But this is a good lesson
#help-0
upbeat gorge
Better to be careful than be fast
lilac plank
I am required to study these titles, and I do not know what this means shourt cut of what (ci) Also, could you please tell me if these two titles are the same topic or not? Because I'm not researching hypothesis & A/B testing. I only find one of them without the other, while in the question here it is written &
zealous lichen
confidence interval
lilac plank
this mean there is 4 topic here right ?
zealous lichen
It seems so
lilac plank
okay thanks
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
how come this became undefined
heady pollen
in this context x is not the same as x^2/x
alpine sable
in this context x is not the same as x^2/x
why?
heady pollen
x^2/x is x when x is not 0
in the case of 0, x^2/x is not defined
but x is
so the two functions
f(x)=x, g(x)=x^2/x
look identical, but one is defined for 0, the other is not
since we cant divide by0
alpine sable
so the two functions
f(x)=x, g(x)=x^2/x
look identical, but one is defined for 0...
ok i got it
domain of f(x) is R
and Domain of g(x) is R-{0}
alpine sable
so the two functions
f(x)=x, g(x)=x^2/x
look identical, but one is defined for 0...
in g(x) cant we cancel x?
heady pollen
we can and then we get f(x)
but by simpliying, we assume that x is not 0, since otherwise g is not defined
since when we have 0^2/0, we cant cancel out a 0 to get 0
otherwise we could do stuff like this:
$\frac{0}{0}=\frac{0^2}{0}=\frac{0\cdot\not{0}}{\not{0}}=0$
ocean sealBOT
Martin
alpine sable
hmm
heady pollen
which is not allowed
alpine sable
but why dont we say 0/0 = 1
see
0/0 = x
0 = 0x
0=0
It works
heady pollen
by that logic:
0/0=x
0=0x
that would be always true, for every x
therefore 0/0=x would be true for all x
which is not really useful
alpine sable
what is lim 0 -> x/x?
heady pollen
an example of how ambiguous this is, look at f(x)=1/x
this f is not defined at x=0
if we get close to 0 from the left, we get -infinity
if we get close to 0 from the right, we get +infinity
heady pollen
what is lim 0 -> x/x?
when getting the limit, we dont look at x=0, therefore we can simplify it to 1, and that stays 1 if we approach 0
but the limit is not always (like in this example) the value at that point
the function f(x)=1/x is a good example for that since the two limits are not even the same there
another example would be sgn(x) which is -1 for negative numbers, +1 for positive numbers and 0 for 0
alpine sable
but while getting the limit why dont we look at x=0?
heady pollen
$\lim_{x\to x_0}f(x)=f(x_0) \ \text{only if f is continuous in }x_0\text{ and around that }x_0 \ \text{of course f also must be defined there}$
ocean sealBOT
Martin
heady pollen
but while getting the limit why dont we look at x=0?
with the limit, we approach a certain x value, we never reach it
therefore the true value of f at that point has nothing to do with the limit
heady pollen
👍
alpine sable
.reopen
lone heartBOT
✅
alpine sable
Hey for any function we have an equation f(x) = x+1 ...
Similarly what's the equation for sin(x)?
sin(x) = ???
buoyant storm
sin(x) = ???
you want a polynomial? that's maclaurin series though its advanced
trig funcs are defined geometrically
alpine sable
you want a polynomial? that's maclaurin series though its advanced
lemme search for this
buoyant storm
$\sin{x}=\sum_{i=0}^{\infty}(-1)^i(\frac{x^{2i+1}}{(2i+1)!})=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}\cdots$
that is maclaurin series
it is advanced so you DO NOT need to know this
you just need to accept that the polynomial form EXISTS
alpine sable
ok
buoyant storm
use the geometric def instead
ocean sealBOT
orthogonal
buoyant storm
also that thing goes on forever
alpine sable
If sin(x) = y and sin^-1 (y) = x
then does it works for every function ?
Like f(x) = 2 then f^-1(2) = x?
buoyant storm
no...
buoyant storm
If sin(x) = y and sin^-1 (y) = x
then does it works for every function ?
Like ...
question: express sin(x+2pi) in terms of sin(x)
lone heartBOT
@alpine sable Has your question been resolved?
barren portal
Is it possible to show natural numbers are closed under addition using peano’s axioms?
worn fox
the definition of addition using peano just uses successor recurisvely so that would be fine
barren portal
so addition is closed as an axiom?
worn fox
it follows from the axioms
worn fox
i didnt mean recurisve, i was thinking of multiplication
just look at the how you define addition using peano
mortal trellis
the definition of addition is that m+(n+1) = S(m+n) and m+1 = S(m)
iirc
so you basically immediately get that its closed
worn fox
think you just need your first one and that m + 0 = m
mortal trellis
depends if 0 is in N or not
barren portal
Isn’t zero in N an axiom?
mortal trellis
depends on who you ask
nothing goes wrong if you let the first element be 1 (or 17 for that matter)
its just a name. at least initially
mortal trellis
basically
peano just says there is some first element
i.e. an element which is not the successor of anything
barren portal
you can all it 1
mortal trellis
whether you call that element 0 or 1 or 17 doesnt matter
barren portal
makes sense
is succesor function same as +1
how do i see it more formally
than just adding 1, im thinking it as +1 always
worn fox
i dont think there anything wrong with seeing it as +1
since thats pretty much exactly what its trying to model
mortal trellis
well initially you dont have something called addition so writing +1 is not yet defined
but the point of defining addition in the way above is that we can then see the successor function as adding 1
barren portal
can you link me to resources please?
I haven’t learned about peano anywhere, heard from internet
most videos are short and quick
mortal trellis
I dont know any resource for that
worn fox
Tao is probably a good one
https://math.unm.edu/~crisp/courses/math401/tao.pdf
barren portal
Thank you
lone heartBOT
@barren portal Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
paper sage
A woman weighing 61.0 kg stands firmly on her ice skates on an icy lake. She shoots one
shot straight ahead with a rifle. She holds the rifle is at the same height as hers
center of mass. The bullet weighs 29.0 grams and leaves the rifle at a velocity of 600 m/s.
What is the woman's speed after shooting the bullet (Enter the answer in km/h)? Suppose that
is no friction between the skates and the ice
near apex
Is the denominator 0.061 ?
paper sage
yes
near apex
That's the issue.
near apex
You aren't converting Kg to gram correctly.
near apex
shoudn't the mass be in kg?
You were already given in KG.
near apex
No propblem.
lone heartBOT
sour dove
im so stupid
You're not stupid, you're learning!
paper sage
You're not stupid, you're learning!
But I just felt it's embarssing, im so tired actually. I think that should mean I should rest
because I tried in 20 min and didn't know what fault I did
sour dove
yes that's a great idea. Our brains can't retain what we've learned without proper rest.
But this is a skill, just like anything else. It'd be like if you were at the gym doing dumbell curls and got mad at yourself that your form is off. Learning is basically correcting mistakes. You fail, you learn.
paper sage
yes that's a great idea. Our brains can't retain what we've learned without prop...
Thanks for ur motivation and beautiful text.
lone heartBOT
Available help channel!
celest cape
Im going into junior year of hs and was planning on taking calc 3 fall semester. The only class I could take (at a local community college) is really hard ... there is no curve ever, more than half the class drops, and usually only 0-1 person gets an A. A couple of my friends saw this and got scared, so they decided to take the class online for essentially, free credits.
Would it be a better decision to take the class and learn the material properly, and take the high risk of not getting an A, or take the online class and get an A guaranteed, but sacrifice actual knowledge.
I have never got a B before so im worried about how that will appear to colleges, especially because I want to go into applied math.
The reason why the class is so hard is because
a) no curve
b) you have to do stupid things like randomly perform synthetic division to get any credit on a problem, and like in unit 3, integrate paraboloids and cylinders in spherical coordinates (why would you ever do that :(((...)
c) tests are nothing like homework problems (much harder)
coral thorn
not really a math question but your decision depends on how much you care about grades versus how much you care about actual knowledge
celest cape
i mean, i care about grades just bc of getting into college
which will lead to more actual knowledge
vs a worse college
coral thorn
there you go
celest cape
but on the other hand, i feel like if i learn it wrong now, i will struggle much more later
sour dove
but on the other hand, i feel like if i learn it wrong now, i will struggle much...
You could always supplement your knowledge. Professor Leonard's videos on YT helped me surivive Calc 3
celest cape
alr ok thanks
i think what ill do is ill apply to another class with a waitlist on it, and if that doesnt work then ill take online
foggy copper
ok
celest cape
ive already watched all of prof leonards calc 3 vids but. i will again
foggy copper
btw if you do decide to use textbooks to help w your knowledge i hear schaum is good
not sure if the material's the same offhand but still
although tbf i don't really understamd how any part of the us edication system works
native cloud
lone heartBOT
native cloud
Please help me with this question..
carmine sage
what have you tried
native cloud
carmine sage
how did you remove the absolute value btw?
finite flax
did you verify all 4 answers?
native cloud
$x=\frac{16\pm\sqrt{158}}{2},\frac{16\pm\sqrt{42}}{2}$
ocean sealBOT
LE SSERAFIM
native cloud
did you verify all 4 answers?
Yes, they result in the same value
native cloud
how did you remove the absolute value btw?
Piecewise functions
carmine sage
you checked for all 3 intervals?
native cloud
Intervals?
carmine sage
yes
near apex
You are supposed to check whether or not the x you got lies in the interval according to which you opened modulus.
In this case, it doesn't.
finite flax
You are supposed to check whether or not the x you got lies in the interval acco...
modulus?
carmine sage
absolute value
finite flax
did you round to one decimal place?
native cloud
Yes
finite flax
correctly?
native cloud
14.3
finite flax
and you separated using semicolons, not commas, right?
finite flax
those are commas
carmine sage
in ]-inf,3[ it is positive
in ]3,13[ it is negative
in ]13,+inf[ it is positive again
this is what i meant
near apex
in ]-inf,3[ it is positive
in ]3,13[ it is negative
in ]13,+inf[ it is positive ...
French ?
carmine sage
oui
finite flax
in ]-inf,3[ it is positive
in ]3,13[ it is negative
in ]13,+inf[ it is positive ...
so?
carmine sage
you have to take that into consideraétion before removing the ablsoute value
nimble fern
yes?
carmine sage
I don't follow
in the first interval you remove the absolute value, and then solve it, then you have to check if the solution falls in said interval
second interval you multiply by -1 and do the same
native cloud
native cloud
in the first interval you remove the absolute value, and then solve it, then you...
Doesn't all four answers fall into the desire interval?
carmine sage
what were the answers
nimble fern
for example, when we change
|2(x-3)(x-13)|=29
into
2(x-3)(x-13)=29
we are assuming
2(x-3)(x-13)≥0
native cloud
I don't have access to the answers
native cloud
for example, when we change
|2(x-3)(x-13)|=29
into
2(x-3)(x-13)=29
we are assumi...
and we're aiming for the value 29, right?
sharp crescent
nimble fern
for example, when we change
|2(x-3)(x-13)|=29
into
2(x-3)(x-13)=29
we are assumi...
therefore when you get the x's from this equation, you'll have to check if
2(x-3)(x-13)≥0 is valid
e.g.
you get 2 roots a,b from
2x²-32x+49=0
then we have to plug
a and b back into
2(x-3)(x-13)
to see if the expression is ≥0
i.e.
check if
2(a-3)(a-13)≥0
and
check if
2(b-3)(b-13)≥0
if not, we'll have to reject the case.
sharp crescent
😲
native cloud
sharp crescent
What's the problem
native cloud
All the answers I got were greater than 0
sharp crescent
sharp crescent
👀
sharp crescent
No problem.
nimble fern
now that we have finished the first part, we can continue with the part that we assume
2(x-3)(x-13)≤0
native cloud
Why ≤ 0?
nimble fern
Similarly
e.g. you get 2 roots c,d from
-2x²+32x-107=0
then we plug them back into
2(x-3)(x-13) to see if it is ≤0
native cloud
all good till here?
No..? 😢
sharp crescent
Similarly
e.g. you get 2 roots c,d from
-2x²+32x-107=0
then we plug them back i...
That's not necessary, is it?
Just remove the absolute value sign and discuss it in different situations.
ocean sealBOT
native cloud
Isn't this different from my answer?
nimble fern
,calc 2(8+sqrt(79/2)-3)(8+sqrt(79/2-13))
ocean sealBOT
Result:
296.74362350009
its positive, so we accept the second case
nimble fern
**LE SSERAFIM**
nah, it's the same as this the first one
native cloud
,calc 2(8+sqrt(79/2)-3)(8+sqrt(79/2-13))
Why did you multiply them?
ocean sealBOT
Result:
29
nimble fern
yes?
native cloud
Oh yeah no wonder it was in the hundreds
nimble fern
no worries
native cloud
and yes it is 29
nimble fern
that's good
native cloud
yay
sharp crescent
native cloud
<:wg:1130147597428998184>
?
nimble fern
oh
native cloud
ocean sealBOT
Result:
29
oh nice
native cloud
Should I submit my answers?
I think they are correct, but idk why it's telling me wrong
I have to solve a different problem if my answer is incorrect
nimble fern
,calc 2(8+sqrt(21/2)-3)(8+sqrt(21/2)-13)
ocean sealBOT
Result:
-29
nimble fern
,calc 2(8-sqrt(21/2)-3)(8-sqrt(21/2)-13)
ocean sealBOT
Result:
-29
all good
sharp crescent
nimble fern
I think they are correct, but idk why it's telling me wrong
yea, you can submit
sharp crescent
Can't you intersect like this?
nimble fern
yey
native cloud
Thank you all!
nimble fern
cheers!
native cloud
.close
pure spear
I am trying to figure out how to evalluate the limits in the expression below, specifically I am stuck on the integral. I am pretty sure this limit exists and is equal to d^n/(dx^n) [f(x)] because I have experimented with numerical means.
$\underset{\alpha\rightarrow n}{\lim}\frac{1}{\Gamma(n-\alpha)}\frac{d^{n}}{dx^{n}}\intop_{a}^{x}(x-t)^{n-\alpha-1}f(t)dt$
ocean sealBOT
YeahJustHi
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pure spear
of course $\Gamma$ is the gamma function
ocean sealBOT
YeahJustHi
winter birch
can someone help wuth my gamma homework
vale wigeon
can someone help wuth my gamma homework
please open your own channel. #❓how-to-get-help
winter birch
neggawattttt
vale wigeon
well, that was short.
pure spear
lol
vale wigeon
anyway this smells like some kind of fractional derivative shit
pure spear
it is
I cant find any papers that prove that the Riemann-Liouville Derivative approaches the classical derivative with the limit alpha->n, so i'm trying to figure it out myself
My first idea was to literally just try to evaluate the limiit, but I have a feeling that's too straightforward
lone heartBOT
@pure spear Has your question been resolved?
lone heartBOT
@pure spear Has your question been resolved?
lone heartBOT
@pure spear Has your question been resolved?
stoic folio
Does anybody know if Khan Academy website makes it a habit of introducing questions on "Course Review" over material not yet covered? I think I am experiencing this in limited fashion now.
tacit arch
Does anybody know if Khan Academy website makes it a habit of introducing questi...
This isn't a Khan academy website
Email Sal
dry matrix
lone heartBOT
dry matrix
would this be a sample or population?
i thought sample since the data is specific to Jason only but im not sure
carmine reef
I'd say sample because it's only the first 10 games
It kinda depends on context a little. If you're using this data to make guesses about a larger set of data then it's a sample
stoic folio
The word extrapolation comes to mind.
If you're looking to fill missing data points, that is.
dry matrix
It kinda depends on context a little. If you're using this data to make guesses ...
oh okay its just mainly talking about jason
versed igloo
The temperature of a cooling cup of boiling -hot water is modeled by f(t) = 147e ^ (- 0.081t) + 65 where f is measured in degrees Fahrenheit and t is measured in minutes after the water is taken off the heat source . How long until the water is cooling at a rate of 3 degrees Fahrenheit per minute ?
carmine reef
In general, how do you find the cooling rate
versed igloo
Idk what I have so far is
147e ^ -0.081 (-0.0.81)
= 11.907e ^ -0.081t
= 11.907e -0.081t
lone heartBOT
@versed igloo Has your question been resolved?
lone heartBOT
@versed igloo Has your question been resolved?
harsh swallow
what is cooling rate in terms of relating to the temperature?
oh wait you already seem to have found the derivative
you missed a minus
although maybe you were talking about the cooling rate terms of how much cooling there is
lone heartBOT
@versed igloo Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
fossil slate
guys pls help me express x and y in terms of theta
lone heartBOT
guys pls help me express x and y in terms of theta
wary stream
im too lazy
We're not here to give you answers
fossil slate
anyone interested in algebraic manipulation?
west girder
if youre too lazy why not just use wolfram
,w solve for x and y, (y-rsin(theta))^2+(x-rcos(theta))^2=((theta*r)/(pi))^2
ocean sealBOT
lone heartBOT
,w solve for x and y, (y-rsin(theta))^2+(x-rcos(theta))^2=((theta*r)/(pi))^2
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.
alpine sable
@west girder make sure not to give out answers bro
west girder
<@886648822606991481> make sure not to give out answers bro
no one wants to do an algebraic manipulation like this, its just tedious and doesnt provide any new knowledge. i just helped them learn what wolfram is
lone heartBOT
sin(2θ) × sin(3θ) × sin(4θ) × sin(6θ) = (sin(8θ)) ÷ 16
Please read #❓how-to-get-help
alpine sable
use identities
wary stream
use identities
If you are responding to isiah, don't. They interrupted someone else's channel and they need to real #❓how-to-get-help and open their own channel
alpine sable
ok
lone heartBOT
@fossil slate Has your question been resolved?
violet ibex
need help in this question have no idea what to do :
The distance of the point on the sphere x^2+ y^2+z^2=3. farthest from the point (2,2,2) is
tacit arch
need help in this question have no idea what to do :
The distance of the point o...
Use distance formula
violet ibex
but what about constarint x^2+ y^2+z^2=3.
tacit arch
but what about constarint x^2+ y^2+z^2=3.
This is one of the points in the distance formula
You can also minimize distance^2 instead of distance
It'll give the same answer
lone heartBOT
@violet ibex Has your question been resolved?
rotund crater
why is negative
lone heartBOT
why is negative
rotund crater
why yes'
wary stream
Because du = -2x dx -> -1/2 du = x dx
rotund crater
Because du = -2x dx -> -1/2 du = x dx
can't change the sign or is it mandatory?
wary stream
What exactly are you asking?
rotund crater
What exactly are you asking?
i mean 2x
lone heartBOT
@rotund crater Has your question been resolved?
fossil slate
yes
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
How are my angles wrong?
hoary ether
pallid glade
...
Idk
alpine sable
?
pallid glade
...
Idk
tight locust
How are my angles wrong?
what is your angle for k = 0?
tight locust
really? so you are asserting that z = 1 is a solution?
you are NOT solving the equation z^9 = +1.
you are solving the equation z^9 = -1
alpine sable
Oh okay
I was just using integers for k that gave me angles in the principle argument
tight locust
right. but theta = 0 cannot be a solution
so you have to "shift your phase"
if that makes sense
alpine sable
so you have to "shift your phase"
Shift my phase?
tight locust
your k = 0 will NOT coincide with theta = 0
basically your zero point should not be the zero angle. it's a phase shift
your solution set should be:
exp(ipi/9 + k 2 i pi/9)
k = 0, 1, 2, ... 8
$e^{\frac{i \pi}{9} + \frac{2 i \pi k}{9}}$
ocean sealBOT
EndTimes
tight locust
@alpine sable
alpine sable
I’m just trying to process this one sec
tight locust
so you get:
pi/9, 3pi/9, 5pi/9, 7pi/9, 9pi/9, 11pi/9, 13pi/9, 15pi/9, 17pi/9
poorly written question in any case, this doesn't help. what you should truly be considering is the 18th roots of +1
north oyster
I need help with this
lone heartBOT
I need help with this
north oyster
Idk where to start
fallen verge
Plug your values (x,y) into their respective equations
north oyster
So for the first equation 5r=(2p)+b and the second 5r=2(2p)+b?
alpine sable
i’m kinda following along here, and i have to admit i’m a bit confused - what level math is this? algebra 2?
north oyster
Ye this is alg 2
alpine sable
ok, no wonder. i take that next year
fallen verge
So for the first equation 5r=(2p)+b and the second 5r=2(2p)+b?
The first equation hits the point (p,r) not (2p,5r)
north oyster
But it's for Sat practice
alpine sable
ok, no wonder. i take that next year
well this year ig, it’s summer now
alpine sable
But it's for Sat practice
good luck!!
north oyster
Thx
north oyster
The first equation hits the point (p,r) not (2p,5r)
Oh
So ig I'm using the second one
north oyster
I only got the second one
north oyster
r=p+b
north oyster
Yes
fallen verge
Subract the second one from the first
fallen verge
That way you get an equation only in p and r, and you can find r/p
-r= p+b```Can you do the subtraction?
north oyster
Yes
4r=3p
fallen verge
4r/3p is not equal to 0
north oyster
What is it equal to then
fallen verge
if you divide 3p/3p, what do you get
north oyster
1
north oyster
r=3p/4
fallen verge
Now divide by p on both sides
lone heartBOT
lone heartBOT
Available help channel!
burnt sable
lone heartBOT
burnt sable
I have to figure out whether this diverges or converges
I tried multiplying by 1/n^2 to the top and bottom and got 0, but am not sure where to go from here
this is what i have so far
burnt sable
Yes
serene junco
What other tests do you know?
burnt sable
I know it as the test for divergence
serene junco
I know it as the test for divergence
if the limit of the sequence isn't 0, the series diverges. that one, right?
burnt sable
geometric, telescoping, p series, alternating, integral, root test, ratio, comparison
those are the ones i know
burnt sable
if the limit of the sequence isn't 0, the series diverges. that one, right?
correct
serene junco
geometric, telescoping, p series, alternating, integral, root test, ratio, compa...
have you tried any of these?
or I guess I should ask, do any of them seem applicable?
burnt sable
I just don't know which one to use, but I don't think I can't use geometric, p series, alternating, integral, or comparison
The sqrt(n) in the numerator is throwing me off
serene junco
well, it's not a geometric, alternating, or p series on its face so I agree with those
serene junco
The sqrt(n) in the numerator is throwing me off
remember sqrt is just an exponent
burnt sable
Right, I put it to n^1/2 /n^2
would the n^1/2 / n^2 require L'hopitals?
since infinity over infinity?
serene junco
nah, you're probably only ever going to use l'h if you're evaluating a limit directly
burnt sable
ahh ok
serene junco
like something that actually has a lim symbol
serene junco
Right, I put it to n^1/2 /n^2
you're thinking the right way
getting rid of the +4
If it wasn't there, you could simplify just n^1/2 / n^2, right?
burnt sable
Correct
Since 4/n^2 is zero when going to infinity
and it's all over 1 so that doesn't matter either
so it would just be 1/n^3/2
It's still going to 0 though
<@&286206848099549185>
lone heartBOT
@burnt sable Has your question been resolved?
burnt sable
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last bobcat
Help
lone heartBOT
@last bobcat Has your question been resolved?
last bobcat
<@&286206848099549185>
tacit arch
For part b, why would we even devide by standard deviation??
To get the z score and use central limit theorem
last bobcat
???
tacit arch
You need to get Z first
How do you get Z from a normal random variable X with mean mu and std dev sigma
last bobcat
Uh
tacit arch
I know this
This isn't a z score
tacit arch
I know both
Are you sure you know what a z score is
alpine sable
im stuck and not sure what to do for the other 3
lone heartBOT
im stuck and not sure what to do for the other 3
gray isle
drawing the diagram first helps
alpine sable
okay
alpine sable
drawing the diagram first helps
is something liket his
good enough
or do i need to make another measurement
for the other side
gray isle
label the l,w,h on the diagram
unknown/unmarked sides can be deteremined from geometric properties
sweet igloo
Could someone please clarify from line 4 to 5 because I got the rest of the proof but couldn't get past this
pale kestrel
sin double angle
astral pawn
lone heartBOT
astral pawn
so basically i was solving a question and the solution that is standard and what i arrived at were a bit different (both of these equations are equations for a line)
are they the same?
near apex
They don't seem same to me.
ocean sealBOT
Enemagneto
near apex
You can check using that. Simpler is to just put values, i think.
astral pawn
doesnt seem to be the same
lemme redo it, maybe i made a mistake
okay yes i did make a mistake
lemme recheck using the formula u posted
yess
its correct
tysm !
.close
placid spire
how did they go from the 1st line to the 2nd line?
lone heartBOT
how did they go from the 1st line to the 2nd line?
vale wigeon
do you know how the distributive law works
placid spire
ye
vale wigeon
here specifically, $(x - a)(x - b) = x^2 - ax - bx + ab$, only $a$ and $b$ happen to be complex numbers.
ocean sealBOT
Ann
rich basin
lone heartBOT
lone heartBOT
@rich basin Has your question been resolved?
rich basin
<@&286206848099549185>
near apex
I'm not sure why (b) is wrong?
Your equation 1 bothers me. It doesn't seem to be correct to me.
At the same time, i'm not adept at this topic so i might just be wrong.
rich basin
(a) is right, but (b) is wrong
all i did was apply the chain rule
I got it, I wrote sin(Pi) = -1
but it is suppose to be 0
.close
simple saddle
lone heartBOT
simple saddle
how to solve shall i consider two novels and bio graphies together?
and subtract it from total without restriction case?
vale wigeon
that will be too hard.
the only way in which you could arrange the books on the shelf such that no two books of the same type are adjacent is N-B-N-B-N-B-N
then there are 4! ways to arrange the novels among themselves, and similarly 3! for the biographies...
simple saddle
that will be too hard.
oh so but regular ways we do that no?
vale wigeon
sorry, i do not understand your question.
simple saddle
ABCD and A,B can't sit together so we consider them together and assign as them as being one member calculate the ways and subtract that from regular case to get the restricted one
@vale wigeon
vale wigeon
that's a different setup.
here you don't just have one particular pair of books that aren't allowed to be together.
you have many.
simple saddle
here you don't just have one particular pair of books that aren't allowed to be ...
yeah right it will be complex
okay
simple saddle
then there are 4! ways to arrange the novels among themselves, and similarly 3! ...
right
thanks
.close
robust cobalt
hi so i have a doubt regarding
lone heartBOT
hi so i have a doubt regarding
warped topaz
lone heartBOT
https://i.imgur.com/qZbW8G8.png
warped topaz
I thought I knew how to do this but I got stuck
A/(x + 9) + B/(x + 9)^2
A(x + 9)^2 + B(x + 9)
Ax^2 + A18x + A81 + Bx +9B
I dont really know what to do next
Like I cant do (A+B)x to get A + B = -3, because of the 18 in A18x
buoyant storm
https://i.imgur.com/qZbW8G8.png
as you said, let $\frac{2-6x}{(x+9)^2}=\frac{A}{x+9}+\frac{B}{(x+9)^2}$
ocean sealBOT
orthogonal
ocean sealBOT
orthogonal
buoyant storm
do you get this
warped topaz
I still dont get it sry, how come its not (2-6x)(x+9)^2
warped topaz
$2-6x=A(x+9)+B$
In fact I dont understand the right side of this equation either
Oh wait
I get it now
Ok 1 moment I will try solve it
Yes I got it
Thank you!
❤️
.close
lament basalt
Prove
lament basalt
frozen tiger
prove what
lament basalt
I tried to do what the addition of fraction is usually being done
frozen tiger
I tried to do what the addition of fraction is usually being done
and what's your answer there?
frozen tiger
Ima try to answer again I'll be back a min
I meant what's your urrent progress
frozen tiger
uh
I think you should
redo it
you got it
a bit
and by a bit it's very wrong
a/b+b/a=(a^2+b^2)/ab
lament basalt
I just did what an addition of fraction is usually being done and that's what I got
Yeah
frozen tiger
I just did what an addition of fraction is usually being done and that's what I ...
well, You forgot to multiply cos a with cos a and 1+sina with 1+sina and add
Oh wait
oh
I thought the topmost was your answer
sina is not squared btw
lament basalt
No like its the middle one between the arrow and the above eq
lament basalt
sina is not squared btw
Denominator?
frozen tiger
Denominator?
numerator
lament basalt
It is
frozen tiger
I think you got that wrong and that's why you were confused
lament basalt
It's squared
frozen tiger
It's squared
(cosa)^2+(1+sina)^2=cosa^2+sina^2+2sina+1
lament basalt
(cosa)^2+(1+sina)^2=cosa^2+sina^2+2sina+1
Focus on first 2 equations
sinacosa* on denominator
Godfuck I'm so bad at math
lament basalt
(cosa)^2+(1+sina)^2=cosa^2+sina^2+2sina+1
Ahhh I got it
Do you mean the topmost equatio?
Equation*?
frozen tiger
Do you mean the topmost equatio?
yeah
lament basalt
No that's not included
lament basalt
I just happened to write the actual equation in between them (the topmost equation and arrow)
@frozen tiger
lament basalt
2
1+1 = 2
The 1 is from sin^2 + cos^2a while the other one is from the 1 + 2sina which both are in this photo. At the numerator of the 2nd equation
.close
long panther
lone heartBOT
long panther
I assume that there is meant to be a log 5 on the left hand side that wasn't written
but how do they get rid of the log5 on the a + 3b-2c
at the end when they divide by it
At step 3 it should be log5 a^x + log 5 b^3x - log5c^2x = 1
so step 4 should be x log5 a + 3x log 5 b - 2x log 5 c = 1
which then becomes x( log5 a + 3 log5b - 2 log 5c) = 1
.close
mellow oasis
can someone help with the mechanics of the pendulum motion?
lone heartBOT
can someone help with the mechanics of the pendulum motion?
royal socket
can you elaborate what part you need help with?
mellow oasis
why do we disregard centripetal force
as far as i understand tehre are two forces action tension and gravity, so they break down gravity into two components but do nothing to tension
royal socket
as far as i understand tehre are two forces action tension and gravity, so they ...
This is because its a fixed rod
The rod doesn't change in length
But tension only acts in the direction of the radius
Therefore the tension does nothing
Well,
Actually it does
Otherwise the ball would fall to the ground
But this is why we are looking at mg sin theta instead of mg
mellow oasis
but since it is a force and it acts on the pendulum shouldn't it be accounted for or something (sorry i am just new to the centripetal force and stuff)
...
lone heartBOT
@mellow oasis Has your question been resolved?
royal socket
but since it is a force and it acts on the pendulum shouldn't it be accounted fo...
It has already been accounted for by you multiplying by sin theta
lone heartBOT
@mellow oasis Has your question been resolved?
dawn estuary
hey, can someone explain what happens in the first line of this boolean equation?
dawn estuary
.close
light quarry
lone heartBOT
light quarry
I don't understand this
I had my 1st day of school Friday and im in honors math geometry
And I don't get anything I was just given a packet and told to do 1-24 on page 7
I just need an explanation on how im supposed to do this
And a little help of how to do it
weak turtle
That's basic alzebra
U just need to rearrange the polynomail in standard form like the highest power first then second highest then 3rd and so on..
and coefficient of polynomial is the coeffeciant of highest power variable
weak turtle
yaa
light quarry
Because the teacher told me to put down like four things
weak turtle
and leading coefficent will be -2
light quarry
Ok
weak turtle
and classification of polynomial is done by looking at there power
weak turtle
So like on 11 would it be
-2r⁴ -3t² +5
like this one is biquadratic as it is of power 4
weak turtle
- -2r⁴ -3t² +5
Degree is 4
Leading coefficient is -2
This polynomial is a trinomial
weak turtle
and classification of polynomial is done by looking at there power
Sorry I said it wrong here classification of polynomial is done by looking no. of terms in euqation
like in 11 we have 3 terms so it is a trinomial ans in 9. there is 1 term so it is a monomial
and in 10 there are 2 terms so it is a binomial
warped topaz
lone heartBOT
https://i.imgur.com/Y6cIati.png
warped topaz
I dont get why is it all numbers?
somber eagle
because its always positive
warped topaz
x^2 => -4 DNE right? So shouldnt it be no numbers?
tardy tapir
why doesnt it exist?
warped topaz
Cant have a negative inside a square root no?
somber eagle
since it is a square root, you are looking for all possible numbers that make the inside of the square root positive
tardy tapir
x^2 => -4 DNE right? So shouldnt it be no numbers?
you said this DNE, why is that?
warped topaz
since it is a square root, you are looking for all possible numbers that make th...
Oke that does make sense kinda
warped topaz
you said this DNE, why is that?
Because the answer is imaginary
tardy tapir
if its x^2 less than or equal to -4, that doesnt exist
somber eagle
but what do you happens when you square any number?
limpid spade
,w plot sqrt(x²+4)
tardy tapir
x^2 is always greater than -4
ocean sealBOT
warped topaz
x^2 => -4 DNE right? So shouldnt it be no numbers?
This doesnt exist right?
tardy tapir
it does
somber eagle
x^2 is always greater than or equal to 0 right?
warped topaz
x^2 is always greater than or equal to 0 right?
yes
somber eagle
therefore x^2 + 4 is always greater than 0
warped topaz
Yes I know
warped topaz
This doesnt exist right?
Im just wondering about this
somber eagle
yeah x^2 never equals -4
tardy tapir
but that inequality is a or
somber eagle
therefore no real numbers make this square root negative
warped topaz
Alright well the bit about x^2 can never be negative makes sense to me so I can just remember that
Thank you everyone
❤️
.close
lone heartBOT
lone heartBOT
Available help channel!
burnt sable
lone heartBOT
burnt sable
Hey I need to find whether this converges or diverges, I'll post my previous work quickly
ive done this so far, but I think I’ve taken the wrong course of action
This just ultimately gives me zero when making it a limit as n goes to infinity
unless that's correct, but im just not sure
tacit arch
It's not correct
The limit of the terms being zero doesn't mean the series converges
Use series comparison test
Compare it to a series that does converge
burnt sable
ah i figured
burnt sable
The limit of the terms being zero doesn't mean the series converges
this just means it can go either way right
if I get zero when the limit goes from n-> infinity
tacit arch
Inconclusive is the word you're looking for
burnt sable
Correct
burnt sable
Compare it to a series that does converge
I thought about doing this
but what do I compare it to since there's two things in the numerator?
tacit arch
There's only 2 things you would try
1/n and 1/n^3
Try both and see which is more appropriate
burnt sable
1/n^3 makes it convergent and 1/n is divergent
but why would I disregard the n in the numerator
I guess that's more my question here
burnt sable
I compare the original equation to the new equation, for this example I'd compare it to 1/n^3
and since the denominator is even bigger in the original equation it would converge since 1/n^3 also converges
making an < 1/n^3
tacit arch
Your explanation needs work but the spirit is correct
burnt sable
ok cool
how could i explain that better?
Since it's a summer class we learned everything about convergence/divergence in 1 week
It's just a lot lol
lone heartBOT
@burnt sable Has your question been resolved?
burnt sable
.close
strong schooner
My task is to prove this a1! * a2! * ... * an! <= (a1+a2+...+an)! It should be proven by the method of induction, so we have the base for n=1 and it's trivial and it's equal a1! = a1!, and we have a hypothesis that it is correct for n=k, so we should prove it for n=k+1, and I think we should probably use the a_k+1 ! member and say, a_k+1! = a_k+1 * a_k * a_k-1 * ... * a2 * a1, and the hypothesis covers the a_k-1 * ... * a2 * a1 part so it's a_k+1 * a_k!
strong schooner
Or maybe the base should be n=2 so it's a1! * a2! <= (a1+a2)! so we could use that in the proof
Is theree anyone that could help?
.close
frank cliff
could someone help me please, it's about statics. i don't understand the topic very well.
mental flame
could someone help me please, it's about statics. i don't understand the topic v...
!15mins
lone heartBOT
could someone help me please, it's about statics. i don't understand the topic v...
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
frank cliff
im so sorry
mental flame
It's alright dw, just don't do it again.
vapid steppe
$\int_{-2}^{4} \abs{x}dx$
lone heartBOT
$\int_{-2}^{4} \abs{x}dx$
ocean sealBOT
Jash
vapid steppe
is it better to use geometry
fallen verge
Yeah
outer elm
somber eagle
but its probably easier just to draw the graph and find the area
somber eagle
true, if it wasnt something as easy as abs(x) then it would be harder to draw
vapid steppe
2?
somber eagle
then it would be easier to do it algebraically
somber eagle
yeah
ocean sealBOT
shadow verge
19 a pls help
lone heartBOT
19 a pls help
shadow verge
<@&286206848099549185>
tacit arch
<@&286206848099549185>
!15m
lone heartBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
potent steeple
19 a pls help
Is this 0606 IGCSE Additional Maths?
shadow verge
Is this 0606 IGCSE Additional Maths?
It's as level statistics 1
potent steeple
oh alr
lone heartBOT
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
shadow verge
But u could probably do it
potent steeple
So there are 900 numbers between 100 and 999
shadow verge
So there are 900 numbers between 100 and 999
Uh
potent steeple
And there are 9!/6! different 3 digit numbers with
Oh no i think it’s j that
Ignore the other message
Try 987
See if that’s the answer
shadow verge
Ok 1 min
potent steeple
84
shadow verge
648 and 64?
Yup it's 648
shadow verge
648 and 64?
Can u tell how?
distant ivy
Yup it's 648
Alr so what I did was
Imagine the number is xyz
x cannot be 0 (it’s the first number)
So it can be from 1-9
This is 9 possibilities
y can be anything except for x
9 possibilities (1-9) includes 0
z cannot be y or x
8 possibilities
9x9x8
lament ferry
