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#help-23
half wadi
<@&286206848099549185> Im really struggling with this specific problem in my homework
safe radishBOT
<@&286206848099549185> Im really struggling with this specific problem in my hom...
half wadi
<@&286206848099549185> Im really struggling with this specific problem in my homework
stray socket
!15m
safe radishBOT
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.
@half wadi Has your question been resolved?
misty bay
<@&286206848099549185> Im really struggling with this specific problem in my ho...
which part
half wadi
which part
It has beeen resolved, thanks.
urban vale
can someone explain how they changed that to that?
safe radishBOT
can someone explain how they changed that to that?
urban vale
I know its the antiderivative but I would think that it would be ln ((y-2)^2)
icy lance
the derivative of ln[(y-2)^2] is (2(y-2))/(y-2)^2
urban vale
yeah
icy lance
what youre integrating is essentially (y-2)^-2 which might make more sense to look at
urban vale
what youre integrating is essentially (y-2)^-2 which might make more sense to lo...
thanks
I get it now
.close
icy lance
np
lean otter
safe radishBOT
lean otter
How would I go about solving this?
keen badge
does anyone know the answer to this? i have tried several times but keep getting it wrong
lean otter
does anyone know the answer to this? i have tried several times but keep getting...
post in a different channel please
keen badge
sorry about that
lean otter
what does sin x = -2/3 tell you
It tells me that sinx terminates in quadrants 3 & 4
misty bay
that statement makes no sense
lean otter
lol
misty bay
how does a number terminate in a quadrant
misty bay
how does the number 4 terminate in a quadrant
misty bay
are you saying that the angle x terminates in quadrants 3 and 4?
lean otter
are you saying that the angle x terminates in quadrants 3 and 4?
no
i just thought because sin was a negative value and negative sin values are in quadrants 3 and 4 so i just assumed
misty bay
angle x does indeed terminate somewhere in quadrant 3 or quadrant 4
because if you think about the unit circle
call the point where it terminates (a, b)
lean otter
ok
misty bay
(a, b) is just (cos x, sin x)
lean otter
yeah
lean otter
yeah
misty bay
what does tan x < 0 tell you?
lean otter
what does tan x < 0 tell you?
its negative
misty bay
well that's basically what I wrote
but what does it tell you about the termination point
lean otter
it can be in quadrant 2 or 4
misty bay
okay
so we're told that both of these have to be true:
angle x terminates in quadrant 3 or quadrant 4
angle x terminates in quadrant 2 or quadrant 4
lean otter
yeah
misty bay
where do you think angle x terminates?
lean otter
o
misty bay
common termination whatever big words is meaningless
lean otter
okay
misty bay
if I say that your car is either red or blue
and that your car is either red or yellow
what colour is it
lean otter
huh
misty bay
can you answer that question?
lean otter
red
misty bay
same logic here
lean otter
yeah
makes sense
can you also help me with a second question? its similar
actually i know this one
because in quadrants 1 and 3 sin and cos values are equal
.close
zealous lake
You are given rectangle ABCD with point E as the intersection of the diagonals. If the measure of angle AEB=13x and the measure of angle ECD=3x-5, find x.
safe radishBOT
You are given rectangle ABCD with point E as the intersection of the diagonals. ...
cedar rivet
safe radishBOT
@zealous lake Has your question been resolved?
safe radishBOT
@zealous lake Has your question been resolved?
blazing shadow
Hi guys, if I have a rectangular area (or square area) and I want to intersect the entire area at repeating intervals both ways, would this formula be correct: Area / (Centre Spacing ^2) to tell me how many intersection points there are in the Area?
The formula would assume Area is in m2 and Center Spacing is in metres.
safe radishBOT
Hi guys, if I have a rectangular area (or square area) and I want to intersect t...
empty gyro
Could you draw what you mean?
blazing shadow
is there a way i can do that in Discord? or i'll just use paint
blazing shadow
Red represents the "Centre Spacing" factor, which in this example is 0.6m
also, picture is definitely not drawn to scale
So what I want to find is "how many blue dots (intersection points) in an Area of 9.92m2 if the intersection points are at 0.6m intervals both ways"
I figured the formula for this was: Area / Centre^2
but I;m not sure that's correct now after I tried it out and thought it through
If the area is 12.4m long, and there's an intersection point at 0.6m each way across the area, on the 0 length, I should have at least ~20ish points, and then there is a second line of intersections at 0.6m intervals 0.6m away from the 0 length line (on the 0.6m length line)
So my estimate for the answer is something like 40 to 42 intersection points
But the formula I thought that would work it out is saying something like 27.5
so my question now is, is there a formula to do this?
safe radishBOT
@blazing shadow Has your question been resolved?
blazing shadow
So I found if I do: (Area / (Center^3)) it gets something pretty close to what I'd expect the answer to be, but ... because there is a mod remainder in the area, I don't understand if the answer i'm getting is actually accurate or just coincidental.
it's very confusing to me because if I use (Area / Center^2) for example on 10m2 area, assume the area's L and W are 5 and 2.
If I make the Center value 0.5 in this example, the formula is: (10 / 0.5^2) which gives: 40 which i think is correct.
5m long with intervals at 0.5m = 10 intervals on the axis
by
2m width with intervals at 0.5m = 4 intervals on the axis
= 10 x 4 intersection points
= 40 intersection points
but if I altered the Center value in this example to 1.0m you get:
(10 / 1.0^2) which gives: 10
5m long with intervals at 1.0m = 5 intervals
by
2m width with intervals 1.0m = 2 intervals
ah no wait... that is right isn't it.
i'm not sure why im so confused now.
ffs maths
i still feel like the formula is not correct, because my original example is giving an answer that seems to be incorrect.
safe radishBOT
@blazing shadow Has your question been resolved?
blazing shadow
i worked it out. the formula is calculating the correct answer. it is ignoring the 0 axis and i was assuming it should add that in. the example i used: (9.92 / (0.6^2)) yields 1 axis of intersections at 0.6m, which is ~20 points.
the answer it gives is ~27.55 intersection points. the additional difference is ~1/3 of ~20 which is ~6.5. This value is coming from the remaining 0.2 towards the next iteration of the center value, which is 0.6. 0.2 = 1/3 of 0.6
So what I need to work out is how to make the formula not give me the remainder value, and instead add an additional complete axis of the intersection points.
So in summary, the formula is correct and entirely accurate. (Area / (Center^2))
safe radishBOT
@blazing shadow Has your question been resolved?
lean otter
can anybody dm me and we can talk about it there. im in 10th grade and i have two math tests tomorrow, its about solving linear equations by substitution and elimination and some other stuff similar about graphing
safe radishBOT
can anybody dm me and we can talk about it there. im in 10th grade and i have tw...
stray socket
.close
lean otter
pseudo scroll
!status
safe radishBOT
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
1
pseudo scroll
And close your old channel
lean otter
And close your old channel
i did
pseudo scroll
Are you aware of the derangement formula
I think its called the subfactorial
,w subfactorial
very useful
lean otter
not what we doing
pseudo scroll
for the first part
pseudo scroll
lean otter
that we doing
pseudo scroll
Rule of sum?
lean otter
ya
pseudo scroll
Do you know about C(n, r)
lean otter
nope
pseudo scroll
Hmm
pseudo scroll
No I mean nCr
pseudo scroll
$\frac{n!}{(n - r)!r!}$
flat frigateBOT
NEONPerseus
pseudo scroll
This ^
Sadly I can't figure out another way to do the first part without dearrangement
opaque sorrel
hi can someone help me with this question?
safe radishBOT
hi can someone help me with this question?
opaque sorrel
@junior smelt by any chance would u be free 
junior smelt
opaque sorrel
deep depot
Oh
junior smelt
hi can someone help me with this question?
Which ones, both of them?
opaque sorrel
yea
for some reason idk why my working is wrong
like there shouldnt be a difference between both expressions
dull echo
b you multiply by 1 twice
opaque sorrel
wym?
dull echo
wym?
multiply by (sqrt(x+1) + sqrt(2x-1))/(sqrt(x+1) + sqrt(2x-1))
then do the same for the numerator
junior smelt
[like I said yesterday 
]
For a I have a feeling in your work you evaluated it wrong 
opaque sorrel
multiply by (sqrt(x+1) + sqrt(2x-1))/(sqrt(x+1) + sqrt(2x-1))
wait didnt i do that
opaque sorrel
For a I have a feeling in your work you evaluated it wrong <:glassescat:10377705...
wait lets solve a) first XD
so my working is probably wrongly evaluated right
junior smelt
That’s what I’m thinking, originally the top and the bottom both evaluate to zero (that was the hint from yesterday, you can factor out an (x+2) and cancel)
opaque sorrel
can I ask how did u know that x+2 is a factor
junior smelt
The manipulation you’ve done seems okay but not really “helpful”
opaque sorrel
The manipulation you’ve done seems okay but not really “helpful”
umm wait but im confused, when i sub in the value x = -2 into the manipulated equation it doesnt have the zero error
junior smelt
Factor theorem, for a polynomial p, you have (x-a) as a factor if and only if p(a)=0
junior smelt
umm wait but im confused, when i sub in the value x = -2 into the manipulated eq...
That’s what I mean by “wrongly evaluated”, let’s see
junior smelt
yea I got that evaluating to zero too
junior smelt
And the bottom too
opaque sorrel
Factor theorem, for a polynomial p, you have (x-a) as a factor if and only if p(...
okay for some reason i didnt know this 
okay lemme factorize out x-2 frm both
x+2*
junior smelt
You might need to do long division
opaque sorrel
right
junior smelt
Anyways from yesterday
opaque sorrel
a moment lemme do the long division
junior smelt
Check you agree with what stabulo got of course 
flat frigateBOT
opaque sorrel
wait why didnt i (wolfram alpha) do this properly
junior smelt
,w factor x^4 + 3x^3 + x^2 + 4
flat frigateBOT
junior smelt
Turns out it’s a double factor then
junior smelt
looks like I need to be called with special comamnds
opaque sorrel
oh wait double factor
hmmmmm
okay but assuming i dont have wolfram alpha (me) on my side
ill just factor once first and then see if its neccessary
junior smelt
To be fair, for the time being it doesn’t really matter that it’s a double factor until we check the denom
opaque sorrel
,w factorize x^4 + 4x^3 + 3x^2 - 4x - 4
flat frigateBOT
opaque sorrel
hmm its also a double factor
junior smelt
If after factoring the denom still evaluated to zero then we’d need to go again
opaque sorrel
To be fair, for the time being it doesn’t really matter that it’s a double facto...
lemme write thsi down
junior smelt
Well, in a way, this is similar to lopitals but not 
(Of course, a way to check for roots of repeated multiplicity would be checking the derivative and if it evaluates to zero as well )
opaque sorrel
(Of course, a way to check for roots of repeated multiplicity would be checking ...
wait so i can check if the derivative of the root evaluates to zero?
wait dont quite get that
junior smelt
Yep, then if that’s a 0/0 again, go and do even more polynomial division (or just use the factors we had from earlier)
junior smelt
wait so i can check if the derivative of the root evaluates to zero?
As if say you had a, then if p(a)=0 and p’(a)=0 then a is a repeated root and so (x-a) is a factor with a power of at least 2
opaque sorrel
,w factorize x^2 - x + 1
flat frigateBOT
opaque sorrel
That can be “trivially” proven <:catThimc:732011802459635713>
"trivially"
"the proof for this is very trivial and is left as an exercise" - every math prof
opaque sorrel
i got 7/3
opaque sorrel
“This homework is trivial and left as an exercise for the grader”
every math students worst nightmare
ends up taking 5 hours to prove it with the wrong proof
and it comes up during the exam
opaque sorrel
kay hmm so now ive learnt two things
the factor theorem: if p(a) = 0, x - a is a root
and if p'(a) = 0 where p'(a) is after factorizing x - a, the multiplicity of x-a > 1
junior smelt
Yep factor theorem is a special case of the remainder theorem, basically the remainder on dividing p by (x-a) is p(a) (and you can show that similarly as for the factor theorem, and if you show this one first, you get the factor theorem for free)
opaque sorrel
yessir i understand 
junior smelt
For the repeated root thingy, assuming p(a)=0 (so you get that as a factor), write p(x) = (x - a)^m * q(x) for some q not divisible by (x - a) (and m being at least 1, so it’s a factor to begin with) and then product rule that, you should get that p’(a) is zero iff m is at least 2
Remainder theorem, division will allow you to write p(x) = (x - a) q(x) + r (where r is a constant - or “a polynomial of degree at most zero” ) and evaluating it at a gives you that r=p(a)
opaque sorrel
seems oddly similar
yessar i understand
will remember this for life
okay now part b
junior smelt
Yep yep
opaque sorrel
i multiplied the expression by sqrt(x+1) - sqrt(2x - 1) and got that
then i subbed in x = 2
and my answer is that
but its wrong 
junior smelt
Remember you needed to 
properly as per my comment yesterday
junior smelt
Doing so gives the denom as -x+2
junior smelt
And of course dividing by zero
junior smelt
Well you can leave it as is for now
junior smelt
For the numerator one
opaque sorrel
wait wym XD
junior smelt
This one
junior smelt
That should give you a cubic that should hopefully evaluate to zero
junior smelt
how did u know <:hmmCat:831508801646755850> <:hmmCat:831508801646755850> <:hmmCa...
magic
opaque sorrel
pls explain ur ways 
junior smelt
That should give you a cubic that should hopefully evaluate to zero
-x^3 + x^2 + 4
I think
And then
,calc -(2^3) + 2^2 + 4
flat frigateBOT
Result:
0
hm
junior smelt
junior smelt
pls explain ur ways <:sully:651816820122189834>
[it’s a common trick in questions like these really]
opaque sorrel
why not these tho
junior smelt
-x^3 + x^2 + 4
But on rationalising the denom and noticing that factor of zero, you could look at that other term and spot it turns into this
junior smelt
why not these tho
It would undo the work we basically just did is a good reason why not
If you multiplied by the conjugate of that it would be like stepping backwards to the original step
opaque sorrel
oh right that maeks sense
ok so what if
its like
some other root is added here
do i choose the first one or the purple one
or like do i just try
luck based
junior smelt
If it were like that I would want to try that purple one (of course in this case, you’d get that making the numerator something that doesn’t cancel down nicely I think?)
That would turn into -1 which is a bit pain 
but these questions usually have a similar feel to them!
opaque sorrel
hmm okay so its like slightly rng
but i need to know which one to not choose
like -x-2 and sqrt(x+1) + .. will be undoing what i did
so i dont choose those
ill simplify this?
junior smelt
Yep by difference of two squares (and leave everything else alone)
junior smelt
-x^3 + x^2 + 4
What we really want is this here
junior smelt
,calc -(2^3) + 2^2 + 4
So that we can cancel out the (2-x) factor in the denom, which is what’s causing our problems right now
opaque sorrel
,w difference of two squares
flat frigateBOT
opaque sorrel
,w definition of difference of two squares
flat frigateBOT
opaque sorrel
junior smelt
Looooool peak 
opaque sorrel
sadge
junior smelt
The whole (a-b)(a+b) = a^2 - b^2 thing
junior smelt
funny enough there’s a lot which I know but don’t know the names for
opaque sorrel
so now im trying to extract (-x+2) from the top so i cancel it
opaque sorrel
<:lolDog:543004265904472065> funny enough there’s a lot which I know but don’t k...
same like me but theres a lot that i dont know
wait so im supposed to use difference of squares on the numerator
junior smelt
You’re “rationalising” this numerator thingy here
We rationalised the bottom already which gave us that factor thing
flat frigateBOT
junior smelt
-x^3 + x^2 + 4
junior smelt
,w factorize (x^2 + 7 - x^3 + 3)
junior smelt
Anyways there’s that factor, which we wanted, that -(x+2) = (2-x)
Cancel them down and we have something nicer
opaque sorrel
junior smelt
With no dividing by zero left haha
opaque sorrel
i think subbing now would be fine
junior smelt
It would be but I think you’re forgetting a factor in the numerator
opaque sorrel
okay so when i have a divide by zero error i should always try to find out which part is the problem, and get rid of it
opaque sorrel
It would be but I think you’re forgetting a factor in the numerator
Ⓜ️inus
okay i got it
junior smelt
okay so when i have a divide by zero error i should always try to find out which...
Pretty much yea
opaque sorrel
then i need to choose what roots to multiply by wisely
opaque sorrel
wait is something wrong
junior smelt
Numerator should have the purple highlighted multiplied by it
junior smelt
thanks alot sir
opaque sorrel
safe radishBOT
@opaque sorrel Has your question been resolved?
little sorrel
After how many months is the number of quokkas greater than half of the maximum number
safe radishBOT
After how many months is the number of quokkas greater than half of the maximum ...
little sorrel
What does this mean
Given for example there is a max of 50 quokkas
Does it mean 1.5x of 50?
safe radishBOT
@little sorrel Has your question been resolved?
safe radishBOT
@little sorrel Has your question been resolved?
safe radishBOT
trim swan
What does this mean
greater than half the maximum
so if the maximum is 50, it means greater than 25
safe radishBOT
Available help channel!
dire junco
hello everyone,
safe radishBOT
hello everyone,
dire junco
So I'm building my summary notes and something seems to me weird
OI=OM, this is logical, it's the radius which is always the same
but without further demonstration it says that OIM is equilateral
incidentaly, MI=OI=OM
empty gyro
Where is M
empty gyro
No trig needed
dire junco
Ooh
the rule that says that the sum of angles is of 180 deg
so we have a first angle of 60 deg
OMI
empty gyro
Yeah that also works
dire junco
the second angle OIM 60 deg
so all angles are the same and the length too
ok thanks
have a nice day
underlated question,
in which year this is taught in us system?
cant understand the last line, in english it would be
"The height (MH) is also a median of the triangle OIM. We can deduce from this that cos(π/3)=x_m=OH=1/2"
I understood by myself
empty gyro
in which year this is taught in us system?
Anywhere from age 12 to 18
dire junco
I just forogt what was the median of a triangle
I'm actually in a french school
next year I plan to go to a boarding school in us
I'm 16, so next year would be my last year of high school and I'm afraid to found a way advanced level in my future school
empty gyro
Good luck in your boarding school. Enjoy the states
twin summit
safe radishBOT
buoyant shadow
the first one
twin summit
when do logarithmic equations have extraneous solutions?
safe radishBOT
when do logarithmic equations have extraneous solutions?
pseudo scroll
Wdym?
As in the solution that you get turns out to make the equation undefined?
(over the reals)
twin summit
yes
pseudo scroll
Honestly I wasn't told of anything personally, you usually just check your solutions by putting them back in the original equation
split ether
You need to make sure that the expressions inside the logarithms are positive
E.g. log_2(x - 2) + log_2(x + 1) = 0 is not equivalent to (x - 2)(x + 1) = 0
But rather (x - 2)(x + 1) = 0 and x-2, x+1 > 0
(Which can be rewritten as (x - 2)(x + 1) = 0 and x > 2)
twin summit
so no negative numbers
split ether
Right
split ether
Most of the times this is neglected as the inequalities can sometimes be implied by the equation that you have
E.g. ln(x) = 2 is equivalent to x = e^2
It just so happens that saying "x = e^2 and x > 0" is the same as "x = e^2"
safe radishBOT
split ether
havent done much with ln and e yet for some reason
Those are introduced in calculus
twin summit
ah that makes sense then
split ether
For now just keep in mind that e is some constant and ln is basically log_e
safe radishBOT
Available help channel!
turbid flare
safe radishBOT
lucid charm
d/dx(x*e^sin(x^2))
safe radishBOT
d/dx(x*e^sin(x^2))
lucid charm
@dusk iron can you help
dusk iron
<@1035917542792908830> can you help
Damn someone pinged me... Why tho I'm such a noob
cerulean chasm
dusk iron
But yea like Martin said show work
grizzled shoal
looks good
cerulean chasm
differentiation is algorithmic, literally requires no brain, computers do it in a flash, actually wolfram alpha can answer this
dusk iron
Ohh i thought logarithmic diff
dusk iron
Ohh i thought logarithmic diff
Somewhere after by parts
grizzled shoal
differentiation is algorithmic, literally requires no brain, computers do it in...
oh yeah? then differentiate f(x)=x! without using wolfram alpha
lucid charm
ohh is this how you do it? this is what I was getting: d/dx(x * e^(sin(x^2))) = 2x^2 * e^(sin(x^2)) * cos(x^2) + e^(sin(x^2))
dusk iron
But nvm
grizzled shoal
oh yeah? then differentiate f(x)=x! without using wolfram alpha
and with f(x)=x!, i mean x in R 💀
dusk iron
differentiation is algorithmic, literally requires no brain, computers do it in...
Wolfram alpha can't solve jee advanced questions forget olympiad
cerulean chasm
and with f(x)=x!, i mean x in R 💀
what is this, factorial?
grizzled shoal
yes
cerulean chasm
hold on I'll try
grizzled shoal
factorial can be expanded onto whole R
$\text{my intuition tells me it is} \ \frac{d}{dx}x!=\Gamma (x+1)\Psi^{(0)} (x+1) \ \text{definitely not wolframalpha telling me this and it totally makes sense to me :)}$
flat frigateBOT
~Martin
dusk iron
Is this solvable by wolfram
grizzled shoal
,w solve the above
flat frigateBOT
grizzled shoal
😦
lucid charm
cerulean chasm
cerulean chasm
Is this solvable by wolfram
no, but it might help you understand the questions
grizzled shoal
hello^^
grizzled shoal
i would like some coding advice
we look at the function f(n)=(n^2)%11
where 11 could be any other number
we expect something like a parabola at multiples of 11
that is also what i got
however, i dont just want points, so i made my dataset more "dense"
the function
the code
the output
the only difference is that for x2, i doubled the number of points, but they still go from 0 to 49
now here we see that if we double our number of points, we will get weird values
for example at around x=11, the parabola is not really there, but actually kinda opposite of what we expect
at around x=22=2*11, the parabola is there but it should also include the point (22,0) right?
i fixed it
i changed 2 * N to 2 * N - 1
.close
safe radishBOT
grizzled shoal
.reopen
safe radishBOT
✅
grizzled shoal
for some reason i still get these weird values
i start to think that this is actually natural
yes, im sure now i think
if we get higher x, we somewhat expect a parabola, but not really
because we would only get that, if x^2 only changed a bit
but for larger x this is no longer true
the odd thing is that it pretty nicely works if i double the number of points
beyond that, it breaks into chaose
.close
west notch
Having a bit of trouble figuring out where I’m going wrong. I’m guessing it might be during the factoring when trying to convert to general form (can’t use decimals for the online portion of this class but I’m still not seeing where I went wrong). Any help would be useful!
safe radishBOT
Having a bit of trouble figuring out where I’m going wrong. I’m guessing it migh...
west notch
I didn’t see the part that it will be graded at a later time so maybe that’s why it’s red. Never seen that before on this site but if anyone could double check that would be great still.
Oh sorry didn’t show the question. Using the graph to get the equation in general form.
safe radishBOT
@west notch Has your question been resolved?
safe radishBOT
@west notch Has your question been resolved?
safe radishBOT
@west notch Has your question been resolved?
hybrid wedge
$-\frac{1}{3}×(-8)$
flat frigateBOT
Anagh
west notch
What is this =?
Oh dang lol did I just mess up with the sign. I do this too much haha
safe radishBOT
Oh dang lol did I just mess up with the sign. I do this too much haha
@west notch Has your question been resolved?
Available help channel!
safe radishBOT
puhahahahhahaahha
quiet crest
pi
south epoch
bruh
south epoch
puhahahahhahaahha
Close it.
timid pasture
.close
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tardy cosmos
Hi! After doing euclidean division (P(x)=2x^3-x^2-5x-2 divided by x-2) I get Q(x)=2x^2+3x+1. The exercise then tells me to solve Q(x) no problem! i get S={-1;-1/2}, but right after it tells me to deduct the solution of P(x), how come?
safe radishBOT
Hi! After doing euclidean division (`P(x)=2x^3-x^2-5x-2` divided by `x-2`) I get...
peak estuary
deduct?
deduce?
so we know that P(x) = (x-2)Q(x)
and then you factored Q(x) further
Q(x) = (x+1)(x+1/2)
so P(x) = (x-2)(x+1)(x+1/2)
and from that you should be able to solve P(x)=0
tardy cosmos
Q(x) = (x+1)(x+1/2)
Isn't the solution negative?
fleet laurel
.help
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fleet laurel
.help open
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fleet laurel
.tag likelihood ratio
what's likelihood ratio ? an exemple ? what it's made for , how use it. may you expain on a easy way that i can understand, because i'm not that good at english
plucky elk
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stoic dune
Probability that you got the results that you did
Note that finding this probability directly is kind of meaningless. However, maximizing it for some parameter gives the MLE, a pretty useful concept.
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pseudo bridge
Help
pseudo bridge
I know it isnt really math but I have no idea where to ask
hearty egret
i really don t know what is the question
frank glen
Hmm this does seem like a white noise sound graph.
They're relatively low and they're very consistent but random
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fickle trail
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fickle trail
anybody else sometimes make the mistake of putting this full term on the denominator? especially when there are a lot of terms in the equation
is there any "trick" that you use to catch yourself before making that fallacy?
math is interesting where definitions can be shared, sometimes a term means "one variable" and sometimes a term means "constant and a variable"
this maybe I should think of as two terms? or a constant raised to the first power, and a variable raised to the -1/2 power?
iron flare
it's not necessarily incorrect to put this full term on the denominator
fickle trail
how so?
peak estuary
well it is two terms. 2 and x^(-1/2). if thinking about 2 as 2^1 helps then do it
iron flare
you mean specifically in the case of when you need to rationalise a denominator?
fickle trail
fickle trail
it's not necessarily incorrect to put this full term on the denominator
do you mean like this?
iron flare
no i mean
i'd literally leave this as is
unless a question required me to rationalise it
it's hard to think of a specific case where it'd really matter, though
fickle trail
well it is two terms. 2 and x^(-1/2). if thinking about 2 as 2^1 helps then do i...
I may need to remember this..
fickle trail
it's hard to think of a specific case where it'd really matter, though
simplification, if a lot of other stuff is included in the expression
iron flare
ah-- sorry, your point of confusin is you're bringing the 2 along with it?
fickle trail
yes
I sometimes do both by mistake
thinking it's a single term
but they are not
but they are
lol
it's confusing, the terminology with math, sometimes
fickle trail
I sometimes do both by mistake
this would be incorrect
fickle trail
it's not necessarily incorrect to put this full term on the denominator
I suppose I could also write it like this
but that would only work for a monomial
not binomials
iron flare
you'd have x^-1/2 in brackets there if you're equating it to the original
fickle trail
oh
I think that's the word I was looking for
monomial
term and monomial are not the same thing
I should start using monomial more often I think that may help me
fickle trail
you'd have x^-1/2 in brackets there if you're equating it to the original
oh ya, good point
lol, simplification at it's finest
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meager shoal
My question is how often do i not get a 5 or 6 when throw a dice 60 times?
safe radishBOT
My question is how often do i not get a 5 or 6 when throw a dice 60 times?
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
3
smoky hamlet
My question is how often do i not get a 5 or 6 when throw a dice 60 times?
Assuming the dice is fair and unbiased, the probability of not getting a 5 or 6 on a single roll is 1/3, as there are four possible outcomes (1, 2, 3, or 4) that are not a 5 or 6, out of a total of six possible outcomes.
meager shoal
smoky hamlet
The probability of not getting a 5 or 6 on 60 independent rolls is the product of the probabilities of not getting a 5 or 6 on each individual roll. This can be calculated as:
(1/3)^60 ≈ 4.71 x 10^-23
So, the probability of not getting a 5 or 6 on 60 rolls of a fair dice is extremely low, about 4.71 x 10^-23 or 0.0000000000000000000000471. In other words, it is very unlikely that you would not get a 5 or 6 at least once in 60 rolls of a fair dice.
peak estuary
is that chatgpt?
peak estuary
well except the math part it's correct. so I guess that's at least something
meager shoal
yea so i need to do 4/6^60
peak estuary
no
meager shoal
can you tell me then what to do because i dont understand the other thing
misty bay
Assuming the dice is fair and unbiased, the probability of not getting a 5 or 6 ...
have you or a loved one ever been on controlled substances in the past 5 minutes?
btw
,w (1/3)^60
flat frigateBOT
misty bay
it's not even the number that chatgpt said it was
meager shoal
xd
but thats so wierd i am in the 10th grade and i have never ever seen such a number
misty bay
so are you asking if you throw the die 60 times, what the probability of never getting a 5 or a 6?
peak estuary
would you be able to answer the question for 3 throws
meager shoal
yes
misty bay
out of curiosity, is this like an assignment problem or are you concerned with the rigging of some die?
meager shoal
would you be able to answer the question for 3 throws
probably not
meager shoal
out of curiosity, is this like an assignment problem or are you concerned with t...
its about a assignment
misty bay
oh okay
peak estuary
so to not get a 5 or 6 for 3 throws, that means you cannot get a 5 or 6 for the first, you cannot get a 5 or 6 for the second and you cannot get a 5 or 6 for the third
meager shoal
i could send you a pic but its german
peak estuary
lets do the first
what is the probability that you dont get a 5 or 6 for the first throw
meager shoal
4/6
meager shoal
4/6*4/6
meager shoal
so i do that 60 times
peak estuary
and now please use correct brackets
meager shoal
sry first time on a math server
peak estuary
,w (4/6)^60
flat frigateBOT
peak estuary
not as extreme as before but still quite unlikely. just like expected
meager shoal
okey ty i just though it cant be like that because we never ever used such a high number
peak estuary
in 10th grade you should be past the part where the actual numbers really matter
the result doesnt matter here
the approach does
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golden imp
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golden imp
How do I find the matrix transformation?
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golden imp
<@&286206848099549185>
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craggy trout
,w derivative x * (x^3+6)^{4}
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,w derivative x * (x^3+6)^{4}
flat frigateBOT
craggy trout
[x(x^3+6)^4]
[\frac{d}{dx} x = 1]
[\frac{d}{dx} (x^3+6)^4 = 12x^{2}(x^{3}+6)^{3}]
flat frigateBOT
dopediscorduser
craggy trout
[(x)12x^{2}(x^{3}+6)^{3} + (1)(x^3+6)^4]
[12x^{3}(x^{3}+6)^{3} + (x^3+6)^4]
flat frigateBOT
dopediscorduser
craggy trout
I am stuck and not sure if I'm applying the product rule correctly here
dull sequoia
I am stuck and not sure if I'm applying the product rule correctly here
Factorise
flat frigateBOT
dopediscorduser
craggy trout
Factorise
I don't see what there is to factor except the 12x^3 term
[12x^{3}((x^{3}+6)^{3} + (x^3+6)^4)]
flat frigateBOT
dopediscorduser
craggy trout
But that just kinda leaves me where I started
misty bay
woah that is not true
craggy trout
?
misty bay
you can't just take A[something] + [something else]
and change it to A([something] + [something else])
craggy trout
Ah you're right
craggy trout
[12x^{3}(a^3 + a^4) = a^3(12x^{3}a)]
flat frigateBOT
dopediscorduser
craggy trout
[12x^{3}(x^{3}+6)^{3} + (x^3+6)^4 = (x^{3}+6)^{3}(12x^{3}+ x^3+6 = (x^{3}+6)^{3}(13x^{3} + 6)]
flat frigateBOT
dopediscorduser
cobalt osprey
Hi im in geo honours, and missed a couple days of school cause I was sick, and now I dont know how to do a topic that we have a test on tomorrow. its trigo. I understand how to find the ratio, but cant figure out how to find the angle and what not.
safe radishBOT
Hi im in geo honours, and missed a couple days of school cause I was sick, and n...
cobalt osprey
like for example, tangent of 30 degrees, or cosine of 70 degrees. or even "what angle measure has a cosine value of 0.9877"
misty bay
oh so you know that the tangent of something = some ratio
but you want to find the something?
cobalt osprey
my teacher told me I want to find the ratio of "tangent of 30" but in decimal form
so yeah basically what you said
could you help me?
<@&286206848099549185>
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drowsy dragon
how do I factor 3x^2-27(2-x)^2 (ping me)
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how do I factor 3x^2-27(2-x)^2 (ping me)
candid storm
@drowsy dragon try expanding what you can first
eventually it should turn into a polynomial
lean otter
Can someone help me create a polynomial with the given roots of: -5 and 2+3i
Both in factored form and standard form, please?
junior smelt
With real/rational/integer coefficients?
lean otter
With integer coefficients
junior smelt
Well in that case, if 2 + 3i is a root, what else must be a root?
lean otter
-5 is another root given
I’m not sure if that answers the question you’re asking
🤔 I really don’t know what to do with the 2+3i root
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toxic raft
🤔 I really don’t know what to do with the 2+3i root
treat it like any other number
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south leaf
I've a function which is defined as $$f(n) = \begin{cases} \frac{n+1}{2},\quad \text{if n is odd.}\\frac{n}{2} , \quad \text{if n is even.} \end{cases}$$
I've to prove that it is surjective function.
safe radishBOT
I've a function which is defined as $$f(n) = \begin{cases} \frac{n+1}{2},\quad \...
flat frigateBOT
innocently.innocent.soul
grim plover
Uhh sorry for being dumb but what is a surjective function
south leaf
I gave a reason that $\forall n \in \mathbb {N}\ \exists f(n) \in \mathbb{N}.$ Therefore $f(n)$ is surjective. Is it right?
compact ferry
$f: \mathbb{N} \to \mathbb{N}$
flat frigateBOT
heavy
compact ferry
for all n in what exactly?
peak estuary
Surjective means that for all n there exists m such that f(m)=n. That's what you have to show
compact ferry
its not quite right
flat frigateBOT
innocently.innocent.soul
grim plover
Surjective means that for all n there exists m such that f(m)=n. That's what you...
Ohhhhh
grim plover
Surjective means that for all n there exists m such that f(m)=n. That's what you...
Hmm..How would u prove that??
peak estuary
My best guess for what you tried to write is that for every n, f(n) is defined and a natural number. Which is trivial
south leaf
What if I define it as... for all n belongs to natural numbers, there exist some natural number m such that f(n) = m?
south leaf
I'm not getting it
south leaf
Lets do an example
Yes
peak estuary
Can you tell me an m such that f(m)=5
peak estuary
m but yes
south leaf
Hm
peak estuary
What about m so that f(m)=61
south leaf
122 and 121
south leaf
Yes I think
n can be anything.... 1,2, 3, 4, ...
Forall n there exist some m such that f(m) = n
peak estuary
And what is that m?
south leaf
Natural number
peak estuary
I mean as a formula involving n
peak estuary
Yes but one is enough
south leaf
Oh
peak estuary
Good. So far all n there exists an m (namely m=2n) so that f(m)=n.
And that shows that f is surjective
south leaf
What if I define it as... for all n belongs to natural numbers, there exist some...
What's the problem in this?
Surjectives are those in which range = codomain right?
south leaf
What if I define it as... for all n belongs to natural numbers, there exist some...
Here I'm talking about existence of m i.e. range.
So why is it wrong?
peak estuary
Well clearly the range exists
And is a subset of the codomain
You have to show that they are equal
So that means every element in the codomain has to be in the range
So every n in the codomain has to "get hit", ie there has to exist an m so that f(m)=n
south leaf
Ohh
That means for all natural numbers to be an output of the function, there exist some domain value for that right?
peak estuary
Yes
nocturne python
i also have notes if needed for additional context
safe radishBOT
i also have notes if needed for additional context
nocturne python
<@&286206848099549185> i also using demos know that this is wrong how do know how to to this i know slope intercept
hybrid fractal
@nocturne python can we use elimination or substitution method to solve this question?
dense prism
<@&286206848099549185> i also using demos know that this is wrong how do know h...
Well firstly, when can we say two linear equations in x and y have a solution?
nocturne python
when two lines intersect?
dense prism
Yes
Now looking at slopes can you get an idea of when two lines will interect?
Slope is nothing but a way to express the inclination of the line with the axes
Now if I tell you the slopes of two line are unequal, it means that their inclinations with the axis are unequal
And if they are inclined differently(i.e. don't run in the same direction), then that means they are bound to meet at some point
Because they extend infinitely
Does that make sense?
nocturne python
yes
dense prism
Now if the slopes of two lines are not equal, that means they're intersect at one point which means the system will have one unique solution
On the other hand
If we have two lines with the same slope i.e. they run in the same direction, there arise two cases:
nocturne python
what is unequal
dense prism
what is unequal
Not equal
dense prism
If we have two lines with the same slope i.e. they run in the same direction, th...
- they have the same intercept
- they have different intercepts
If you think about it, having the same slope and same intercept would just make it the same line
That is, if I say line 1 has slope equal to slope of line 2. And line 1's intercept is equal to line 2's intercept, it just means line 1 is the same as line 2
Does that make sense?
And dw for now I'm just explaining things, at the end I'm gonna give you a sweet shortcut to determine the nature of solutions (solution type)
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random mural
safe radishBOT
https://cdn.discordapp.com/attachments/903463353417072641/1081223018778460270/im...
random mural
how do u find the normal vector here with the 2 vectors given
hexed dune
how do u find the normal vector here with the 2 vectors given
cross product
random mural
cross product
in the video it says to find the determinant
but in my question i got an 2 x 3 matrix
random mural
oh
random mural
you get a 3 by 3 matrix
btw is it poss to find the determinant of non square matrix?
random mural
did he then made a mistake? I came at [-3,5,3]
oh wait nvm
I forgot a -
btw he is doing the cross product like this
but I have never seen someone doing it like this
I was used to do it like this
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hexed dune
but I feel like the matrix method is more writing
the matrix method is easier to remember
fickle trail
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fickle trail
is a dot required here?
icy nymph
i mean you can add it if you want. people sometimes don't bother when its multiplication. it's kind of implied
fickle trail
OK thanks, just making sure for notation on dy/dx
lean otter
is a dot required here?
would it hurt to click once to add the dot in anyways?
fickle trail
more effort haha
lean otter
i doubt there is anyone that would mind u adding it or not tbh
fickle trail
no brackets needed either
ya, I guess it's implied with multiplication
and commutative so front or back doesn't matter
d/dx would not be commutative however
that needs to go in front
and have brackets
to show what is being differentiated
lean otter
yeah think of the dy/dx as some function, or write it as y' whatever, you can treat it as how u would do for any other variable letter lke x,y,z,etc..
fickle trail
in that same sense wouldn't d/dx also be considered a term? if it was written just like that, no brackets or function to differentiate, d/dx [x]
or do we know that d/dx on it's own is a big no no
it's like saying f()?
lean otter
uh
d/dx is a linear operator
like it can be its own thing like with
(d/dx)^2 + (d/dx) and stuff
fickle trail
lean otter
but thats getting into stuff that u are not really concerned with
for calculus consider it as a simple operator similar to addition or whatever
fickle trail
in higher level math, this makes sense?
sand minnow
this would be a completely new operator
lean otter
idk what "makes sense" to you means because it is literally just letters to me without any form of context of what this is meant to be
fickle trail
it's like saying 3y +?
sand minnow
for example in quantum mechanics you have the momentum operator $$\hat{p}=-i\hbar\pdv{x}$$
flat frigateBOT
Duh Hello
fickle trail
OK I think I'm opening up a can of worms with this question haha
for Calculus 1 I will prob avoid d/dx without brackets afterwards... d/dx [x], etc. is the only way I will write that
sand minnow
it's like saying `3y +`?
its not like saying this, what you posted means "this is an operator where you take the derivative with respect of x of the argument, then multiply the argument with 3y"
sand minnow
well it will be saying the same in any context, its math with very well defined conventions
but you shouldnt be writing d/dx alone very often in calc1
icy nymph
there was a good video by Krista king which explained the meaning of dx. at high school level it's just a notation, but it means different stuff at higher level
fickle trail
but even this is being multiplied by ih
I'm just talking about d/dx on it's own
with nothing next to it