Du willst ja den Winkel, die die Ebene mit der z-Achse einschließen
#help-17
bitter pilot
der blaue Vektor, das ist ja nicht der Normalenvektor, sondern einer, der parallel ist zum Normalenvektor
Also ein Vektor der in der Ebene liegt
und deswegen kannst du einen der beiden Richtungsvektoren auswählen
Habe (-4,-2,9)v gewählt
vocal sleetBOT
tardy peak
.reopen
vocal sleetBOT
✅
bitter pilot
Also du hattest Recht mit dem Normalenvektor
Das Problem mit den Richtungsvektoren werde ich an einem Beispiel zeigen
Das Problem ist, wenn man irgendeinen Richtungsvektor nimmt man dann unterschiedliche Winkel bekommt
Man gut sehen, wenn man einmal um den Uhrzeigersinn einen Richtungsvektor dreht, dass der Winkel sich vergrößert
Bei dem Normalenvektor ist es aber so, dass er überall konstant ist, was das ganze Problem easy löst
twin meteorBOT
bacc
bitter pilot
bitter pilot
Hoffe das erkennt man hier
alpha ist der Winkel zwischen dem Normalenvektor und der z-Achse
du willst aber den Winkel zwischen der z-Achse under Ebene
Das gesamt ist ja also 90° davon nehmen wir alpha weg, um beta zu kriegen
gleaming owl
Could I get some help on the steps when it comes to doing Average Rate of Change problems but in word form?
vocal sleetBOT
Could I get some help on the steps when it comes to doing Average Rate of Change...
gleaming owl
So here's the problem
blazing wigeon
So here's the problem
Where
gleaming owl
I'm typing it out hold on 🙂
blazing wigeon
Sorry
gleaming owl
In 1991 the moose population was measured to be 580 by 1999 the population was measured again to be 6020 if the population continues to change linearly. Find a formula for the moose population P in terms of t, the years since 1990 P(t)=
I know how to do average rate of change but I need help on how to do it with a word problem
blazing wigeon
there we go
Is this the full problem? It doesnt seem to ask about average rate it's talking about linear change
gleaming owl
Oh yeah that's the full problem then that's my fault
blazing wigeon
Do you need help with it anyway?
gleaming owl
Yes
blazing wigeon
Okay, what are you struggling with about the problem
gleaming owl
Okay so first of all Linear change is the difference between two functions right or is that Average? and if so what's the difference?
blazing wigeon
Linear change just means the slope will be constant, the function P will be written in point slope or slope intercept form
A "straight line" so to speak
blazing wigeon
so what is a constant slope? aren't all slopes constant?
Yes, all slopes are constant, but when I say that the slope will be constant I mean that the slope will remain the same for the whole function
gleaming owl
Oh Okay regardless of what values I input?
blazing wigeon
y=x is a linear function, the slope is always 1
The slope will always be something for all of function P
gleaming owl
Oh okay
So if I go p(3) or p(4) if the function is linear the slope will be the same regardless?
blazing wigeon
So if I go p(3) or p(4) if the function is linear the slope will be the same reg...
Yes
At all points the slope will be the same
But this isn't helping you solve the problem
gleaming owl
I'm just clarifying
okay so what would the formula be for finding the slope of a linear function? and is that what the problem want's me to solve?
blazing wigeon
okay so what would the formula be for finding the slope of a linear function? an...
You need to find the slope to solve the problem yes. The answer to the problem will be a function
The slope is needed to form the function
The slope is
$\frac{P(t_2)-P(t_1)}{t_2-t_1}$
mari
blazing wigeon
You need to know two coordinates on P to find the slope
Can you think of how to find those points
vocal sleetBOT
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forest rock
hello anyone know how to work out the value of k without technology: (k+1)e^2k = 4
vocal sleetBOT
hello anyone know how to work out the value of k without technology: (k+1)e^2k =...
silk osprey
lambert W
forest rock
ok... so true
oh we dont have that in our study design
yea thats like way ahead like wtf even is this
forest rock
this is pre-uni
we're not meant to know lambert w
and if we do use it we have to prove it and im not gonna memorise the proof if i dont understand it yet
vocal sleetBOT
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crude wing
.reopen
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@forest rock Has your question been resolved?
forest rock
*part a isn't needed but helps antidiffing part d
forest rock
.close
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short kraken
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short kraken
Is this a trick question
"Antiderivative" applies to f'(x)
the anti derivative of f'(x) is f(x)
inner osprey
can you integrate x with respect to x and tell me what you get?
heavy yoke
let f(x) = g'(x), then g(x) is the antiderivative of f(x)
short kraken
f(x) is already in its barest form
short kraken
let f(x) = g'(x), then g(x) is the antiderivative of f(x)
Oh
I thought it was the other way around
antiderivarice is when you undo a derivative
inner osprey
the anti derivative of f'(x) is f(x)
this is true
short kraken
can you integrate x with respect to x and tell me what you get?
c?
inner osprey
let f(x) = g'(x), then g(x) is the antiderivative of f(x)
this is also true
heavy yoke
"antiderivative" is also the same as "indefinite integral"
short kraken
oh hold up I interpreted the question as "is f(x) an antiderivative"
Well isn't it always unique then
Cause of + C
heavy yoke
yes
short kraken
but that's just vertical translation
short kraken
really? I thought the point of + C is that we don't know if there was a constant
And that if there was we don't know the value
Cause it could've been + 2 or + 2583953
inner osprey
that is true
heavy yoke
really? I thought the point of + C is that we don't know if there was a constant
that means that every value of C produces a different antiderivative
inner osprey
that is true
short kraken
That C can be a random value we have no idea
so what determines uniqueness?
If + C doesn't
inner osprey
could it be you don't know what the word unique means?
short kraken
One of a kind? Idk 😭
inner osprey
something is unique when there exists only one of it, or one possilibity of such a thing
ok good then we're on the same page there
short kraken
2x + 1 is a different function from 2x+ 2
heavy yoke
so that means that g(x) = 2x + 2 is an antiderivative of f(x) = 2, and h(x) = 2x - 7 is another antiderivative of f(x) = 2, and 2x + C is an expression that tells us the form an antiderivative should take
inner osprey
2x + 1 is a different function from 2x+ 2
and both of these are antiderivatives of 2, as you've stated
short kraken
something is unique when there exists only one of it, or one possilibity of such...
so there exists multiple 2x
nvm
so 2x is contingent on the C value to make it unique?
Im getting confused what is the logic supposed to look like
inner osprey
so 2x is contingent on the C value to make it unique?
the idea is that the presence of the + C makes the antiderivative non-unique
C is not a variable that has a 'value', so to speak. rather, it is an indication that the antiderivative is only defined up to an additive constant
short kraken
C is not a variable that has a 'value', so to speak. rather, it is an indication...
I was interpreting it is as a placeholder
inner osprey
i see
inner osprey
i see
(it's typically defined using the phrase 'arbitrary constant', i.e. it could take any value but it'd be meaningless to assign it one)
inner osprey
but the antiderivative isn't
these assertions are correct yes
short kraken
I keep interpreting it as unique cause my textbook illustrated it as a function with multiple vertical translations
short kraken
these assertions are correct yes
so say f(x) = 2x. The derivative of 2x is 2, and only one f'(x) = 2 exists
Am I on track?
inner osprey
yes the derivative is unique
vocal sleetBOT
inner osprey
yw
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knotty wyvern
Could I get help with the left and rule hand rules ?
vocal sleetBOT
Could I get help with the left and rule hand rules ?
knotty wyvern
I don’t know why the rotations work the way they do
Starting in the original position with thumb pointing left, index pointing up, and middle pointing out , why am I not rotating my hand downwards if my thumb represents the axis of rotation? Unless I am wrong
I guess in my scenario the z axis should become the -y axis
But instead I’m rotating my hand right and down ish ? Idk
vocal sleetBOT
@knotty wyvern Has your question been resolved?
rigid wind
What is the definition of zero angle
knotty wyvern
Like no rotation?
rigid wind
Like no rotation?
U r drunk
winter hawk
@rigid wind dont be rude to others. come back in 24h
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knotty wyvern
.close
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flat steppe
.reopen
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spice grove
Does anyone know how to find the range of this function algebraically?
g(x) = x+3/x^2+1
spice grove
$(x+3)/(x^2+1)$
twin meteorBOT
bruhomomento
vocal sleetBOT
@spice grove Has your question been resolved?
spiral turtle
Not algebraicly. I know how to do it with differential calculus though.
fickle rose
Does anyone know how to find the range of this function algebraically?
g(x) = x...
assume it to be y, you get a quadratic, it should have positive discriminant
spiral turtle
assume it to be y, you get a quadratic, it should have positive discriminant
Oh! Smart!
And the zeroes of the discriminant are the extreme points of the range.
spice grove
oh I see
spice grove
And the zeroes of the discriminant are the extreme points of the range.
I don't understand this part tho...
spiral turtle
@spice grove start by setting g(x) = y and finding a quadratic in x.
Your answer should be ax^2 + bx + c = 0, where a, b, and c are possibly functions of y.
For instance (not the actual answer just an example) 2y x^2 + (6+y) x - y+2
In the above example, a = 2y, b = (6+y), and c = (2-y)
cosmic cloud
I don't understand this part tho...
Maximum/minimum values
spiral turtle
Now imagine I pick a particular y value. I can find all the points (x, y) that correspond to that y value by substituting it into the quadratic equation, and then solving for x.
If my y value is too high or too low, then I only get imaginary solutions.
If I choose one somewhere in the middle of the range, then that's all well and good, most of the time I'll get exactly two solutions
But at the maximum and the minimum, I'll only get one solution.
One solution corresponds to when the determinant is 0
So essentially, find the quadratic, construct the discriminant, set equal to 0, then solve.
The solution will be the y values you seek.
vocal sleetBOT
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glacial zealot
Show that the equation x ^ 2 + y ^ 2 + z ^ 2 + t ^ 2 = 2 ^ 2004, where 0 <= x <= y <= z <= t has exactly two solutions in Z
vocal sleetBOT
Show that the equation x ^ 2 + y ^ 2 + z ^ 2 + t ^ 2 = 2 ^ 2004, where 0 <= x <=...
@glacial zealot Has your question been resolved?
vocal sleetBOT
@glacial zealot Has your question been resolved?
glacial zealot
<@&286206848099549185>
rare elbow
hi
glacial zealot
Show that the equation x ^ 2 + y ^ 2 + z ^ 2 + t ^ 2 = 2 ^ 2004, where 0 <= x <=...
.
I found the solutions, but idk how to show that there are only 2
x = y = z = 0, t = 2 ^ 1002
x = y = z = t = 2 ^ 1001
inner osprey
I found the solutions, but idk how to show that there are only 2
to prove this, use (mod 8)
glacial zealot
a perfect square is 0, 1 or 4 (mod 8)
glacial zealot
ohh so all of them have to be even
vocal sleetBOT
inner osprey
yvw
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hoary warren
can anyone help me with this question? the power source wasn't provided so how could I find the rest?
vocal sleetBOT
can anyone help me with this question? the power source wasn't provided so how c...
twin horizon
Were you told if they are connected in series
twin horizon
I think you have to find it on your own
Probably
twin horizon
Were you told if they are connected in series
If they are then the current is the same
hoary warren
I think you have to find it on your own
yea my teacher said use formula but I assume it is impossible without any given clues?
cosmic cloud
I meant finding those appliances in your home and then checking
hoary warren
feel like need to ask teacher for further clarification, thanks for the help
.close
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hollow plinth
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outer panther
for rational functions the domain restrictions come from the denominator
they happen when a value of x results in division by zero
hearty jungle
at x = 0 it's 0 and at x = infinity it's 1, so 0 <= y < 1
outer panther
i thought this was asking for domain?
hollow plinth
No lol
cosmic cloud
I don't understand what it means by boundaries
hearty jungle
range
hearty jungle
]0, 1[
vocal sleetBOT
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Available help channel!
polar hawk
I dont understand how to simplify and calculate this lim
lim (x->inf) (1/x^{2}+2/x^{2}+...+(x-1)/x^{2})
twin meteorBOT
Danya
polar hawk
i need a hint
dim pumice
whats 1+2+...+(x-1)?
azure flame
use sigma n=n(n-1)/2
gentle sleet
you can factor out the x^2 stuff
vocal sleetBOT
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feral drift
The input range is between 0 and 1, and so is the output range. The probability density function pr(r)= ar^2 of the input image is quadratic, while the probability density function pz(z)=bz of the output image is linear (where a and b are unknown constants).
Find the transformation function z=Q(r) analytically using the relationship between the input and output PDFs.
vocal sleetBOT
The input range is between 0 and 1, and so is the output range. The probability ...
feral drift
can you please verify my solution
visual canyon
can anyone help me with bearings?
feral drift
can anyone help me with bearings?
what do u mean
visual canyon
bearing in geometry
feral drift
bearing in geometry
please ask in another thread, this room for specific question i raised
<@&286206848099549185>
flat whale
can you please verify my solution
Your cdf looks wrong. Follow the definition
feral drift
Your cdf looks wrong. Follow the definition
which lines you mean can you elaborate
flat whale
"get cdf of input" top left
rocky lichen
||use /spoiler for this secret method||
feral drift
Is this correct?
flat whale
Is this correct?
Yes
flat whale
but is it true that z = square root of r power3?
Show the original question
feral drift
The input range is between 0 and 1, and so is the output range. The probability ...
here
vocal sleetBOT
@feral drift Has your question been resolved?
vocal sleetBOT
@feral drift Has your question been resolved?
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@feral drift Has your question been resolved?
mild trench
I know this is a VERY dumb question
vocal sleetBOT
I know this is a VERY dumb question
mild trench
but I haven’t done this in a long time
and I know how to do it the long way
but is there a short method to work out the LCM of 2 numbers
cedar burrow
but is there a short method to work out the LCM of 2 numbers
With or without calculator (namely one that can return fractions)?
mild trench
With or without calculator (namely one that can return fractions)?
both
feral drift
question, 2 please also check if my histogram is correct for the input and outpu...
<@&286206848099549185>
cedar burrow
<@&286206848099549185>
Open a new channel, this one is no longer yours
cedar burrow
both
One I can think of is
For lcm(a, b), put a/b in its simplest form (let it be c/d), then ad=bc=lcm(a, b)
mild trench
One I can think of is
For lcm(a, b), put a/b in its simplest form (let it be c...
yes
I know this
how about
3 numbers?
cedar burrow
Shouldn’t rinse and repeat work?
mild trench
hmm lemme try
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tardy peak
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vast shale
factor the numerator and denominator
there's a common factor that can be cancelled from both expressions
vast shale
ye, try that and see if it works
tardy peak
Denominator is still 0
vast shale
Denominator is still 0
okay this needs a bit of extra explaining
tardy peak
6/0
vast shale
if a limit statement from direct evaluation results in both the numerator AND denominator being 0
it is an "indeterminate form"
like 0/0
but since now the numerator is 6 and the denominator is 0 it is no longer indeterminant
tardy peak
But its not indeterminate i think
vast shale
yes
vast shale
but since now the numerator is 6 and the denominator is 0 it is no longer indete...
because of this
so the answer is simply infinity
tardy peak
Ohh okay
tardy peak
Why
tardy peak
<@1074347191029739560> does that make sense??
Im not sure hhe
vast shale
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
6/0 is inf doesnt make a sense to me
bitter pilot
6/0= infinity
no
vast shale
in the context of limit statements yes
twin meteorBOT
bacc
bitter pilot
If x < 4 then that expression is negative
vast shale
hmm wait youre right
is there a specific method to instantly determining that
because if you square the entire expression ((x+2)/(x-4))^2 the limit all of a sudden exists
bitter pilot
We can make a substitution $x = u+4$ to see that it has the form of $\frac{1}{x}$ [ \lim_{u \to 0} \frac{u+6}{u} = \lim_{u \to 0} 1 + \frac{6}{u} ]
bitter pilot
because if you square the entire expression ((x+2)/(x-4))^2 the limit all of a s...
cause the square makes it from both side approaching +inf
vast shale
cause the square makes it from both side approaching +inf
yes ofc
bitter pilot
the rule is if your linear factor has an odd power in the denominator then it changes sign around the vertical asymptote, but if the power is even it doesn't
vast shale
well thats just a logical statement to make though
i cant remember but i couldve sworn there was another thing
not sure what it is tho
ig i forgot about it now
twin meteorBOT
bacc
bitter pilot
I hate the formatting sometimes
vast shale
lol just type it normally its fine
vast shale
alright then well good luck
bitter pilot
,w plot y=(x^2-2x-8)/(x^2-8x+16) between 0 and 8
twin meteorBOT
vocal sleetBOT
If you are done with this channel, please mark your problem as solved by typing .close
bitter pilot
Is it 0?
Does not exist
From the right you approach a different limit then from the left
vocal sleetBOT
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inland sail
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inland sail
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
vocal sleetBOT
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vast shale
Can i get some help
vocal sleetBOT
Can i get some help
vast shale
Okay thanks
Its statitsc
Statistics
So for 1i dont understand how x^2f
Im tryinng to find the phito
So apprently the correct answer for x^2f is this bottom photo
And i dont get how its that
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
<@&286206848099549185>
vast shale
<@&286206848099549185>
broken glacier
it seems there's outright refusal to help with stats on this server
vocal sleetBOT
@vast shale Has your question been resolved?
plush tinsel
could anyone help me with micro
pls
I’m having a hard time
<@&286206848099549185>
<@&286206848099549185>
vast shale
it seems there's outright refusal to help with stats on this server
So not sigma
carmine cedar
$\int {{2xsin{x}} \over {3 + cos{2x}}}dx$
vocal sleetBOT
$\int {{2xsin{x}} \over {3 + cos{2x}}}dx$
twin meteorBOT
daniel_zein
carmine cedar
how am I supposed to do this?
flat whale
,w int (2x sin(x))/(3+cos(2x))
twin meteorBOT
flat whale
$\int {{2xsin{x}} \over {3 + cos{2x}}}dx$
!original
vocal sleetBOT
$\int {{2xsin{x}} \over {3 + cos{2x}}}dx$
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
pale perch
oh dear lord
carmine cedar
holy hell
bitter pilot
pov you forgot the bounds
warped prairie
How do I verify if this is true: column space of AB is a subspace of column space of A
vocal sleetBOT
How do I verify if this is true: column space of AB is a subspace of column spac...
@warped prairie Has your question been resolved?
warped prairie
<@&286206848099549185>
warped prairie
<@&286206848099549185> 
cunning basin
lol
flat whale
Either check for the definition of subspace using what it means to be in the column space of AB or find a counter example
cunning basin
warped prairie
That's exactly my question, what does it mean when we talk about a column or row space of AB
vocal sleetBOT
@warped prairie Has your question been resolved?
little isle
What are the root(s) of x²=0 ?
vocal sleetBOT
What are the root(s) of x²=0 ?
torn oracle
just 0
flat whale
solve for x² in 3mx² +mnx - 3nx -n² =0
,tex .quadratic formula
twin meteorBOT
riemann
flat whale
but like its not in standard form..
Put it in standard form
little isle
Howww
flat whale
**riemann**
Get x by itself
little isle
@flat whale
flat whale
Get x by itself
Did you read this
little isle
<@&286206848099549185>
flat whale
Welp I'm being ignored
pine hull
Welp I'm being ignored
pine hull
solve for x² in 3mx² +mnx - 3nx -n² =0
You can solve for x not x²
kind light
you can technichally just square it :3
kind light
**riemann**
anyways use thos
noble gyro
solve for x² in 3mx² +mnx - 3nx -n² =0
pine hull
you can technichally just square it :3
vocal sleetBOT
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.
noble gyro
As a helper, please do not give out answers that could be copied as a homework s...
noted
kind light
you should delete it
vocal sleetBOT
@little isle Has your question been resolved?
little isle
what
pine hull
@little isle your question is this
solve for 3mx² +mnx - 3nx -n² =0
To solve any quadratic equation you need to convert it into form
ax²+bx+c=0
pine hull
**riemann**
Once you do that use this formula to find values of x
little isle
Guys ..
Guys what is the function of this
Quadratic function for that graph
Equation
pine hull
Quadratic function for that graph
Maybe paste a screenshot of your actual question
That way others can understand what's your actual doubt
twin citrus
vocal sleetBOT
fading plume
what approximation techniques have you learned in class
newton's method comes to mind
twin citrus
no no this is not calculus
its precalculus
there is no method to approximate square roots yet
fading plume
oh interesting? not sure if we can help without knowing the method then
heavy yoke
are you meant to use a calculator?
fading plume
not much of an approximation then is it
heavy yoke
it's still approximate if you round it(?)
edgy gulch
and if so how to do that without pain ?
you could round everything down to just a whole number, but thats probably not what you're supposed to do
twin citrus
my consern is that why authir nit allowed to use calculator here ?
fading plume
i guess you could binary search
but again i'm not sure what the context of this question is
vocal sleetBOT
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Available help channel!
prisma parcel
Simply: why do we need the assumption of the AoC here?
vocal sleetBOT
Simply: why do we need the assumption of the AoC here?
tawny nacelle
iirc, you need Zorn’s lemma to find a maximal linearly independent set in this proof
which is equivalent to AoC
in finite dim, you don’t need it
but in inf dim, you do
oh wait, I literally misread the question lol
I thought this was every vsp has a basis for some reason zz
dense moon
I mean it trivally proves every vector space has a basis
the vector space spans itself ofc
prisma parcel
I thought this was every vsp has a basis for some reason zz
I thought that it was just by definition of a vs that they all had bases but thinking back on it, that's not an axiom 
prisma parcel
the vector space spans itself ofc
Could you elaborate a bit on that pls, we thought that normally you'd consider some basis which would be a subset of V that spans V
dense moon
I'm just making the observation that "every spanning set contains a basis" implies "every vector space has a basis" since you can take the vector space itself as the spanning set.
vocal sleetBOT
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formal nymph
hello can someone help me get the common ratio or common difference in this..
formal nymph
and can you check if this is correct
we were tasked to identify of it was either arithmetic or geometric sequence, and then we will put the common difference or ratio
<@&286206848099549185>
wise cape
Hello
wise cape
I have no clue as I haven’t done this yet
cunning ingot
can u check my answers 😿
Correct
cunning ingot
i dont have an answer for 4, and 8
Process is the same
formal nymph
Process is the same
but i dont seem to find a common difference and ratio in them
isnt this what we should do to get the ratio
i dont get it huhu
i need helpp
@hel
<@&286206848099549185>
spice kestrel
if so then question 7 fails right ?
formal nymph
what you need
i cant aeem to get the common ratio or difference for no. 4 and 8
<@&286206848099549185>
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verbal coyote
Is this an quadratic equation?
vocal sleetBOT
Is this an quadratic equation?
verbal coyote
Can I just put
a = 1
b = -4 +2i
c = 12-4i
neat dawn
vocal sleetBOT
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Available help channel!
ionic marlin
can we write
vocal sleetBOT
can we write
ionic marlin
f_0cos(wt) as F_0e^(iwt)?
hard atlas
if you put a real part somewhere in there, sure
ionic marlin
this is the differential equation
and the solution we get is Bcos(wt-phi)
which we can express in exponential form
which I get
i dont get what happened after that
can you please help me out
@hard atlas
so is this right
this is what i understand
e^i*y = cos(y) + i sin(y)
the only real part is cos(y)
where y = wt-phi
so Re(e^iy) = cos y
thats it right
hard atlas
yes
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whole gale
why are the limits in a miltiple integral called the rectangular region
full summit
integrating a function is finding the area under the curve
whole gale
yes
full summit
rectangular region refers to the limits of integration over a rectangular shaped area?
vocal sleetBOT
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tawny nacelle
does this proof work?
vocal sleetBOT
does this proof work?
tawny nacelle
what are all those reacts for 
fervent wasp
An admiration to JEE 🫡
loud walrus
dull bear
Nah I'm just here to add to the reacts 
tawny nacelle
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torn timber
An admiration to JEE 🫡
damn i didnt know jee had proofd
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Available help channel!
latent eagle
can someone explain how to do this without expanding the brackets completely
twin horizon
Maybe try
(1+x²)^5=(1+x²)^4*(1+x²)=
Then you can bring (1+x²)^4 with (2+x)^4
Apply law of indices
And next binomial theorem
I hope this makes sense 😅😔
peak matrix
can someone explain how to do this without expanding the brackets completely
Alternatively,
The only way you can get x^3 is as
x^0 * x^3
x^1 * x^2
x^2 * x^1
x^3 * x^0.
So find the coefficients of x^0, x^1, x^2, x^3 in (2+x)^4 and (1+x^2)^5 seperately
peak matrix
And next binomial theorem
im worried that you'll get a trinomial
peak matrix
how are you gonna apply binomial theorem to that
twin horizon
Sub
peak matrix
sounds painful
peak matrix
<:catglasses:1037770587235434567>
wait do you get my approach or not?
it might be unclear
twin horizon
wait do you get my approach or not?
I do
Since you are only concerned about the power "3" on x so you only need to find the coefficients and add them right
latent eagle
yes
peak matrix
Since you are only concerned about the power "3" on x so you only need to find t...
Yep
so you need to find coefficients of
x^0 * x^3
x^1 * x^2
x^2 * x^1
x^3 * x^0
where the first x comes from (2+x)^4 and the second x comes from (1+x^2)^5
latent eagle
so find x^3 coefficient for both brackets ?
peak matrix
I'll temporarily adapt notation Ca(x^n) for coefficient of x^n in the first multiplicand (2+x)^4 and Cb(x^n) for the coefficient of x^n in the second multiplicand (1+x^2)^5
Then the coefficient of x^3 in the result should be:
Ca(x^0) * Cb(x^3) + Ca(x^1) * Cb(x^2) + Ca(x^2) * Cb(x^1) + Ca(x^3) * Cb(x^0)
peak matrix
so find x^3 coefficient for both brackets ?
you will need coefficients of x^0, x^1, x^2 and x^3
peak matrix
so you need to find coefficients of
x^0 * x^3
x^1 * x^2
x^2 * x^1
x^3 * x^0
wh...
because x^3 can be written in all those 4 ways
once you find the coefficients, the result can then be written as
(a + bx + cx^2 + dx^3 + [useless...]) * (e + fx + gx^2 + hx^3 + [useless...])
and if you were to expand that out, the coefficient of x^3 will be
ah + bg + cf + de
peak matrix
,w (2+x)^4(1+x^2)^5
twin meteorBOT
peak matrix
,w expand (2+x)^4(1+x^2)^5
twin meteorBOT
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Available help channel!
thick niche
vocal sleetBOT
thick niche
is there a way to solve this algebraically
inner osprey
no matter what u do u would need some kind of estimation
thick niche
no matter what u do u would need some kind of estimation
well i estimated the first 10 and turns out n. = 10
took me 9 whole mins
knotty lynx
9 minutes?
inner osprey
took me 9 whole mins
ye when doing smth like this u might consider some rough argument to start at a later number instead of doing all of n = 1, 2, etc until u find the ans
thick niche
yea :/
knotty lynx
Did you evaluate the binom as-is?
thick niche
ye when doing smth like this u might consider some rough argument to start at a ...
i did n = 1 first then n = 100 just to get a rough idea
thick niche
Did you evaluate the binom as-is?
no i just suck at arithmetic
i dont know how to get better
inner osprey
Did you evaluate the binom as-is?
wt about this
thick niche
its dragging me down and i feel depressed
inner osprey
did u simplify the binomial coefficient
thick niche
no i estimated
inner osprey
how did u estimate?
brisk moss
maybe you could do something with stirling’s approximation first to get a place to start
inner osprey
stirling?
thick niche
maybe you could do something with stirling’s approximation first to get a place ...
what is that
inner osprey
note (10n + 2) - (10n - 1) = 3
inner osprey
so did use property n C k = n C (n - k)
thick niche
10n + 2 (10n +1 (10n
inner osprey
ok very good
thick niche
divdide by 6
inner osprey
ye nice ok
thick niche
how do i
get better at arithmetic
i tried doing worksheets
idk if im getting faster or not
inner osprey
if ur issue is only ‘arithmetic’, then nothing but practice will help i think
but for this problem in particular i think some bit of intuition may help you
inner osprey
10n + 2 (10n +1 (10n
also i would probably approximate this as 1/6 * (10n + 1)^3
inner osprey
is it useful
stirling approximation is a way to approximate the factorial function
thick niche
o
inner osprey
it is typically used when u have limits involving factorials
(i do not see use for it here)
thick niche
is that like taylor serie or something
inner osprey
is that like taylor serie or something
is this
in most cases where stirling approximation is necessary, you would use this statement and that would be sufficient
thick niche
in most cases where stirling approximation is necessary, you would use this stat...
i see
thanks
!
.close
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inner osprey
yw
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short rover
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short rover
how did we go from step 1 to step 2
sullen shoal
Divide by 4^n
sullen shoal
Divide by 4^n
Both numerator and denominator
vocal sleetBOT
pallid trout
(1+2)^2006=a+b√2. calculate a^2-2b^2
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knotty wyvern
can i get some help identifying the handedness of a 3d coordinate system either with maybe a resource or given questions?
vocal sleetBOT
can i get some help identifying the handedness of a 3d coordinate system either ...
knotty wyvern
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ocean shale
Does anyone know what kind of question this would be called? I'm trying to find videos for it on khanacademy but googling "how to make a fraction/division problem undefined" really isn't getting the videos I want.
vocal sleetBOT
Does anyone know what kind of question this would be called? I'm trying to find ...
heavy yoke
something like "domain of a rational function"
ocean shale
that seems similar I'm not sure if that is what the problem is called
very close though because it's algebra 1
vocal sleetBOT
@ocean shale Has your question been resolved?
oblique kettle
poles, singularities of functions
alpine trout
where did 12 come form
vocal sleetBOT
where did 12 come form
red ridge
where did 12 come form
like the 12.0000 g/mol part?
alpine trout
its the bottom part
the 1 amu=1.9927e-23
/12
like i know its the mass number/ avvogadro number to get gram but the second part of it is confusing
heavy yoke
1 amu is supposed to be roughly the weight of 1 proton or 1 neutron, a carbon atom has 12 (6 protons and 6 neutrons)
storm terrace
Does anyone know what kind of question this would be called? I'm trying to find ...
just wanted to really quickly say that fractions become undefined when there's a zero in the denominator
alpine trout
1 amu is supposed to be roughly the weight of 1 proton or 1 neutron, a carbon at...
omg ty
vocal sleetBOT
@alpine trout Has your question been resolved?
ocean shale
just wanted to really quickly say that fractions become undefined when there's a...
I know they but my issue is that it wants me to find a number that would make the fraction undefined
although what you are saying is giving me a brainblast currently and I think I almost get what you are saying
storm terrace
I know they but my issue is that it wants me to find a number that would make th...
in your question, it just means you have to solve x^2+2x = 0
of which the solutions are x = 2, 0
hence the answer is i and iii
cedar kernel
I needed help with this differential equation and these type in general
cedar kernel
L and C are constants
And I need to solve for I
Can anyone give a basic idea to solve these , I will try to adapt , I have not exactly studied differential equation of these types before but came across it while doing physics
lavish river
second order de
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Available help channel!
vast shale
how would i start this (assignment title is induction and binomial theorem)
vast shale
please @ me if u have an answer
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@vast shale Has your question been resolved?
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@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
@vast shale Has your question been resolved?
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@vast shale Has your question been resolved?
random ice
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oblique kettle
$4^x + 4^{x+1} = 4^x + 4^1 \cdot 4^x = 4^x + 4 \cdot 4^x = 4^x (1 + 4) = 5 \cdot 4^x$
twin meteorBOT
Emily
vocal sleetBOT
@random ice Has your question been resolved?
sturdy crag
does this mean that the answer of km/h and m/s should have 5 significant figures? because of 86400?
vocal sleetBOT
does this mean that the answer of km/h and m/s should have 5 significant figures...
warm vine
yes
sturdy crag
so does the two 0's after 4 also count?
vocal sleetBOT
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Available help channel!
livid prairie
how many 50 x 50 grids of white and black cells are there such that
- no two white cells touch
- every black cell touches a white cell
(diagonal touching by corners counts as touching)
vocal sleetBOT
how many 50 x 50 grids of white and black cells are there such that
1) no two wh...
livid prairie
we've solved it for nx1 grids
gonna update this over time:
f(m, n) = f(n, m)
f(1, 1) = 1
f(2, 1) = 2
f(3, 1) = 2
f(4, 1) = 3
f(5, 1) = 4
f(n, 1) = f(n - 1) + f(n - 5)
@brisk moss
so
for nx2 grids
f(2, 1) = 2 (W/B, B/W)
f(2, 2) = 4 (WB/BB and rotations)
now how to extend
if last column is W/B or B/W you can do B/B
if it's B/B you can do W/B or B/W
livid prairie
i'm making the recursion for f(n, 2) not f(n, 1)
dense eagle
how many 50 x 50 grids of white and black cells are there such that
1) no two wh...
was this something u came up urself or did it come from somewhere?
livid prairie
this is not a traditional help channel question, layla found a problem and a few of us started working on it, we realized that we were clogging up discussion so we made a help channel
inner osprey
i'm making the recursion for f(n, 2) not f(n, 1)
wt else would i be referring to 👀
livid prairie
ok
inner osprey
ur recursion for f(n, 1) is not right
livid prairie
how
brisk moss
layla found a problem
not quite the correct lore but ok lol
livid prairie
lol
if it ends in B you can add W, if it ends in W you can add B, if it ends in B you can add WBBWB
there
computer verified up to n = 20
lol
brisk moss
ur recursion for f(n, 1) is not right
i think it's ok? it might be different than ours but offset
brisk moss
computer verified up to n = 20
can you post, say, 50 values?
livid prairie
my school chromebook isn't powerful enough to run that
brisk moss
ok i can do it
livid prairie
for tests up to n = 50 we need a good computer
it would still take several days tho
brisk moss
no i meant with your recursion
livid prairie
oh
inner osprey
i think it's ok? it might be different than ours but offset
ok that is true
livid prairie
if the last column is WB or BW you can add BB and (WB or BW), if it's BB you can add WB or BW
brisk moss
can you post, say, 50 values?
ok nvm that if mqnic agrees now
livid prairie
does this produce everything?
livid prairie
if the last column is WB or BW you can add BB and (WB or BW), if it's BB you can...
this produces f(n, 2) = f(n - 1, 2) + f(n - 2, 2)
actually
lemme try computer generation
brisk moss
||incorrect buzzer sound||
vocal sleetBOT
@livid prairie Has your question been resolved?
vocal sleetBOT
brisk moss
.reopen
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✅
inner osprey
brisk moss
inner osprey
🫵
brisk moss
flat whale
brisk moss
vocal sleetBOT
@livid prairie Has your question been resolved?
untold arrow
Why did they move pho out? Isn't the inner integral related to pho? Then why can pho be moved out
vocal sleetBOT
Why did they move pho out? Isn't the inner integral related to pho? Then why can...
spiral turtle
That's not phi or pho
bronze osprey
I mean rho
spiral turtle
that's rho
outer warren
its rho
twin meteorBOT
icannotdoanymorecauchy
bronze osprey
rho rho rho your boat
gently down the stream
bitter pilot
bro's getting bullied 💀
bitter pilot
vocal sleetBOT
bitter pilot
does this make sense
cobalt crypt
💀
dense moon
<@&268886789983436800>
dense eagle
<@&268886789983436800>
bitter pilot
he got smayed out
arctic mantle
?
dense moon
does this make sense
No, it doesn't
dense eagle
i think ur lacking words basically
bitter pilot
sometimes i talk too much
dense moon
each one of your inequalities is unjustified (and incorrect, even)
to be a bit direct
bitter pilot
each one of your inequalities is unjustified (and incorrect, even)
to be a bit d...
why
dense moon
The first inequality might be okay
dense moon
why is |x-1|/|x| less than delta/|x|
bitter pilot
seriously
dense eagle
we're taking the limit as x -> 0, not 1
bitter pilot
oh
dense moon
anyways, one hint for why your proof couldn't work is that you didn't use any properties of sin
i.e. the same reasoning could be applied to x^2/x, which goes to 0
or sqrt(x)/x, which diverges
flat whale
you sometimes have to do something like delta = min{eps, 1}
dense moon
it helps to think about this a bit more loosely
dense moon
|sin x| is going to be close to |x|
bitter pilot
how
dense moon
well that's what you're trying to prove, no?
bitter pilot
oh
dense moon
so (|sin x| + |x|)/|x| is going to be close to 2 for small |x|, loosely speaking
so it doesn't really help to bound by that
I mean it should converge to exactly 2, if what you're proving is correct
flat whale
min is basically cheating
it's either this or really cheat and use taylor expansion
bitter pilot
i actually thought about taylor expansion and then i imagined how everybody would flame me
flat whale
doing this problem deserves flaming when you already know squeeze theorem and trig
bitter pilot
I do this specifically with epsilon delta cause I never did it really
and I wanna practice that
flat whale
do real problems for practice
dense moon
I mean you need properties of sin for this
dense moon
a good exercise is to prove that arithmetic of limits works
dense eagle
should warn u that q14 is like really hard
(actually idk how to do the latter part of 14, and i don't think i know anyone who does)
vocal sleetBOT
@bitter pilot Has your question been resolved?
mystic tide
Here’s another approach, if you agree 0<cos(x)<sin(x)/x<1 when x is close to zero the proof becomes much easier. This is easy to show using trig.
vocal sleetBOT
@bitter pilot Has your question been resolved?
bitter pilot
Y'all ain't ready for this
tight hearth
yo guys i have a problem with this im in the first year baccalaureate so please can some one help me to solve this
bitter pilot
yo guys i have a problem with this im in the first year baccalaureate so please ...
bro delete this
thats my channel
bitter pilot
<@&268886789983436800>
tight hearth
bro delete this
bro if you have solution give it to me please
bitter pilot
my poor proof
limber falcon
yo guys i have a problem with this im in the first year baccalaureate so please ...
open your own help channel please
use one of these
chilly prawn
bro lock im a new in this server
Ask qna
cobalt crypt
that was for the spam earlier that got nuked 💀
flat whale
why use alpha and omega instead of epsilon and delta
bitter pilot
😕
bitter pilot
that was for the spam earlier that got nuked 💀
🥺
dense moon
why should that first inequality work?
a < b doesn't imply |a - c| < |b - c|
also if you're ok with using the fact that sin' = cos then you can just use the definition of the derivative with sin'(0) = cos(0) = 1.
vocal sleetBOT
@bitter pilot Has your question been resolved?