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#help-28
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stiff quartz
Hello, say I have a 2d orientation basis matrix, for example the identity matrix, and I have a 2d vector [x, y]. How would I get the angle between the heading direction and the 2d vector.
gritty rose
Hello, say I have a 2d orientation basis matrix, for example the identity matrix...
what is the "heading direction"
gritty rose
okay so you want pi/4 from the matrix?
stiff quartz
ye
gritty rose
you can take arcsine and/or arccos of the entries
stiff quartz
gritty rose
or just take the arccos of that of the normalized dot product of the two vectors
stiff quartz
the column vector?
gritty rose
stiff quartz
yea
so the 2nd column vector represents the y?
my linear algebra skills are rusty lol
gritty rose
what don't you understand here? do you not understand the dot product
stiff quartz
i dont really understand the matrix
the basis matrix
I know I can represent the heading angle as a scalar
but im trying to do it with a 2d basis matrix
gritty rose
stiff quartz
ye I know the dot product
gritty rose
why do you need to understand the matrix at all?
you just need to understand matrix-vector multiplication
stiff quartz
this formula is for two vectors
gritty rose
matrix times vector = vector
stiff quartz
ye
gritty rose
yes you should be using the formulas that give you the angle
stiff quartz
i see thank you
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mortal owl
what is 2x^2 + 3x^3
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what is 2x^2 + 3x^3
keen shoal
what are you trying to solve
mortal owl
okay and
wide sundial
That’s it
keen shoal
basic addition and subtraction
mortal owl
I'll type out my answer and you guys can check if it's right
-x^2+7x^3 2y^2
yeah I think I didn't get the idea
wide sundial
Show your working out
mortal owl
I made it into 9x^2 y^3 -10x^2 y^3+4x^3 y^2 + 3x^3 y^2
keen shoal
subtract/add like terms
mortal owl
I made it into 9x^2 y^3 -10x^2 y^3+4x^3 y^2 + 3x^3 y^2
is this even right though
keen shoal
looks right
keen shoal
where is y^3 - y^3
mortal owl
2xy?
mortal owl
-xy?
keen shoal
yes
torn jolt
@mortal owl i need help with the square root
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<@453930365946429442> i need help with the square root
rugged narwhal
What’s the question?
mortal owl
wait what
crystal delta
crystal delta
HELP PLEASE
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junior geode
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junior geode
I need help on question 61
I have (y-1)^2 = -x
and then im lost
because no negative square roots on the real plane
viral jasper
You are correct
So ask yourself what the domain could be to make the square root not be negative
junior geode
-x >= 0
x <= 0
Any x equal to or less than zero
junior geode
Alright
Nearly there
Just still need to determine how to find the bottom half of the parabola
viral jasper
You can try graphing
junior geode
,w plot(1 + sqrt(-x))
glossy valveBOT
junior geode
,w plot(1 - sqrt(-x))
glossy valveBOT
rugged narwhal
Did i answer question 5 correctly?
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Did i answer question 5 correctly?
rugged narwhal
astral sinew
a doesnt even make sense
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crystal delta
Bro fr? @viral jasper
crystal delta
I asked for help for so long
stiff musk
!15min
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stiff musk
emphasis: Please do not ping or DM individual users about your question.
viral jasper
Bro fr? <@374795910032523266>
Where do I come in on this? 
crystal delta
I was asking for help for so long I pinged helpers twice and nobody came!
I still need help@
!
viral jasper
So why you pinging me specifically?
crystal delta
Because you are in chat which means you saw me pings and ignored them!
viral jasper
I don't get notified from Helpers ping, and even if I did, I have no obligation to help
keen shoal
no one will help if the question isn’t even readable
upload a better picture or type it
empty sapphire
Mm sure
The fact of the matter is that we're here on a volunteer basis, which unfortunately means that
- help will not always be available
- helpers can and are selective about what they work on
- there's not an obligation to help out with a problem if they don't feel like they're up to the task or if they decide there's a personality conflict with a person
- Just because someone's a helper doesn't mean they know how to solve problems. For example I help out here mostly with calculus problems and maybe some adv math stuff but I'm super weak on my geometry stuff since I haven't done any of it since like the 6th grade
crystal delta
O
Anyway i will be super respectful and post a clearer image
If anyone can help me It would be amazing this is one of the last problems i need help with before I finish my finals!
viral jasper
this is your final?
crystal delta
No it is a homework that I need to finish before I start my finals
My teacher is cool and he is about to lose his job so he made the final another home work assigment
professor*
viral jasper
Wish I could help, but I don't know econ
empty sapphire
oh damn I wish I could help with this.
yeah same
econ is not something i've taken before :/
crystal delta
dang this is super hard and I find patterns but they always mess up
stiff musk
i'm no expert on these sorts of questions, but i would first try working out what the balance is on day 14 before the $57.92 purchase is made
then add the purchase
then work out the balance on day 23 before the late fee
then add the late fee
etc
terse karma
Yeah
terse karma
dang this is super hard and I find patterns but they always mess up
Start with it
crystal delta
Ok i will try!
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crystal delta
Yea It isn't working
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runic spruce
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runic spruce
in this step i dont get why 1 + h -1 is important
because in our formula booklet it just says h
so i dont get where that comes from?
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@runic spruce Has your question been resolved?
robust slate
because in our formula booklet it just says h
You're conflating the gradient expression with the limit definition of the derivative
The x coordinates of the points are 1 (from point P) and 1+h (some small distance away)
calm sun
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calm sun
can someone help me through this? I don't understand how sir got to that answer
robust slate
can someone help me through this? I don't understand how sir got to that answer
Expand out the numerator, divide all the terms in the numerator by $2\sqrt{x}$, and apply power rule
glossy valveBOT
Civil Service Pigeon
calm sun
Expand out the numerator, divide all the terms in the numerator by $2\sqrt{x}$, ...
how do you divide it by 2 root x?
robust slate
Rewrite $\sqrt x$ as $x^{1/2}$
glossy valveBOT
Civil Service Pigeon
calm sun
is 2 root x the same as root x?
robust slate
No
calm sun
what can root x be re-written as then? x^2?
robust slate
**Civil Service Pigeon**
...
calm sun
oops I meant 2 root x
robust slate
$2\sqrt x$ is the same as multiplying $\sqrt x$ by $2$
glossy valveBOT
Civil Service Pigeon
robust slate
Take that as you will
terse karma
$2\sqrt x$ is the same as multiplying $\sqrt x$ by $2$
He mean $\sqrt[2]{x}$ I guess but idk
glossy valveBOT
fäf
calm sun
Expand out the numerator, divide all the terms in the numerator by $2\sqrt{x}$, ...
I got it now, I was just very confused on how to take 2 root x as, but you helped a lot so thank you !
runic spruce
for 10b
runic spruce
they've let m = that so it remains positive?
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faint bobcat
pls help justify option b
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pls help justify option b
faint bobcat
<@&286206848099549185> waited half an hour in other channel for this already no response pls help
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faint bobcat
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dim compass
If $$B=C$$ Can you premultiply A on both sides if $$|A|=0$$
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If $$B=C$$ Can you premultiply A on both sides if $$|A|=0$$
dim compass
context...
I mean if you can premultiply A on both sides of B=C if |A| is equal to 0
brave blaze
but what are A, B, C
you didnt define anything
glossy valveBOT
Calamity
dim compass
but what are A, B, C
you didnt define anything
Oh, mb they are square matrices
brave blaze
and what |.| means ?
dim compass
It's sign for determinant of Matrix
In this case it's determinant of A
I had this question because when it's AB=AC but |A|=0 you can't get to B=C as A inverse doesn't exist
brave blaze
If B = C
you can still multiply A on both sides
its a thing about regularity if I remember
dim compass
If B = C
you can still multiply A on both sides
And also if |A|=0
dim compass
its a thing about regularity if I remember
I see
brave blaze
but I could be wrong too, so lets wait for someone to confirm
dim compass
Oh okay!
Even if you can get from B=C to AB=AC when |A|=0, you don't seem to be able to reverse the process
brave blaze
Yea
dim compass
So I found this weird
brave blaze
But if AB = AC implies B=C, it means A is regular on the left
but I think A must be invertible
dim compass
But if AB = AC implies B=C, it means A is regular on the left
Wait, what does regular means?
brave blaze
oh its just some words we use in group theory lol
dim compass
but I think A must be invertible
Yeah only then you can premultiply A inverse to make that into B=C
dim compass
oh its just some words we use in group theory lol
I see
brave blaze
but maybe thats not the correct word in english
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strange sonnet
hello
strange sonnet
need some help finding total distance traveled
if v(t) = 8-2t over [0,0.5]
what i did was set the equation to 0 and found t = 4
oak shadow
@strange sonnet
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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
strange sonnet
could you delete that message i would like to work through the problem
i already know the answer from before hand
just trying to understand step by step
oak shadow
The function is linear, with a negative slope of -2. This means that the object is slowing down at a constant rate.
The initial velocity is 8, and the final velocity at t = 0.5 is 7. This means that the object is moving in the negative direction (since the velocity is decreasing), and is still moving in the negative direction at the end of the time interval.
The distance traveled may not be the same as the displacement, since the object changes direction at some point during the interval. If the object changes direction exactly once, then the distance traveled will be the sum of the distances traveled in each direction.
strange sonnet
okay so i have the value t = 4
now how would i know which interval is positive and negative?
oak shadow
You can determine the sign of the velocity function over each subinterval to determine the direction of motion, and therefore the sign of the distance traveled on each subinterval.
For the subinterval [0,4], the velocity function is v(t) = 8 - 2t. This function is positive for t < 4, which means that the object is moving in the negative direction (since the velocity is decreasing). Therefore, the distance traveled on this subinterval will be negative.
For the subinterval [4,0.5], the velocity function is v(t) = 2t - 8. This function is positive for t > 4, which means that the object is moving in the positive direction (since the velocity is increasing). Therefore, the distance traveled on this subinterval will be positive.
So the total distance traveled will be the sum of the absolute values of the distances traveled on each subinterval. The sign of the total distance traveled will be negative, since the distance traveled on the first subinterval is negative.
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scenic wren
heyyy
scenic wren
i have this proof
which is not entirely correct
as far as i know, the fact that f is bounded is important
any idea which step depends on that?
torn jolt
wouldn't bounded be used for existence of the integral?
scenic wren
uhm
torn jolt
ie, everything is finite
scenic wren
but aren't there improper integrals?
where stuff is not finite
or is that not yet a thing with riemann integrals
yeah i think you are right
torn jolt
I cant think of a counterexample rn
ocean helm
Is there a symbol to represent a concatenation of numbers? Like I have X = 1 and Y = 42, and I want to represent the concatenation of X and Y, in a way that X (concatenation annotation symbol) Y = 242
ocean helm
I have searched but I didn't find anything relevant
upbeat crag
draw a line above XY
torn jolt
Is there a symbol to represent a concatenation of numbers? Like I have X = 1 and...
X||Y is a common way to write it
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torn jolt
X||Y is a common way to write it
By the way, this is where I got it from:
https://www.youtube.com/watch?v=pasyRUj7UwM&t=30s&ab_channel=Numberphile
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vocal coral
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vocal coral
how would you do this
torn jolt
use a calculator and the unit circle
proud briar
or… just a calculator
vocal coral
could i just do sin 3/4
torn jolt
ok but on my test im not allowed a calculator
this type of question will not be given in a no calculator test
proud briar
But considering the correct to three 3 decimals
torn jolt
unless you are given tables
proud briar
yeah
vocal coral
unless you are given tables
what tables?
torn jolt
trig tables
vocal coral
trig tables
isnt the unit cricle basically a table?
torn jolt
it depends how detailed your circle is
vocal coral
oh
vocal coral
it depends how detailed your circle is
ok so i get how to do the x term
but in the answers it is a coord pair
torn jolt
wdym?
vocal coral
for sin0=3/4
you can do sin inverse 3/4
to get the x term
and i got 0.848
but idk how to get 2.294
vocal coral
use the unit circle
idk how
vocal coral
or draw sine
what is this
torn jolt
vocal coral
<https://www.youtube.com/watch?v=kEcbxiLeGTc>
all of the values used in the video are on the unit circle
3/4 is not
torn jolt
use a calculator
torn jolt
and i got 0.848
like this
torn jolt
but idk how to get 2.294
you are asking how to get this
in which case follow the video
vocal coral
in which case follow the video
ok i did it
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broken rain
why the cos(u) is positive if g = -cos(u) the same with u*cos(u)?
umbral dome
,w integrate xsin(x)
hot herald
show the full thing
glossy valveBOT
umbral dome
yeah it's just wrong
broken rain
this minus
umbral dome
that would reverse the sign then
hot herald
well yeh, they had a - in front
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hot herald
so book is actually fine
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sterile ledge
im just confused on what this is asking
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im just confused on what this is asking
sterile ledge
you have to show that A^-1 = q(A) for some polynomial q
ok i think i get it
Im not sure where I would start
does this have to do with CH theorem?
fast peak
more or less
sterile ledge
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buoyant ivy
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wheat sinew
find the length and width (they should be the same number) and multiply one of the sides by 0.10
then you have your answer
buoyant ivy
Huhh
wheat sinew
@hot herald i'm wrong?
hot herald
yes, you're wrong
hot herald
overcomplicating a lot of it
buoyant ivy
overcomplicating a lot of it
😔
hot herald
you are told that you have a square garden
buoyant ivy
Why did I think of it as a rectangle 
buoyant ivy
all sides are equal in a square
Yes
wheat sinew
so what x what gives you 10,000?
buoyant ivy
Yes
hot herald
doesn't actually make a difference to the answer if it was a rectangle
buoyant ivy
B is the answer right ?
hot herald
note that you know w * l
and to find the increase, subtract the original area
buoyant ivy
2100
Danggg
Tysm, I really need to acquire some skill at solving these problems
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wheat sinew
👍🏾
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pliant finch
fast peak
!status
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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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
also, what is P
fast peak
very handwavy
you arent really using the definitions of injective and surjective
your argument is based on "same size". but you also need to use that the set is finite.
pliant finch
How would you incorperate that
pliant finch
very handwavy
Would u just say that they are the same size and finite then
cause otherwise idk where to add it
fast peak
I'm not sure what the cleanest way to prove this is. I would use induction probably
pliant finch
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pliant finch
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torn jolt
try drawing it first
pliant finch
try drawing it first
I think the tan function might work
torn jolt
that's a good start
pliant finch
im not sure it works though cause isint tan from -pi/2<x <pi/2
torn jolt
try using suitable linear transformations to get it where you want
pliant finch
What like multiplying the bounds?
torn jolt
glossy valveBOT
AKAPROTYPE
torn jolt
almost
pliant finch
what am I missing
What if instead of straching the bounds I reduced the bound of tanx and then said because tan has a bijection over -pi/2 < x < pi/2 it should have one over this interval
@torn jolt
simple plume
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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
tulip beacon
do you have an idea of which one to go with|?>|
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tepid root
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hollow sable
Multiply numerator and denominator by sqrt(2)
This is known as rationalizing the denominator
cosmic crag
help with part b pls
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help with part b pls
red onyx
Rotation by 60 degrees and dilation by a factor of 2 I think
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Rotation by 60 degrees and dilation by a factor of 2 I think
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
fathom saddle
Definitely have rotation matricies in the back of your mind, they tend to take that diagonal form
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stiff geyser
I need help with Task 9, I believe task 8 is related to it but I'm not sure how to do it either can someone help me please
upbeat crag
what's "the string"?
stiff geyser
I'm not exactly sure myself but I believe its referring to the order of the euler path ACDA for example
<@&286206848099549185>
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ionic gate
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ionic gate
so i have this question
the answer was this
why did they do the times thing on the left row
and not the top colom?
2 is properly the determent so every thing divided by 2
but they did it for the numbers on the left
how whould you approch this querstioin
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vale glacier
hi, how do I show that this limit approaches -inf
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hi, how do I show that this limit approaches -inf
keen shoal
hi, how do I show that this limit approaches -inf
0 or -inf?
vale glacier
-inf
worthy coral
x -> -∞?
vale glacier
i forgot how to deal with limits like this, do I just plug in the 0, get -1/0 and then say it equals -inf?
vast fossil
Generally it would be more accurate to pick something like 0.001 and -0.001
keen shoal
0 in the denominator is undefined?
vast fossil
In limits, a/0 = ±∞
That in no way defines 1/0
vast fossil
Generally it would be more accurate to pick something like 0.001 and -0.001
Anyways, stick with this
vast fossil
the goal is to get rid of the 0 in the denominator
You can't
keen shoal
hmm
worthy coral
You have to evaluate lateral limits
vale glacier
Anyways, stick with this
are there any other ways?
worthy coral
That's an option
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vocal coral
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vast fossil
If you don't see it, you can substitute for cos(theta)
Let's say x = cos(theta)
Then the equation becomes 2x^2 - x - 1 = 0
Can you solve this now?
vocal coral
Then the equation becomes 2x^2 - x - 1 = 0
yeah i can
vast fossil
Right, the answers for x will also be the answers for cos(theta)
Yet make sure that x is not outside of [-1, 1]
vocal coral
Yet make sure that x is not outside of [-1, 1]
wdym
rough tundra
vocal coral
After doing part a, like MrFancyu2 suggested
couldnt i also just use unit circle
and find where cos -1/2 is
vast fossil
That's good as well
ashen bluff
I'm using a statistical learning python library called scikit-learn and it has an implentation of Principal Component Analysis for dimensionality reduction. It also an implementation of Incremental Principal Component Analysis whereby the samples can be provided in batches. My understanding of PCA is that the PCs are obtained by performing eigendecomposition on the covariance matrix. I want to understand, which part of this is possible to do in batches?
ashen bluff
I want to know for sure that the result of using IPCA will be equal/v.similar to that of PCA.. or at the very least I woud like to know where the drawbacks would be if there are any
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red girder
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red girder
how do i do this ?
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sterile heath
I asked help with this same question a wee while ago and got good help but i wonder if theres a simpler way to solve. I was told to use a probability tree but I think I can use probability with combinations instead
summer echo
Yes you can, note that the probability of at most three kings is 1 - P(all 4 kings)
Now find the number of hands with 4 kings and the number of total possible hands
sterile heath
the number of hands with all four kings is 48 i think
summer echo
Yes, because the last card has 48 options
sterile heath
and the possible hands is 52C5
summer echo
Yup, so what's P(all 4 kings)?
sterile heath
48/52c5
summer echo
Now the probability of at most three kings is just 1 - 48/(52C5)
Which is really close to 1
sterile heath
So, you won't ever get 4 kings in your hand
its always possible
just a 0.002% chance
summer echo
I think the expected value of games is 50000 before you get 4 kings, but I have to go now
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sinful onyx
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sinful onyx
this is a regular tetrahedron, M divides DB perfectly in half
i need to find the angle between the line AM and the plane ABC
which is the same as the angle between AM and AM', where M' is the orthogonal projection of M onto ABC
but how do I know where this projection is
<@&286206848099549185>
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sinful onyx
<@&286206848099549185>
mossy halo
ортогональная - это то как она будет лежать на плоскости ABC
подожди я нарисую
Нет там это не будет половина
Это будет 1/4
У тетраедара все углы 60?
sinful onyx
Только если они принадлежат к одной стороне
mossy halo
mossy halo
Только если они принадлежат к одной стороне
У тетраедра все грани равны все ребра тоже
sinful onyx
Какова мера угла M'AM
mossy halo
не знаю
наверное 45
а нет
он вроде 30
потому что у тебя треугольник ADC подобен AMK
короче фигня
короче как-то через углы
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torn jolt
The central rectangle of a small carpet in the shape of
mosaic is 5 m by 3 m. Its plain border is a uniform width.
If the total area of the carpet is 24m2, determine the width of the border.
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torn jolt
The central rectangle of a small carpet in the shape of
mosaic is 5 m by 3 m. Its plain border is a uniform width.
If the total area of the carpet is 24m2, determine the width of the border.
this is so weird
atomic blade
Now you have to get your own channel yourself
You locked this channel and it's heading towards its demise
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winged rock
help
fossil stump
sinful onyx
just shade everything that isn't inside circle C
the first () is part of a union with everything that isn't C and a union just adds stuff together
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winged rock
can u show it?
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frozen portal
Hi everyone!!
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Hi everyone!!
frozen portal
How would I do this problem?
I want to know an intuitive way to do it
All I know is that the line of reflection cuts through C/C' because C and C' have the same coordinate
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serene sage
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serene sage
how does the first part turn into 1/e?
torn jolt
e^(n+1) = e*e^n
next zephyr
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viral jasper
what have you tried
next zephyr
what have you tried
i figured it out i forgot the most basic power property 💀
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harsh cairn
on step 2 how did they change -7 to -42
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on step 2 how did they change -7 to -42
stuck summit
harsh cairn
pls
stuck summit
it looks like they multiplied it by the 6 in front of x but i cannot for the life of me understand this
ivory cairn
oh that is an awful way to teach factoring
stuck summit
this looks like it was scanned in the 90s
harsh cairn
did they do it wrong?
stuck summit
i dont understand this step at all
light sonnet
on step 2 how did they change -7 to -42
There's a factoring method, I forget the name, but you divide and slide the a coefficient, where you divide that a coefficient to get 1 and "slide" it to do a * c
ivory cairn
they're doing the AC trick of multiply the leading coefficient and constant terms. 6 * 7 = 42
light sonnet
So you can have a = 1
stuck summit
that works??
light sonnet
Which makes factor easier
harsh cairn
what
ivory cairn
technically.
harsh cairn
whats another factor trick?
harsh cairn
explain pls
light sonnet
The video I linked explains it
stuck summit
woulda saved me hours of testing combinations of factors
harsh cairn
theyve never taught this in class tho
harsh cairn
woulda saved me hours of testing combinations of factors
pls explainn
light sonnet
As mentioned, you slide the a coefficient, to do a * c, and then divide to make a = 1
Because factoring equations when a = 1 is easier
harsh cairn
i just divided the whole thing by 6?
harsh cairn
ok
harsh cairn
https://www.youtube.com/watch?v=TU15PaFhj5o&ab_channel=Cole%27sWorldofMathematic...
bro doesnt this like defy all the laws of mathematics
light sonnet
bro doesnt this like defy all the laws of mathematics
No
Just watch that video, it explains it
lucid oasis
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grand hound
so if i get infin over infin what does that mean
That means it is indeterminate. This mean you still have to continue solving or find alternative ways to find the limit
lucid oasis
but lopital would just make it infin over infin again rightr?
oh wait its infin minus infin over infin
so 0
grand hound
you would have to continue doing l'hopital
sometimes you have to do l'hopital multiple times till it stops being indeterminate
grand hound
oh wait its infin minus infin over infin
actually this is incorrect
infinity - infinity is also another indeterminate form
here is all the indeterminate forms
sudden yoke
i thought 0^0 = 1
olive plaza
i thought 0^0 = 1
It leads to division by 0
grand hound
yeah it's a weird circumstance, if you are taking AP it probably won't show
sudden yoke
yeah i'm in bc rn and never had to deal with 80% of that chart
grand hound
yeah i also taken it and i haven't seen it
however, ive seen it in college
so it's good to know if you are doing higher level math
lucid oasis
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next zephyr
yeah
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lucid oasis
thank man you too
next zephyr
thx
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dim elm
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dim elm
Unsure how to do this
I was gonna try replacing it as a1 and a3 and use formulas but I’m kinda tripped up on the algebra equation part about the sequence. I’ve never done that before.
plush egret
they give you choices so
you could just guess and check
probably the most reasonable way to approach this problem
boreal marlin
B is the only formula that's correct for a_9
dim elm
How do you know?
dim elm
you could just guess and check
I mean I could do that but this is my final review and I kinda wanna be able to know how to do it for the final 
boreal marlin
No, that's the value of a_9
You're given a_9 and a_11, and multiple choices for a_n, to check which one is correct replace n for 9, also for 11, in each formula
dim elm
So then the values are just to be able to see if the formula is correct?
boreal marlin
Well, it asks for a_6
So once you have a formula that matches you could replace n for 6, but it's already given in each option
dim elm
So how would I find the formula for a^n if it wasn’t multiple choice?
smoky root
You're told it's an arithmetic sequence, so the difference between consecutive terms is always the same
Since your given a_9 and a_11, you can find the difference between them and cut it in half to find the difference between each term
then, you can work backwards to find a_0 and come up with the formula
dim elm
How would I find that difference? Subtract a^9 from a^11?
dim elm
But a^9 and a^11 are kinda far apart so how could U determine the difference after subtraction?
Would the answer be a^10 or d? Im a bit confused on that part
smoky root
what do you get when you subtract them?
boreal marlin
In general you can't know the formula for any sequence
smoky root
In general you can't know the formula for any sequence
they're told it's arithmetic, though
boreal marlin
You're right, my bad
smoky root
np
dim elm
When I subtract a^9 from a^11 I get 2x+6?
smoky root
good, so since they're two apart, the common difference is half of that, or x+3
dim elm
So d=x+3
smoky root
yup
boreal marlin
Careful with notation, a^n is the nth power of a, not the nth value of the sequence a
glossy valveBOT
Lemma
dim elm
And then youd plug that into the arithmetic sequence formula
smoky root
yeah
dim elm
Ahhhhh
smoky root
but we want to find a_0
dim elm
Careful with notation, a^n is the nth power of a, not the nth value of the seque...
Oh thank uou!!
So would it then be a_n okay noted
dim elm
but we want to find a_0
a_0?
smoky root
well, do you have a formula for arithmetic sequences?
(I might be using different notation)
dim elm
Yes, a_n=a_1 + (n-1)d
dim elm
Ohhh
smoky root
they're equivalent
but you'll want to find a_1 then
and you can use a_9 to do it
since
$a_9=a_1 + 8d$
glossy valveBOT
Lemma
smoky root
but as the others have said
if it's multiple choice, just plugging 9 into all of them is faster, lol
dim elm
That’s true honestly. I think my final is multiple choice so I’ll probs just do that but i wanna know just in case lol
smoky root
that's good!
dim elm
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woeful cave
I need to compute in Z13, in the form [k] where 0 <= k <= 12
25^513 + (-2)(9)
woeful cave
Im struggling with figuring out how to convert the 25^513
i know its something like
25= -1(mod)13 but i dont know what to do with that
vast fossil
And (-1)^513 = -1
vast fossil
-1 - 18 you mean?
vast fossil
-19 + 23 = 4
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grand kiln
a drawer contains 8 black,5 red and 4 blue pencils. assuming you remove them without looking what is the minimum of pencils you should take to ensure that you get at least one of each color? need some help with this question
upbeat crag
pigeonhole principle
hot herald
think about the worst case scenario
and/or consider if you were able to look,
how could you maximise the amount of pencils you could pick before getting one of each colour
grand kiln
think about the worst case scenario
and/or consider if you were able to look,
h...
worst case scenario would be getting pencils only in 1 color?
hot herald
and what happens after picking pencils only in one colour
grand kiln
and what happens after picking pencils only in one colour
i'll be left with the other colored pencils
hot herald
yeh, and after picking all pencils of the same colour, how can you keep picking that avoids getting one of each colour
grand kiln
by getting 8 black ones, 5 red, 4 blue ones
grand kiln
so i should pick all the pencils without picking 3 of each color?
hot herald
you don't want at least one of each
how could you pick them without getting one of each
grand kiln
i'll pick 7 black, 4,red,3 blue ones?
hot herald
no
you'd have 3 of each there and more
pick these one at a time
the second you've got at least 1 black, red, blue,
you've failed for what i'm trying to get you to consider
grand kiln
i'll pick the black ones and red ones or black and blue or red and blue
hot herald
now, which of those combinations will require the most picks
grand kiln
black and red?
hot herald
yes
and the pick after that guarantees that you'll have (at least) one of each colour
grand kiln
so the minimum picks would be 13?8+5?
grand kiln
14?
grand kiln
so i'll have 8 black ones, 4 red ones and to get all three colors i'll need to pick from 4 blue ones SO i'll just need to pick one. so 14, does this make sense?
hot herald
yes
slender pond
Can someone help me with 6 please
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Can someone help me with 6 please
torn jolt
.
slender pond
?
torn jolt
U already claimed it sry
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vernal haven
Hello
vernal haven
Use an appropriate compound angle formula to determine an exact value for tan (19π/
12 ). Do not use a calculator.
Leave your answer in proper radical form, fully simplified.
hallow walrus
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4
hallow walrus
show your work
vernal haven
hello There
hallow walrus
for future reference, you can just send in your work directly
hallow walrus
if youre having trouble you can just tell me over text your process
vernal haven
hallow walrus
,w tan(19pi/12)
glossy valveBOT
hallow walrus
looks good
hallow walrus
sure but dont ping me
hallow walrus
what's cot2theta
vernal haven
The cotangent of 2θ
vernal haven
cot(2θ) = (cot²(θ) - 1) / 2cot(θ)
vernal haven
like the solution
vernal haven
The expression 2cot(2θ) represents the value of the cotangent function for an angle that is twice the size of θ.
hallow walrus
are you giving these answers from chatgpt
torn jolt
help
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3. I got an answer but I'm told it's wrong
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6. None of the above