so
#help-33
marsh peak
Yes
severe briar
,w (pi+arctan(9/5)*(180/pi)
elfin berryBOT
elfin berryBOT
severe briar
elfin berryBOT
severe briar
is it just me or are those answers exactly the same? @marsh peak
ohhh
cos first then sin
i got it
alr moving on
i assumed u just multiply here is that right?
marsh peak
Yes
severe briar
u just add the values together right
its not uploading ;-;
its fine im pretty sure im right
subtracting vectors is the same as adding a negative one right
marsh peak
<x1, y2> + <x2, y2> = <x1 + x2, y1 + y2>
marsh peak
subtracting vectors is the same as adding a negative one right
Yes
marsh peak
6 - (-3) = 9
marsh peak
Yes it's s
Scaling a vector changes its magnitude
Unless you multiply it by a negative number
Then its direction will also be affected (it start having the opposite direction to the initial one)
marsh peak
Just do arctan(160/180) + arctan(128/123)
elfin berryBOT
severe briar
forgot to convert to degrees
88 ish degrees
whats orthogonal, either, or parallel mean
@marsh peak
marsh peak
Orthogonal is the same as perpendicular, making a right angle together
And parallel is parallel 
severe briar
ooohhh
marsh peak
Well, in the context of vectors you could say parallel means having exactly the same or the opposite directions
severe briar
makes sense
marsh peak
Do you know what the dot product is?
severe briar
nope
but thats the next question
isnt it multiplying the components and adding them together
marsh peak
<x1, y1> * <x2, y2> = x1x2 + y1y2 yeah
But there's another formula
a * b = |a||b|cos(theta)
Theta being the angle between the vectors a and b
severe briar
a * b = |a||b|cos(theta)
those are the magnitudes right
marsh peak
Yes
severe briar
so i take the dot product here right?
marsh peak
Yes
If it's zero, then the vectors are orthogonal
If |cos(theta)| = 1, then they are parallel
severe briar
I got like -428
severe briar
<x1, y1> * <x2, y2> = x1x2 + y1y2 yeah
using this
marsh peak
,w 6 * (-24) + (-9) * 36
elfin berryBOT
marsh peak
Yeah alright then let's calculate the cosine
severe briar
a * b = |a||b|cos(theta)
how do i find the magnitude of a and b and find cos theta
marsh peak
a * b = |a||b|cos(theta)
According to this formula cos(theta) = (a * b)/(|a| * |b|)
severe briar
yep
severe briar
We already know a * b
i think this is right
marsh peak
Yes
severe briar
a * b = |a||b|cos(theta)
how do i use this formula
marsh peak
i think this is right
For this?
severe briar
no for the other one from earlier
marsh peak
Did you get the magnitudes?
elfin berryBOT
severe briar
,w sqrt(36+81)
elfin berryBOT
severe briar
for v
elfin berryBOT
marsh peak
,w calculate the angle between the vectors (6, -9) and (-24, 36)
elfin berryBOT
severe briar
oh ok
severe briar
So cos(theta) = -468/(12 * 3 * 13)
ohhh so a*b iss the dot product
marsh peak
Yes
severe briar
So cos(theta) = -468/(12 * 3 * 13)
wait im not fully understand the denominator
those are the magnitudes?
marsh peak
Yes
marsh peak
Oh you basically do |u|cos(theta)
But that can be rewritten as |u||v|cos(theta)/|v|
Or just (u * v)/|v|
severe briar
,w (-40+-44)/sqrt(80)
elfin berryBOT
severe briar
(4^2+8^2)=16+64 = 80 btw
marsh peak
Oh wait (u * v)/|v| would be the length of the projection 
Okay I guess you normalize v and multiply it by |u|
So do v/(|u| * |v|)
Has to work
Wait no
(|u|/|v|) * v
marsh peak
Interesting, that's the same as what I wrote except it's multiplied by the cosine
Oh okay I see why
Nvm
elfin berryBOT
marsh peak
Isn't 80 getting squared though?
severe briar
well i didnt write the exponent or the root cuz they cancel
elfin berryBOT
Requested by A Lonely Bean#7998
severe briar
-44/10,-88/10
,w -44/10
elfin berryBOT
severe briar
,w -88/10
elfin berryBOT
marsh peak
Really close to the third option though
Wait what did you get for the dot product?
-88 right?
elfin berryBOT
severe briar
,w (-21/20)*4
elfin berryBOT
severe briar
,w (-21/20)*8
elfin berryBOT
severe briar
there it is
XD
lmfao
oh my gosh
so adding angles is just adding the arc tan values right?
we already did this i just wanna understand it better
marsh peak
Yes
severe briar
Yes
so i might text thru here to make sure im right lol
theyre taking long to call on me
severe briar
nvm the questions were all easy
thx so muchh
ill be back tmrw
or later today with calculus
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
sudden bluff
marsh citrusBOT
marsh citrusBOT
@sudden bluff Has your question been resolved?
red sierra
marsh citrusBOT
marsh citrusBOT
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pale canyon
can someone guide me through solving this problem?
marsh citrusBOT
can someone guide me through solving this problem?
pale canyon
for the left endpoint i did f(2)*0.5 + f(2.5)*0.5 + ...+ f(5.5) * 0.5 = (2+3.4375 + 3.75 + 3.9375 + 4 + 3.9375+3.75+3.4375)*0.5 = 14.125 but it says its incorrect and im not sure why
twilit grove
what did you put for f(2)?
twilit grove
is it -(x^2 / 4)?
pale canyon
-(2)^2/4 + 2(2) = 2?
pale canyon
oh
yea it should be 3
idk how i got 2
im gonna try again
yea
got it
.close
wicked gazelle
how do i change the bases so that theyre all the same in the expression (2^7x + 8^X) / (4^2x)
marsh citrusBOT
how do i change the bases so that theyre all the same in the expression (2^7x + ...
leaden monolith
use logs
u cant add them tho
u have to distribute the divide first
in this case since the bases are special you can write 8 = 2^3 and 4 = 2^2
wicked gazelle
what do u mean distribute the divide first
leaden monolith
(2^7x + 8^X) / (4^2x) = (2^7x) / (4^2x) + (8^X) / (4^2x)
wicked gazelle
oh i see you wanted me to split up the fraction
how does that help tho?
i think i see actually let me tryh
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marsh citrusBOT
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odd jungle
Each of five, standard, six-sided dice is rolled once. What is the probability that there is at least one pair but not a three-of-a-kind (that is, there are two dice showing the same value, but no three dice show the same value)?
my work rn is to split it up into two cases, one being there's 1 pair of same values and 3 different numbers, and 2 pairs of same values (although these pairs have different values) and 1 different number. also total amount of ways is 6^5, so that's the denominator.
for the first case, i did 5 choose 2 x 6 x 5 x 4 x 3 to pick 2 slots for the pair, and then choose numbers for the pair and the different numbers.
for the second case, i did 5 choose 2 x 3 choose 2 x 6 x 5 x 4 to choose 2 slots for the first pair, 2 slots for the second pair, then to choose numbers for the 2 pairs and number.
for both cases, you get 3600 ways, and adding both them up gives 7200 ways, so the probability should be 25/27, but its not so im confuz
marsh citrusBOT
Each of five, standard, six-sided dice is rolled once. What is the probability t...
@odd jungle Has your question been resolved?
odd jungle
<@&286206848099549185> i think im allowed to ping now, the rules say so so yes ping
sleek lake
maybe it's correct but they mean other rules than you inferred
let me check the calculations first though
odd jungle
alright
sleek lake
uh
ok, the second case should be 1800
you would do 5 choose 2 x 3 choose 2 / 2
another way to get 1800 is you pick the 3 numbers, 6c3
then pick which one is the lone not paired number ×3
and permute the result: 5!/2/2
the rules are not so ambiguous, that's the only reasonable interpretation anyway
odd jungle
you would do 5 choose 2 x 3 choose 2 / 2
oh wait yeah because you could choose the second pair first!!!!
ok, if we add those up we and simplify we get 25/36 for the probability. gonna try it
i got it! tysm and have a good day
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marsh citrusBOT
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oblique hollow
Hey guys, coud you help on this question please?
marsh citrusBOT
Hey guys, coud you help on this question please?
cobalt sentinel
I'm blanking. How did they get <cos(t), sin(t)> when they plugged in for N in the solution. (N denoting the unit normal vector)
marsh citrusBOT
I'm blanking. How did they get <cos(t), sin(t)> when they plugged in for N in th...
fair fulcrum
I'm blanking. How did they get <cos(t), sin(t)> when they plugged in for N in th...
because... cos(t), sin(t) maps out the unit circle?
from 0 to 2pi
that's how they parameterized it
there are other ways
cobalt sentinel
how can the unit normal vector to the unit circle be the same as the parameterization
fair fulcrum
ah
because the normal vector from a point is the same as the radius segment
it's perpendicular to the circle
cobalt sentinel
yes that makes sense
im still not able to connect how that links to the parameterization tho 
ohhhhhhhhhhhhhhhhhhhhhhhhhhhh wait i get it
thx zfn
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vague ocean
I have a general question about power series to help me understand better hopefully:
marsh citrusBOT
I have a general question about power series to help me understand better hopefu...
vague ocean
So when we have a power series we take the ratio test in order to determine if the common ratio is under one
but since power series has a variable x, we need to define when that variable gives us convergence (in an interval) ?
and from there we are able to take the average of that interval to determine the radius R
And then a taylor series is basically just cascading derivitives of a function at a certain point which gives us an infinite polynomial. And this polynomial can be written in the form of a series
If there is anything incorrect about this please let me know. I am trying to dumb down all of this information to make it simple to remember for finals
marsh citrusBOT
@vague ocean Has your question been resolved?
mystic minnow
the word 'average' for your radius is a little concerning, but i think you have the right idea and the wrong word.
vague ocean
the word 'average' for your radius is a little concerning, but i think you have ...
I guess I use average because you can add the left and right point then divide by two to get the middle.
But usually it is centered at 0 if it isn’t infinite
At least the basic problems I’ve encountered
mystic minnow
so that would give you the middle, not the radius
celest finch
can someone help me solve 5^(x-2) = 300 without a calculator
marsh citrusBOT
can someone help me solve 5^(x-2) = 300 without a calculator
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
uh
number 1
like i only know how to solve it using base 10 logs
but that requires a calculator and i cant use one
eternal tundra
logarithm,
you dont need a calculator for that
think about: what power do i have to take 5 to, in order to get 300
sleek lake
what
sweet pawn
oops
eternal tundra
i was wrong
celest finch
this is what i know how to do
eternal tundra
i thought we would get a nice number, but we dont
sleek lake
i'm sure there's a way, but like it's not easy
celest finch
is there not like a simple algebra way to solve it
sleek lake
no
celest finch
so the answer is just what i have on the right + 2
sweet pawn
yep
celest finch
thats so odd
sweet pawn
not really
celest finch
we’ve never done it like that
sweet pawn
log(23148) is just as much of a 'number' as 2 is
sweet pawn
yeah that's the change of base formula
celest finch
?
marsh citrusBOT
@celest finch Has your question been resolved?
untold gust
I have a complex number plane question
marsh citrusBOT
I have a complex number plane question
untold gust
bitter dawn
What have you tried so far?
untold gust
i mean
i tried to set
cos(theta) = -1/2
and sin (theta) = sqrt(3)/2
but there is no solution
untold gust
so is my setup right?
where i do cos(theta) = -1/2
and sin (theta) = sqrt(3)/2
?
fair fulcrum
yes
untold gust
yea i know
for the cos(theta) = -1/2, we get 2pi/3 +2pi*n
for sin(theta) = sqrt(3)/2, we get pi/3 + 2pi*n
those two have no common solutions
<@&286206848099549185> ???
fair fulcrum
for sin(theta) = sqrt(3)/2, we get pi/3 + 2pi*n
that is not the only solution set for sin(theta)
the other one is 2pi/3 + 2pi*n
the other solution set for cos(theta) is 4pi/3 + 2pi*n
(2pi/3 or 4pi/3) and (pi/3) or (2pi/3)
untold gust
are they the answer?
so
sin : 2pi/3 + 2pin, pi/3 + 2pin
cos: 4pi/3 + 2pin, 2pi/3 + 2pin
what do we do from there
<@&286206848099549185> ???
fair fulcrum
the answer is where those are the same
which is at 2pi/3
- 2pin
I'm sorry for my tech support response times
helping too many people (>1) at once
untold gust
all good man
right
oh and we have the limit of -4pi~4pi
so shouldn't it be
-4pi/3
2pi/3
and 8pi/3?
fair fulcrum
but what else can there be
-10pi/3
untold gust
oh how'd i miss that
i'm so stupid for that
thank you so much for the help
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marsh citrusBOT
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Available help channel!
royal stone
so in a slope, is it x/y or y/x
marsh citrusBOT
so in a slope, is it x/y or y/x
wise jackal
Slope is the change in y over change in x
royal stone
is slope and gradient the same thing
wise jackal
Yes
tawny vapor
did i do this properly? for f-1(-3) i did does not exist and for the 2nd question i got f-1(-2)= f(2)
marsh citrusBOT
did i do this properly? for f-1(-3) i did does not exist and for the 2nd questio...
brave jacinth
marsh citrusBOT
@tawny vapor Has your question been resolved?
tawny vapor
why did u pick (3,-2)?
brave jacinth
in the picture
tawny vapor
in the picture
so if i plug in -3 in 1-x i get 4
if i inverse it i should get -3 again right?
tawny vapor
oh
i thought it was weird cuz i was getting -3 again
and for (f-1 o f)(x) it should be -1?
f(3) = -2
f-1(-2) = -1
brave jacinth
and for (f-1 o f)(x) it should be -1?
no
brave jacinth
tawny vapor
so by inversing it gives 3?
marsh citrusBOT
tawny vapor
.reopen
marsh citrusBOT
✅
brave jacinth
so by inversing it gives 3?
yes
marsh citrusBOT
marsh citrusBOT
Available help channel!
tawny vapor
did i do this properly?
marsh citrusBOT
did i do this properly?
tawny vapor
marsh citrusBOT
@tawny vapor Has your question been resolved?
tawny vapor
.close
dusk terrace
marsh citrusBOT
stoic saddle
if the equation didn't have a trig function in it would you be able to solve it?
dusk terrace
if the equation didn't have a trig function in it would you be able to solve it?
I don't believe so
stoic saddle
are you ok with me giving you a simpler equation and having you attempt to solve it
dusk terrace
are you ok with me giving you a simpler equation and having you attempt to solve...
of course
stoic saddle
36/z = 5
stoic saddle
correct, but do you have work to show?
dusk terrace
correct, but do you have work to show?
i used calculator
and i dont understand where that really came from either, never learned it that way
im wondering the trig function if im doing that right
stoic saddle
i used calculator
mkay so like do you know your way around basic algebra in general
shit like adding the same thing to both sides, multiplying the same thing to both sides, etc.
dusk terrace
mkay so like do you know your way around basic algebra in general
yes i do
stoic saddle
okay in that case
for the equation 36/z = 5, multiply both sides by z and tell me what you get
stoic saddle
your problem asks for it, mine does not
anyway
okay, so then coming back to your problem, you have 60/x = sin(28°)
can you solve it in a similar token
dusk terrace
can you solve it in a similar token
i would usually do that if the 60 was denominator
i didnt know what to do with x
stoic saddle
... "in a similar token" meant "similarly to what has just been discussed".
stoic saddle
xsin(28)=60?
yes. keep going.
stoic saddle
or the other way around
what "other way around"?
stoic saddle
no such thing as "moving"
dusk terrace
so sin28 is 0.47
dusk terrace
no such thing as "moving"
0.47x=60?
stoic saddle
keep sin(28) as sin(28) until the end.
stoic saddle
you have (a number)*x = 60
you had no problem dividing both sides by 5 in the toy equation i gave you earlier
dusk terrace
x = 127.8
stoic saddle
,calc 60/sin(28 deg)
elfin berryBOT
Result:
127.80326809137
ok checks out
marsh citrusBOT
@dusk terrace Has your question been resolved?
long cape
marsh citrusBOT
glacial grotto
marsh citrusBOT
fair fulcrum
glacial grotto
TY
fair fulcrum
lol
glacial grotto
i missed class last friday so i assume we learned that formula
fair fulcrum
that only works for arithmetic sequence ofc
glacial grotto
.close
prisma vessel
why is the series 1/n divergent? Dont the numbers get smaller and smaller so it should converge to a certain value?
marsh citrusBOT
why is the series 1/n divergent? Dont the numbers get smaller and smaller so it ...
prisma vessel
it is tho
desert socket
I mean its divergent
prisma vessel
acc to p series
desert socket
It is not convergent
prisma vessel
It is not convergent
yeah but why
desert socket
Yeah lemme explain
prisma vessel
the numbers im adding is smaller and smaller
desert socket
1+1/2+1/3+1/4+1/5+1/6+1/7+1/8 and so on
1/3 is larger than 1/4
So if we add 1/4 instead of 1/3 the sum of series should be smaller
Now 1+1/2+1/4+1/4+1/5+1/6+1/7+1/8
1/4+1/4=1/2
So, 1+1/2+1/2+1/5+1/6+1/7+1/8
Now all of 1/5,1/6,1/7 are larger than 1/8
We can put all of them equal to 1/8 to get yet smaller sum
1+1/2+1/2+1/8+1/8+1/8+1/8+1/8
=1/2+1/2+1/2
Similarly the numbers add up and the series diverges
prisma vessel
but the change in the sum is rlly small tho?
desert socket
but the change in the sum is rlly small tho?
The change actually makes the sum smaller. But it still diverges, so the larger sum obviously diverges
prisma vessel
The change actually makes the sum smaller. But it still diverges, so the larger ...
oh then why does 1/n^2 converge then
desert socket
oh then why does 1/n^2 converge then
Well, I'm not too sure about that onw
Yeah but it has a similar explanation
The series goes 1+1/2²+1/3²+1/4² and so on
prisma vessel
idg how squaring n makes it convergent like it doesnt feel logical
desert socket
idg how squaring n makes it convergent like it doesnt feel logical
I'm here man
desert socket
The series goes 1+1/2²+1/3²+1/4² and so on
Clearly 1/3² is less than 1/2³
So the higher sum is 1+1/2²+1/2³+1/2⁴+1/5²+1/6²+1/7²+1/8²
prisma vessel
ok...
prisma vessel
.close
prisma vessel
What is a power series representation for x/(5-x)
marsh citrusBOT
What is a power series representation for x/(5-x)
quaint pilot
need help in a statistics assignment.
question is find an unbiased estimator of frac{\mu}{\sigma^2} and frac{\mu}{\sigma}
given X1,.....,Xn ~ N(\mu, \sigma^2)
I know what is an unbiased estimator, what does that mean. but I dont know how to find one
Please help
marsh peak
I would rewrite that as 5/(5 - x) - 1 and found the pattern in derivatives
marsh peak
need help in a statistics assignment.
question is find an unbiased estimator of...
Post your question in an available help channel
prisma vessel
I would rewrite that as 5/(5 - x) - 1 and found the pattern in derivatives
how do u get rid of the x in the numerator
prisma vessel
i actually dont get how x disappeared
marsh peak
How do you simplify (x - 5)/(5 - x)?
marsh peak
Yeah
marsh peak
What
marsh peak
Ah yeah you can just use the geometric series
prisma vessel
but i cant cuz of -`1/5
marsh peak
5( 1/(1-x/5)) - 1/5
Just use it on 5/(5 -x) and then add -1
prisma vessel
5 series (x/5)^n - 1/5 like this?
marsh peak
5/(5 - x) = 1/(1 - x/5) = 1 + x/5 + x^2/25 + x^3/125 + ...
marsh peak
5 series (x/5)^n - 1/5 like this?
Yeah but only -1
marsh peak
5/(5 - x) = 1/(1 - x/5) = 1 + x/5 + x^2/25 + x^3/125 + ...
Actually, if you wanted to use the geometric series
Okay nvm it might not be simpler
marsh peak
so 5 series (x/5)^n - 1
Anyway yeah that can be rewritten as the series of (x/5)^n starting with n = 1
prisma vessel
btw if I have a power series, and Im asked to evaluate it at f(2023) (1) how do I do that
marsh peak
And the textbook is asking you for 2023th derivative of that at 1?
prisma vessel
<:thonk:406575732563902485> And the textbook is asking you for 2023th derivative...
Its part of the exam
like were supposed to know how to evaluate derivs
given a power series
marsh peak
Oh actually look
Bo matter how many derivatives you take
They will be of the form some number + powers of (x - 1)
And when you plug in x=1 those terms become 0
So we have to figure that number out
prisma vessel
isnt x 1?
marsh peak
Yeah so (x - 1) = 0
prisma vessel
so if my f(1) = 0, f'(1) = 0.... am I right?
marsh peak
And if you notice, the 1011th term of that series is x^2023/(4^1011*1011)
marsh peak
so if my f(1) = 0, f'(1) = 0.... am I right?
No not like that
prisma vessel
And if you notice, the 1011th term of that series is x^2023/(4^1011*1011)
how did you come to this assumption
marsh peak
No matter how many derivatives you take here, there will still be powers of (x - 1) present, right?
prisma vessel
No matter how many derivatives you take here, there will still be powers of (x -...
wdym powers of (x-1)
marsh peak
wdym powers of (x-1)
k1(x - 1) + k2(x - 1)^2 + ...
marsh peak
What happens to this when you plug in x = 1?
prisma vessel
What happens to this when you plug in x = 1?
its 0
marsh peak
k1(x - 1) + k2(x - 1)^2 + ...
This*
prisma vessel
its always gonna be 0 right cuz 1-1, (1-1)^2, (1-1)^3
marsh peak
Yeah
So we just need to find the term in the series which, after 2023 differentiations, becomes a constant rather than a power of (x - 1)
prisma vessel
ohh
marsh peak
Namely, that term is gonna be the one that has (x - 1)^2023 in it
Because generally nth derivative of x^n is n!
marsh peak
And, like I already mentioned here, the 1011th term is (x - 1)^2023/(4^1011*1011)
Just plug in n = 1011
Which is the solution to 2n + 1 = 2023
marsh peak
And, like I already mentioned here, the 1011th term is (x - 1)^2023/(4^1011*1011...
So, after 2023th differentiation, this becomes 2023!/(4^1011*1011)
The only problem now is that this is hard to simplify
Assuming it's possible at all
marsh peak
So, after 2023th differentiation, this becomes 2023!/(4^1011*1011)
I guess you just leave the answer like this
prisma vessel
Which is the solution to 2n + 1 = 2023
wdym by this btw
marsh peak
wdym by this btw
We wanted to find the term which has (x - 1)^2023 in it, right?
prisma vessel
ya nvm i get it
marsh peak
So, after 2023th differentiation, this becomes 2023!/(4^1011*1011)
So this must be it
prisma vessel
btw dyk how to express an integral as a series of constant terms
marsh peak
Image is not loading wait
Oh
I think you need to express e^(x^2) using its power series
marsh peak
Yeah so e^(x^2) is x^(2n)/n!
Multiplying that by x^2 gets you x^(2n + 2)/n!
And just integrate that from 0 to 1
prisma vessel
but idg why power series is a form of "series of constant terms"
marsh peak
All of those terms will be constant after integration
prisma vessel
All of those terms will be constant after integration
u mean after integration, Ill end up with some number?
marsh peak
With an infinite sum of numbers
prisma vessel
With an infinite sum of numbers
ohh
marsh peak
Which is just a series anyways idk why they mentioned constant terms
honest kindle
I am a total beginner in Math, any suggestion for books that can kick start my quest
marsh citrusBOT
I am a total beginner in Math, any suggestion for books that can kick start my ...
stark trail
marsh citrusBOT
@honest kindle Has your question been resolved?
worn sluice
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marsh citrusBOT
marsh citrusBOT
Available help channel!
tender minnow
Hey
I’m kind of confused how to create the right formula when the graph has two zeros.. do I just use point slope formula?
marsh citrusBOT
Hey
I’m kind of confused how to create the right formula when the graph has two...
marsh citrusBOT
x²(x+4)(x-3
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.
@tender minnow Has your question been resolved?
tender minnow
Oh so would that just be the formula? The roots?
Sorry for taking 27181 years to reply lol
violet glacier
idk if itts calldd a formula
tender minnow
Oh ok
keen zephyr
marsh citrusBOT
keen zephyr
where do i start with this ?
twilit grove
what is this notation and what is the second term?
keen zephyr
what is this notation and what is the second term?
C stands for combinations
twilit grove
and what does the second term say? is that an s? an incompletely written 4?
keen zephyr
ive never seen a factorial use S as a exponent
twilit grove
well what is it?
zinc crest
Have you tried rewriting each with the n!/r!(n-r)! then expanding the numerator to remove your factorial for each Cn from the denominator?
knotty trellis
Im getting cubic polynomial unfortunately
kinda hard but nvm
rational root theorem should work
knotty trellis
Have you tried rewriting each with the n!/r!(n-r)! then expanding the numerator ...
start with this
knotty trellis
the worst part is expanding the product
there will be really huge absolute coefficient, rrt wont work I guess
twilit grove
it works out actually
knotty trellis
oh it's actually not too bad
knotty trellis
the left fraction is incorrect I think
zinc crest
Where did the /24 on the RHS come from as well?
knotty trellis
it's modifying both sides of equation I guess
it means that in next step they want to multiply both sides by 24
zinc crest
But you should have 2! and 4! ?
twilit grove
$\frac{n!}{2!(n-2)!} + \frac{n!}{4!(n-4)!} = \frac{n(n - 1)}{2} + \frac{n(n-1)(n-2)(n-3)}{24}$. then combine
keen zephyr
this is what it should be
and then : n^2 - 25 = 0
n = +-5 = S: {5}
i dont believe i made any mistake
twilit grove
I don't think that's right
zinc crest
24/2 = 12 not 4?
sick creek
tell me actual meaning of deteminant rather than definition , why we use it so much?
marsh citrusBOT
tell me actual meaning of deteminant rather than definition , why we use it so m...
proper zodiac
Roughly: Tells you how much things scale up by when you apply the transformation
proper zodiac
Yes but Google will do a better job
Will be a million resources on surface integrals
proper zodiac
Paul's online maths notes probs has some
Only you know what you think good references are, look around and find out
main idol
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haughty vault
A strip of floor measures 𝑛 ft. by 2 ft. where 𝑛 is a positive whole number.
The floor is to be covered by using two types of tiles.
One type of tile measures 2 ft. by 1 ft..
The other type measures 2 ft. by 2 ft..
Compute 𝑡1,𝑡2,𝑡3,𝑡4 and 𝑡5.
The answers I got are 1,2,2,3,3. I'm unsure whether I got the right answer and am overthinking or if there is more to this.
marsh citrusBOT
A strip of floor measures 𝑛 ft. by 2 ft. where 𝑛 is a positive whole number.
T...
@haughty vault Has your question been resolved?
haughty vault
<@&286206848099549185>
keen cradle
Your answers are correct
haughty vault
Ohh, perfect. Thank you!
How would I got on about, doing a recurrence relation with this?
sleek lake
they seem to small
i think that's wrong
yeah
you;re missing most of the ways
for t(4)
+6 others
haughty vault
t1 = 2x1
t2= one 2x2 and two 2x1
t3 = three 2x1 and one 2x2 & one 2x1
t4 = four 2x1, two 2x2, and two 2x1 & one 2x2
t5 = five 2x1, two 2x2 & one 2x1, and three 2x1 & one 2x2
marsh citrusBOT
@haughty vault Has your question been resolved?
marsh citrusBOT
@haughty vault Has your question been resolved?
marsh citrusBOT
@haughty vault Has your question been resolved?
rugged dust
my question is the red line one period?
marsh citrusBOT
my question is the red line one period?
rugged dust
from 0 to 38
proud ice
yes
supple walrus
can anyone help me understand how the dim(N(A)) = 1?
marsh citrusBOT
can anyone help me understand how the dim(N(A)) = 1?
supple walrus
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wary wolf
marsh citrusBOT
wary wolf
having trouble with this
fair fulcrum
what's the slope
wary wolf
-7,0\
wary wolf
I dont really know the slope
fair fulcrum
pick 2 points on the line, like, (-1, -6) and (0, -7)
then slope is (y2 - y1)/(x2 - x1)
fair fulcrum
1 over -1
wary wolf
y=1/-1x
wary wolf
y=1/-1x - 7
wary wolf
fraction
wary wolf
1
fair fulcrum
nope
wary wolf
-1
fair fulcrum
yes
wary wolf
y=-8
fair fulcrum
no
fair fulcrum
y=1/-1x - 7
you forgot the x
fair fulcrum
yes
y = (1/-1)*x - 7
viral quest
If I have a sequence $y_m$ where $y_{m+1}$ is not in the span of $y_1,...,y_m$, is it true that there are no convergent subsequences?
marsh citrusBOT
If I have a sequence $y_m$ where $y_{m+1}$ is not in the span of $y_1,...,y_m$, ...
elfin berryBOT
dream was legit
viral quest
each $y_m$ lives in the infinite dimensional normed linear space X
elfin berryBOT
dream was legit
unique venture
.
fair fulcrum
If I have a sequence $y_m$ where $y_{m+1}$ is not in the span of $y_1,...,y_m$, ...
I believe you can make the whole sequence converge to the 0 vector pretty simply
viral quest
guh
Ok I'm trying to show that the unit ball is not compact
I've shown riesz's lemma, and I'm just trying to apply it
by constructing a sequence (each element norm 1, on unit ball) such that no subsequence of it converges, so it's not compact
fair fulcrum
ah
xy problem, perhaps
I still think the answer is you can find a convergent subsequence
oh you're trying to make one where that no subsequence converges
viral quest
yea
fair fulcrum
<1,0,0..> <0,1,0..> ?
hushed egret
riesz's lemma will let you conclude that no convergent subsequence exists if you construct your sequence correctly
marsh citrusBOT
@viral quest Has your question been resolved?
Available help channel!
Available help channel!
wary wolf
marsh citrusBOT
nova totem
!status
marsh citrusBOT
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
valid lantern
i cant find which test to use
marsh citrusBOT
i cant find which test to use
valid lantern
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severe briar
anyone up
severe briar
marsh citrusBOT
@severe briar Has your question been resolved?
still temple
hello!
river grove
Look at the denominator... take out 4 common from denominator... you will see something
still temple
so divide everything by 4?
still temple
ok
river grove
to compensate for what u divided
marsh citrusBOT
@still temple Has your question been resolved?
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.
river grove
As a helper, please do not give out answers that could be copied as a homework s...
okay
main dew
=?
dire spire
common factor
marsh citrusBOT
@alpine wigeon Has your question been resolved?
rugged dagger
marsh citrusBOT
rugged dagger
How do I verify if my integration is correct?
proper zodiac
,w int sin^5(x)cos^3(x)
elfin berryBOT
proper zodiac
Plot that against yours in desmos
rugged dagger
Hmm its different
Can you help me figure out where my mistake is? I've look through it 3 times and it seems fine
minute 15:38
I've plotted the answer in the video and it's also different from wolfram alpha's answer
this is the answer in the video
marsh citrusBOT
@rugged dagger Has your question been resolved?
obsidian shard
,w diff cos^6(x)/3 - cos^6(x)/4 - cos^8(x)/8
elfin berryBOT
obsidian shard
,w diff cos^6(x)/3 - cos^4(x)/4 - cos^8(x)/8
elfin berryBOT
obsidian shard
,w simplify sin(x) cos^3(x) (cos^2(x) - 1)^2
elfin berryBOT
marsh citrusBOT
@rugged dagger Has your question been resolved?
eternal tundra
marsh citrusBOT
eternal tundra
I tried the special case that P=Q and got nonesense
I did that to get intuition, not a proof
Then a=r
Scalar prd of e*r=-e
so we get
e^2-e=a^2-a^2=0
e=1
Which is not generally true
eternal tundra
e*r is projecting e onto r right?
Or projectibg r onto e
And since we are in a right triangle if we set P=Q
green sky
You can take it anyway
green sky
And since we are in a right triangle if we set P=Q
I'm a bit doubtful
marsh citrusBOT
@eternal tundra Has your question been resolved?
marsh citrusBOT
@eternal tundra Has your question been resolved?
marsh citrusBOT
@eternal tundra Has your question been resolved?
fleet onyx
marsh citrusBOT
fleet onyx
what is the formula for when exactly x amount is taking something
is it like 12! / 7! or something
marsh citrusBOT
@fleet onyx Has your question been resolved?
hearty reef
How is the product of a complex number and it's conjugate equal to the absolute value of that complex number squared?
marsh citrusBOT
How is the product of a complex number and it's conjugate equal to the absolute ...
hearty reef
Z x Z* = [Z]^2
elfin berryBOT
MathIsAlwaysRight
knotty trellis
try to expand this
hearty reef
that would be a^2 + b^2
hearty reef
I have no idea
glass quiver
Absolute value = magnitude
hearty reef
This is according to the distance formula right?
knotty trellis
yep
aka pythagoras theorem
the magnitude is just hypotenuse of triangle with side lengths a and b
hearty reef
Ok
knotty trellis
and when you do sqrt(a^2+b^2)^2 (the absolute value squared)
you will get a^2+b^2
hearty reef
So this square is a^2 + b^2
knotty trellis
**MathIsAlwaysRight**
Which is same as expansion of this