
torn jolt
yeah
magic harbor
so A->B = b-a
torn jolt
So from B to C is A->B and A->?
magic harbor
not quite
torn jolt
?
magic harbor
i u want me to draw for ya
torn jolt
Wait
let me draw
cause im learning
you already know
Wait let me make it bigger
Is AB and OC parallel?
wait no..
magic harbor
ye
torn jolt
;o
magic harbor
so O->C is y(A-B)
magic harbor
they are parrel, therefore u need to find what u can times b-a by to find O-C