#help-28
brittle steeple
woven snow
brittle steeple
cheater
woven snow
0205 is cool
if it would’ve been 2005 tho
i’d have bought ur account
if that’s allowed
brittle steeple
wow
woven snow
woven snow
woven snow
brittle steeple
2005 would be same rotated 180°
glossy valveBOT
woven snow
okay had to make sure
brittle steeple
lol
woven snow
woven snow
no, non nitro tags cool
brittle steeple
tru
brittle steeple
There's a 2² in there lmao
woven snow
brittle steeple
I didn't think 8817 was even
woven snow
its not
brittle steeple
lmaoooo
woven snow
,w 0205
glossy valveBOT
woven snow
wow
woven snow
brittle steeple
I didn't realize I don't see it when you expand more lol
woven snow
brittle steeple
,w 23/33
glossy valveBOT
woven snow
woven snow
,w 33*36+13
glossy valveBOT
woven snow
oh
brittle steeple
,w 1201 in base 36
glossy valveBOT
woven snow
xd
glossy valveBOT
brittle steeple
,w first ten terms of (10^a-1)/9
glossy valveBOT
Requested by monikanicity#0205
brittle steeple
f
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@spare basin Has your question been resolved?
spare basin
Yes
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tranquil rivet
I hope I'm doing this right.
Can anyone help me with elementary functions ? (Linear, exponential, goniometric, logarithmic and so on..)
College requires them as the basics of basics and I have no idea how to correctly calculate the equations, get the roots, domains, ranges, asymptotes, intersections and graphs.
rapid rock
We can if you have a concrete question...
tranquil rivet
We can if you have a concrete question...
Ah, I guess I asked at the wrong place then.
My problem is that I don't know how to solve elementary functions in general.
I guess I should ask elsewhere, then ?
rapid rock
Its a vast subject. Have look at youtube! Or khan academy. And the you can ask here if theres something that you dont understand.
But i am new here, so what do i know?
lofty hemlock
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fast peak
what have you tried
lofty hemlock
uh i forgot how to do A'
fast peak
well what is A'
lofty hemlock
i dont remember how to find A'
fast peak
what does the notation mean
lofty hemlock
differentiate?
lofty hemlock
go open up your notes and search for it
i apparently only have notes for the inverse part
torn jolt
A' is unconventional notation, we can't help without know what it is. Perhaps its a transpose? Can you check your text book?
lofty hemlock
uhhh i left my stuff at school, i'll just ask my teacher tmr haha, thanks for trying to help me
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lyric sand
Can someone help with this
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Can someone help with this
lyric sand
burnt trail
A' is A transpose
basically switch rows and columns
usually At is the correct notation, but people use A' as well
@lofty hemlock
lyric sand
A' is A transpose
is that the same thing as the derivative
burnt trail
for a 2d matrix just switch the non diagonal matrix
no it is not
you cant differentiate matrices
lyric sand
why does it ask for the product rule then
lyric sand
oh
lyric sand
college
lyric sand
im in 12th grade
💀
burnt trail
thought that was vector calculus
lyric sand
well kinda
burnt trail
you can go to the college channels
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elfin flicker
There is a bowl with small black and white balls, we take one ball and then another ball. The probability of the first ball being black is 0.615. The probability that the first ball is black
and the second ball is white is 0, 256. So what is the probability that the second ball is white given that the first was black?
So I have P(A|B)= P(A|B) x P(A)
I know that P(A|B)= 0.256 and P(B)= 0.615 but I don't know how to find P(A)?
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There is a bowl with small black and white balls, we take one ball and then anot...
wild sleet
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@elfin flicker Has your question been resolved?
buoyant goblet
Shouldn't this be floor (n/2). Because if we have n= 5, then 5/2=2.5
buoyant goblet
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torn jolt
Can anyone help me with question 8B?
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Can anyone help me with question 8B?
gritty rose
gritty rose
did you plug your x into the curve?
torn jolt
Not yet, Im confused on why in the book the 2 is supposed to be negative
So the x is supposed to be -2 instead of 2
gritty rose
Not yet, Im confused on why in the book the 2 is supposed to be negative
show this
gritty rose
,w plot y=2x^3-4x^2+5 and y=8x-11, for 0 < x < 4
glossy valveBOT
gritty rose
,w solve 2x^3-4x^2+5 =8x-11
glossy valveBOT
gritty rose
this line is wrong. not sure why you differentiated it
you're just supposed to solve for the intersection of the two equations
torn jolt
you're just supposed to solve for the intersection of the two equations
Oh
So i dont need to differentiate?
gritty rose
unless you have a reason to, don't use the derivative
"intersection" means setting the two equations equal
gritty rose
slopes, tangent lines, when it tells you to use the derivative
torn jolt
slopes, tangent lines, when it tells you to use the derivative
Ohhh okay
Thankss
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native briar
For part 6, use the matrix from part 5 and properties of inverses.)
How am I supposed to solve this question without actually going and getting the inverse for question 6 here?
torn jolt
,w invert([[5,-2,0],[4,1,-2],[-3,0,1]])
glossy valveBOT
torn jolt
For part 6, use the matrix from part 5 and properties of inverses.)
How am I su...
use your answer from q5
native briar
I don't see how it translates over, or how I should transform it.
torn jolt
the inverse of the matrix in q5 looks suspiciously similar to the coefficient matrix of q6
native briar
I understand that much but I still don't know what to do with it.
torn jolt
$Ax=b\iff x=A^{-1} b$
glossy valveBOT
Toby
native briar
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scarlet socket
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hard siren
Write cos theta as ratio of base and hypotenuse and use Pythagorean identity, you'll get what you want
scarlet socket
what do you mean by that
hard siren
Means, basic defination of trigonometry, right? $cos \theta = \frac {base}{hypotenuse}$ and like that sin theta and tan theta...?
glossy valveBOT
Gamin8ing
scarlet socket
so do i have to find hypotenuse
brittle steeple
**Gamin8ing**
Usually adjacent is used
Not hypotenuse
Ehhhhh ignore that
Adjacent instead of base
I think my discord is glitching out tho 1 sec
Ok yeah it was
Since theta won't be an angle from 0-90 here
Your best bet is probably to use sin^2+cos^2=1 to find theta
To find sin theta anyways
and then calculate tan theta from that
But just to find theta you need to use inverse trig functions
scarlet socket
so i would do sqr75/10 first ?
is there a way you can make it visual bc i really dont understand what the message is explaing if possible.
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timber hatch
Hi, can someone help me figure out how to get the indefinite integral here ? I already know the solution from an online calculator, but I'm not getting a clear understanding of the steps followed to find it.
dim wolf
Hi, can someone help me figure out how to get the indefinite integral here ? I a...
once you get to line two what happens if you try a u-sub
so like sin = u
so du = cosdx
so dx = du/cosx
which would eliminate cos
then its just integral of 1/u^2
which you should be able to do
I think this would work from a quick glance but not 100% sure
timber hatch
so like sin = u
so du = cosdx
so dx = du/cosx
Sorry I'm just a bit confused since I'm not used to that notation
So what you're saying is the equivalent of :
u = sin(x)
u' = cos(x)
F(x) = u'/cos(x) ?
That last line kind of lost me, what happened to sin^2(x)
dim wolf
So we are saying sin = u so the point of solving for du/dx is to get the integral in terms of u. So you can solve for u. And since sin is u. Then you can just see it as u^2
timber hatch
So we are saying sin = u so the point of solving for du/dx is to get the integra...
Oh I think I got it. The notations is really what threw me off haha x) Thanks for explaining !
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dim mulch
So I was making an exp curve for a game and I thought of this but I was wondering if there were a way to generalize it into a function with polynomials or exponents or whatever, instead of calculating it sequentially and storing it into a table. Any ideas? The next level costs the level% more than the previous one basically
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So I was making an exp curve for a game and I thought of this but I was wonderin...
@dim mulch Has your question been resolved?
torn jolt
Short answer: yes
Your reccurence relation is very similar to the reccurence relation used to define the factorial function.
torn jolt
I am looking for an example of a convergent sequence whose square does not converge.
torn jolt
For the opposite case, I've figured it out (-1)^n
simple totem
I am looking for an example of a convergent sequence whose square does not conve...
i don’t think there are any
full marsh
$\lim_{n \to \infty} a_n^2 = \left(\lim_{n \to \infty} a_n\right)^2$
torn jolt
it was an exams question and im pretty sure that there was a solution
glossy valveBOT
RedstonePlayz09
simple totem
it was an exams question and im pretty sure that there was a solution
what was the exact wording?
torn jolt
**RedstonePlayz09**
The Sum of an converges the sum of an^2 does not
the task is to find an example
torn jolt
yeah i used one for the opposite direction
torn jolt
For the opposite case, I've figured it out (-1)^n
.
torn jolt
The Sum of an converges the sum of an^2 does not
but i cannot come up for this one
full marsh
(-1)^n * something
simple totem
((-1)^n)/sqrtn maybe?
full marsh
I'm not sure aswell
torn jolt
((-1)^n)/sqrtn maybe?
but when i square it wouldnt it be 1/n?
fleet cedar
torn jolt
yeah sry i was talking about the sequence
simple totem
what’s the question then
torn jolt
in my language series has the same definition as sequence:D
torn jolt
To find a sequence that coverges but the sequence squared not
simple totem
there’s no such sequence
full marsh
As we said, that's not possible
torn jolt
how do they differentiate between them then
well the translator screwed up we have a word to seperate them
full marsh
(a_n)^2 will converge to the limit of a_n, squared.
torn jolt
so its a contradiction
full marsh
No?
simple totem
there’s no contradiction there just isn’t a sequence with that property
full marsh
It's just not possible
stray wraith
With no calculators in mind, can anyone check to see if my answer was correct?
Given: x = 1, y = sqrt(3), dx/dt = 5
Find: dy/dt
d/dt[x^2+3y^2]=d/dt[0]
2x(dx/dt) + 6y(dy/dt) = 0
2(1)(5) + 6(sqrt(3))dy/dt = 0
10 + 6sqrt(3)dy/dt = 0
6sqrt(3)dy/dt = -10
dy/dt = -10/6sqrt(3)
dy/dt = -5/3sqrt(3)
Final answer: dy/dt = -5/3sqrt(3) units/sec
twilit leaf
i think it looks good
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@stray wraith Has your question been resolved?
stray wraith
i think it looks good
Thanks! I just want to know from a few more people just in case 👍
twilit leaf
ok
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stray wraith
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silk solstice
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silk solstice
correct me please
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limpid wolf
correct me please
what's wrong with it?
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@silk solstice Has your question been resolved?
limpid wolf
correct me please
have a look here https://math.stackexchange.com/a/3938666
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runic bloom
am I doing c right?
I found the average velocity using x(4) - x(0) over 4-0 which I found was 4
and then I set the velocity function to 4?
but that results in an irrational number
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runic bloom
<@&286206848099549185>
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<@&286206848099549185>
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placid storm
does this make sense? im not sure how else to write it
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does this make sense? im not sure how else to write it
@placid storm Has your question been resolved?
placid storm
<@&286206848099549185>
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crimson tiger
i need help brother
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i need help brother
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jaunty onyx
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west geyser
yes i believe that would be the first step in order to obtain angle DEB
jaunty onyx
I need ade
west geyser
yes, which is an angle from a quadrilateral, which are shapes whose angles add up to 360
and since you can get DEB, and you have all other angles besides ADE, you can do 360 - 90 - 46 - (180-62)
which i think will get you ade
jaunty onyx
224?
west geyser
well thats if you just subtract 90 and 46 from 360
you need to also subtract the value of angle DEB from that
jaunty onyx
so 106
west geyser
yes
west geyser
no problem
do you know if i can directly ask for help from someone in this discord
instead of just posting in a server
west geyser
ah ok
jaunty onyx
yeah
west geyser
thank you then
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neat scarab
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sharp vine
,w lim x to 1 of ln((x+1)/2)/(x^2-1)
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gusty shoal
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sacred fog
<@&268886789983436800>
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@gusty shoal Has your question been resolved?
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@gusty shoal Has your question been resolved?
gusty shoal
rationalise the denominator useing congjuates
what?
hollow marlin
Does anyone know how I could go about explaining this?
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Does anyone know how I could go about explaining this?
hallow cedar
Does anyone know how I could go about explaining this?
a vertical asymptote implies that g(x) can be written in a single fraction such that it has denominator (x-a)k where k is the remaining factor of the denominator
so if you square the fraction you'd get [(x-a)k]^2 in the denominator however if x=a this would still equal 0 so a vertical asymptote would still exist
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north spade
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molten island
Consider the cubic function f(x)=2x^3 + ax^2 + bx + c
find the values of a, b, c
if the graph of the function passes through the points (1,0), (-1,2) and (0,3)
I dont know the method of finding this out please guide me
calm osprey
you can create a equation system with these three points and the function. then solving the system will give you the value of a,b and c
molten island
what is an equation system
also without calculator
no calculators will be allowed
in my upcoming test
calm osprey
these are for an example equation systems
molten island
but how will i make an equation system using the values, where will the values go?
calm osprey
you take the function you have and plug a point in and do so for all the points then you should have a three line equation system
molten island
sorry still dont get it
calm osprey
i will write it on paper and send a pic just give me a min
molten island
ok thank you
fast peak
for example, the function goes through $(-1, 2)$. that means $-2=f(-1)=2(-1)^3+a(-1)^2+b(-1)+c$
glossy valveBOT
Denascite
fast peak
so this gives you the equation $-2=-2+a-b+c$
glossy valveBOT
Denascite
molten island
okay and then what
fast peak
repreat the same for the other two points
you'll get two other equations
in total 3 equations and 3 variables
molten island
**Denascite**
so the variable will be -2 in this case?
fast peak
the variables are a, b and c
calm osprey
fast peak
oh whoops I included a minus too much in my equation. disregard that
molten island
ya this will give the answer for c but what about a and b
calm osprey
you use the points to formulate three equatiions where only a,b and c are unknown then put them together and solve the system
calm osprey
jupp seems correct to me. you think you got how the strategy works or are you still confused about any part?
calm osprey
no problem, take care 🙂
molten island
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torn jolt
Can someone help me with question number 5? I don’t understand what it means by (3, 4-b) belongs to X - axis
calm osprey
,rotate
glossy valveBOT
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@torn jolt Has your question been resolved?
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@torn jolt Has your question been resolved?
torn jolt
can someone help
torn jolt
<@&286206848099549185>
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pearl nimbus
If I have 5g bread and put that into 200mL hydrochloric acid. If I've determined there to be 5.0635 micrograms/gram of sodium from the calibration curve. How many micrograms/gram would there be from the diluted 5g bread in 200mL hydrochloric acid?
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If I have 5g bread and put that into 200mL hydrochloric acid. If I've determined...
@pearl nimbus Has your question been resolved?
rancid notch
Bro how did they just whip out (5C1) in question 3 bro
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Bro how did they just whip out (5C1) in question 3 bro
hallow cedar
Bro how did they just whip out (5C1) in question 3 bro
it's this formula
hot herald
again, they're only considering the terms they need and used binomial theorem to get those terms specifically
the x^2 in the final expansion comes from
1 * x^2 term in (a+x)^5
+
-2x/a * x term in (a+x)^5
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torn jolt
what exactly do I do for this one
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what exactly do I do for this one
torn jolt
part a
rapid rain
Mmmmh, the question is cheeky, it's almost as if you had to find a linear combination of the first 2 vectors that is an eigenvector of M.
But it couldnt be something as easy as their sum, right ? ...
:)
torn jolt
Mmmmh, the question is cheeky, it's almost as if you had to find a linear combin...
i was looking at their difference instead lol
@rapid rain
not working
resultant vector isnt a direct scalar multiple
rapid rain
Or at least show what M × that vector is
torn jolt
,rotate
glossy valveBOT
glossy valveBOT
torn jolt
@rapid rain
rapid rain
try calculating (1,-1,-1) + (-2,-3,1) again and you ll see
rapid rain
It happens
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rapid rain
No problem
torn jolt
Same q ii part now 😭
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Same q ii part now 😭
glossy valveBOT
idecanymore
torn jolt
It's only 4 marks
That's why I'm a bit hesitant to do something too substantial
R+
Mn
Mb*
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@torn jolt Has your question been resolved?
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@torn jolt Has your question been resolved?
chrome hull
anyone knows this? ive been looking for yt vids to solve this found nothing
topaz valley
🔭
onyx glen
factor a two out of every fraction
get 2^(some power) * 2/3 * 3/4 * 4/5 * ... * 98/99 * 99/100
topaz valley
thanks
chrome hull
get 2^(some power) * 2/3 * 3/4 * 4/5 * ... * 98/99 * 99/100
thnks ill try again
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next knoll
where is the 3rd point of intersection?
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where is the 3rd point of intersection?
onyx glen
somewhere further down, offscreen
summer echo
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torn jolt
,w intersections -x(x+2) and -x^3
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torn jolt
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timid atlas
So I have homework to prove two parallel lines form a plane
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So I have homework to prove two parallel lines form a plane
timid atlas
I tried saying that since they are paralell there exists two distinct lines that intersect both of them
But I didnt manage to prove they make a plane
rocky vale
But I didnt manage to prove they make a plane
You could say that there exist two distinct non-parallel lines that intersect them both. Then the direction vectors of those two lines span a plane containing the parallel lines
timid atlas
You could say that there exist two distinct *non-parallel* lines that intersect ...
Well we are supposed to use the axioms of incidence
rocky vale
Can you show me what those are? The ones I'm familiar with are only applicable to two dimensions and not concerned with planes
timid atlas
Ok now Im just more confused
rocky vale
I'm just asking you what axioms you're allowed to use
rocky vale
And you have to prove that two parallel lines uniquely define a plane?
Really the lines don't even need to be parallel.
Say we have distinct lines j and k.
Axiom 1.3 states that there exist two distinct points A and B on line j.
Similarly, there are two distinct points C and D on line k.
By axiom 1.2, at least one of C or D is not on line j, else j and k would be the same line.
Therefore, either (A, B, C) or (A, B, D) are a set of three distinct points not on the same line.
By axiom 2.2, this defines a unique plane.
graceful hamlet
So I have homework to prove two parallel lines form a plane
Distance vector between two parallel lines is constant and summation of it will give what's in between
timid atlas
By axiom 2.2, this defines a unique plane.
Oh
graceful hamlet
Distance vector between two parallel lines is constant and summation of it will ...
Perpendicular distance vextor
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rocky vale
You might be able to simplify the part about C and D to just a single point if you can assume that parallel lines don't share any points
👍
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torn jolt
wait
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torn jolt
proud willow
plug x=-4 I think
hot herald
also this channel will close any minute since you deleted the original
torn jolt
so its -4?
hot herald
wdym by "it"
torn jolt
the value of z(-4)
hot herald
the answer to the question? no.
you are given the equation
z(x) = 2(x-5)^2 + 8
to find z(-4), substitute -4 for all the xs in that equation
(the resulting equation will tell you exactly what z(-4) is equal to)
torn jolt
-9
hot herald
how are you getting -9
torn jolt
i js put -4 in for x then did the exponent and put it in google
lol
oh
nvm
wait
i got 74
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hidden garnet
Is the product of 2 square numbers always a square number?
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Is the product of 2 square numbers always a square number?
sharp vine
Is the product of 2 square numbers always a square number?
$$a^{2} \cdot b^{2} = (ab)^{2}$$
glossy valveBOT
Modus
hidden garnet
i see. so i take that to be a yes?
sharp vine
yep
hidden garnet
One more question, is the product of two or more cube numbers a cube number?
tired quarry
One more question, is the product of two or more cube numbers a cube number?
$a^3b^3\stackrel{?}{=}(ab)^3$
glossy valveBOT
tomzizek
tired quarry
what do you think?
hidden garnet
ig it is a cube number too
tired quarry
yeah it is
hidden garnet
thanks
tired quarry
$a^nb^n=(ab)^n$
glossy valveBOT
tomzizek
tired quarry
property
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torn jolt
What are the probabilities for x = 0-3?
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What are the probabilities for x = 0-3?
torn jolt
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bitter beacon
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brave blaze
what have you tried ?
brave blaze
do you know about summation ?
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
@bitter beacon
bitter beacon
yes
brave blaze
can you rewrite your expression with it ?
bitter beacon
no
brave blaze
Ok, do you know about partial fraction decomposition ?
brave blaze
$\frac{1}{i(i+2)} = \frac{a}{i} + \frac{b}{i+2}$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
you calculate the right side and you find a and b by identification
bitter beacon
like this ?
brave blaze
yea
brave blaze
huh the second part, it's i+2, not i+1
brave blaze
and why it is i+2 ?
$\frac{1}{i(i+2)} = \frac{1}{2i} - \frac{1}{2(i+2)}$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
$\sum_{i=1}^{99} \frac{1}{i(i+2)} = \sum_{i=1}^{99} \left( \frac{1}{2i} - \frac{1}{2(i+2)} \right)$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
$= \frac{1}{2} \left( \sum_{i=1}^{99} \frac{1}{i} - \sum_{i=1}^{99} \frac{1}{i+2} \right)$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
we will use telescopic sum
but first we will rearrange the index
do you know that ? :
$$\sum_{i=1}^{99} \frac{1}{i} =\sum_{i=0}^{99} \frac{1}{i+1} = 1 + \sum_{i=1}^{99} \frac{1}{i+1}$$
bitter beacon
Ok i agree
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
$= \frac{1}{2} \left( \sum_{i=1}^{99} \frac{1}{i} - \sum_{i=1}^{99} \frac{1}{i+2...
we will sub this in that
$$= \frac{1}{2} \left( 1 + \sum_{i=1}^{99} \frac{1}{i+1} - \sum_{i=1}^{99} \frac{1}{i+2} \right)$$
oops
glossy valveBOT
Ｈｅｒｅｌｓ
bitter beacon
ok
brave blaze
and we will use something called telescopic sum
$$\sum_{i=1}^{99} \frac{1}{i+1} - \sum_{i=1}^{99} \frac{1}{i+2} = - \left( \sum_{i=1}^{99} \frac{1}{i+2} - \sum_{i=1}^{99} \frac{1}{i+1} \right)$$
glossy valveBOT
Ｈｅｒｅｌｓ
bitter beacon
ok
brave blaze
telescopic sum says that :
for any sequence $(a_k)$, we have :
$$\sum_{k=0}^n (a_{k+1} - a_k) = a_{n+1} - a_0$$
glossy valveBOT
Ｈｅｒｅｌｓ
brave blaze
so thats what we will apply here
$$\sum_{i=1}^{99} \left( \frac{1}{i+2} - \frac{1}{i+1} \right) = \frac{1}{99+2} - \frac{1}{1+1} = \frac{1}{101} - \frac{1}{2} = \frac{-99}{202}$$
glossy valveBOT
Ｈｅｒｅｌｓ
bitter beacon
now we have to calculate 1/2(1-99/202) ?
brave blaze
1/2 (1+99/202)
brave blaze
$$\sum_{i=1}^{99} \frac{1}{i+1} - \sum_{i=1}^{99} \frac{1}{i+2} = - \left( \sum_...
here's why
bitter beacon
ok
brave blaze
and that's it
brave blaze
thats correct
bitter beacon
but my book's answers page says that it is actually 100/101
brave blaze
🤔
bitter beacon
maybe this is incorrect
brave blaze
you add 1/(99+1) - 1/(99+1)
bitter beacon
ok tnx for your time man but i have to go to sleep now . I get the main idea here
.close
fervent raptor
Any intuitive methods of doing this.
full forumBOT
Any intuitive methods of doing this.
fervent raptor
I’ve solved it but want to see different approaches.
hallow cedar
time going up will be half
so you juse use that in distance time formulae
idk what you mean by intuitive but that seems pretty inuitive to me
torn jolt
Any intuitive methods of doing this.
Just solve $\frac{x}{2} + \frac{x}{4} = \frac{9}{2}$
glossy valveBOT
idecanymore
torn jolt
Any intuitive methods of doing this.
don't think you'll find something more intuitive than addition
fervent raptor
**idecanymore**
Can you use the regular s=d/t formula ?
I didn’t know that you can spilt speed up like that
I thought it has to be one average speed
@torn jolt
torn jolt
Can you use the regular s=d/t formula ?
thats what I've done
x is the distance
2 km/h is the speed
time taken to reach the post office will be x/2
time taken to reach back home will be x/4 since speed for getting down is 4km/h
total time is 4.5 hours
so x/2 + x/4 = 4.5
fervent raptor
Got it thanks. But I had no idea you can spilt d/s up like that
can you think of a way of doing with ratios
I got the answers luckily using ratios
Want a proper method of that makes sense
torn jolt
Got it thanks. But I had no idea you can spilt d/s up like that
but i didnt split anything
full forumBOT
@fervent raptor Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
main slate
ive simplified a counting problem to $(d_1) + (d_2) + (d_3) + d_4 = 31$ where $d_1 \geq 0, d_2 \geq 0, 10 \geq d_3 \geq 0, \text{and } d_4 \geq 0$
glossy valveBOT
ChiliLion
main slate
the generating functions for $d_1, d_2, d_4$ would be $\dfrac{1}{1-x}$
glossy valveBOT
ChiliLion
main slate
and then for $d_3$ it would be $\dfrac{1-x^{11}}{1-x}$
glossy valveBOT
ChiliLion
main slate
And then i multiply them together to get $\dfrac{1-x^{11}}{(1-x)^4}$
glossy valveBOT
ChiliLion
main slate
aaaaand now im stuck
partial fraction decomp spits out the ugliest looking thing i've ever seen
glossy valveBOT
ChiliLion
$= -x^7 - 4x^6 - 10x^5 - 20x^4 - 35x^3 - 56x^2 - 84x - 120 - \frac{165}{x-1} - \dfrac{55}{(x-1)^2} - \dfrac{11}{(x-1)^3}$
main slate
<@&286206848099549185>
can i just keep them seperate and not do partial fractions? how would you represent that
original question:
if you have $d1 + d2 + d3 + d4 = 31 \text{where } d_1 \geq 0, d_2 \geq 0, 10 \geq d_3 \geq 0, \text{and } d_4 \geq 0$, how would you find the formula for the coefficients of the corresponding generating function
noble zodiac
**ChiliLion**
```latex
$= -x^7 - 4x^6 - 10x^5 - 20x^4 - 35x^3 - 56x^2 - 84x - 12...
well you know the power series of 1/(x-1)^2 right?
@main slate
main slate
$\sum_i^{\infty}ix^i$?
glossy valveBOT
ChiliLion
main slate
i'm just not sure what to do with all of the x^7 x^6 etc terms
noble zodiac
wait you only want the coefficient of the x^31 term right?
main slate
yeah
noble zodiac
so those don't matter
noble zodiac
wait do you just want to find the coefficient of the x^31 term or do you want a general form for the coefficients?
noble zodiac
oh
ok perhaps my gen func knowledge is very rusty but the coefficient of x^n should be the number of ways to sum to n
main slate
yeah but how do i find that
noble zodiac
**ChiliLion**
```latex
$= -x^7 - 4x^6 - 10x^5 - 20x^4 - 35x^3 - 56x^2 - 84x - 12...
this?
noble zodiac
well -165/(x-1) = sum_i 165 x^i so the contribution to the coefficient of x^31 is 165
main slate
i'm just not sure what to do with all of the x^7 x^6 etc terms
then what do i do with these
main slate
you're probably right, i just don't understand what this is doing enough to get it
kek
.close
dense apex
clarification
full forumBOT
clarification
dense apex
@heavy wolf
heavy wolf
ye
dense apex
after solving i get (u +7)(u - 3)
then after substituting for x
i get 49 + 4 sqrt -7 = 21 and 9 + 4 sqrt 3 = 21
where to go next?
sqrt(-7) is imaginary
so
¯_(ツ)_/¯
heavy wolf
solve for u first. So waht is u equal to in this case
dense apex
Btw
dense apex
solve for u first. So waht is u equal to in this case
U = -7 or u = 3
heavy wolf
Now sub in $\sqrt{x}$
glossy valveBOT
clip
heavy wolf
Nope remember that $\sqrt{x}=u$ so you would have $\sqrt{x}=-7$ and $\sqrt{x}=3$
glossy valveBOT
clip
heavy wolf
So you would just square both equations then
dense apex
wait
OH WAIT
omg
i forgot
we're solving for x
and i tried getting an equivalent equation by LHS = RHS
fuck
i solved that like 8 mins ago
How would i check my answer?
heavy wolf
Plug your values into the original equation
So I believe you should have that x=49 and x=9
dense apex
and i can't solve
dense apex
So I believe you should have that x=49 and x=9
yeah thats what i have
but in the 4 sqrt(x) part
heavy wolf
Put those into the original equation and see if it holds
dense apex
i got stuck
dense apex
Put those into the original equation and see if it holds
No?
heavy wolf
whats the original equation
heavy wolf
Oh brain fart lol. $\sqrt{x}=-7$ cant hold
glossy valveBOT
clip
glossy valveBOT
clip
heavy wolf
Yeah but remember that sqrt(x)=3
proper python
full forumBOT
proper python
I’m currently finding the domain of this function
but I’m having trouble isolating x
would I just divide by e?
oak basin
are you sure e^(1-x^2)=-1 is equivalent to 1-e^(1-x^2)=0?
oak basin
yes
proper python
yes i just noticed lol
oak basin
note that e^x is a one to one function, so if you want this equation to be true, the power must be equal
proper python
oak basin
you can get rid of the minus sign
oak basin
do you agree that in order for e^(1-x^2)=e^0, then 1-x^2=0
proper python
make my left side of eq. exponent =0?
proper python
do you agree that in order for e^(1-x^2)=e^0, then 1-x^2=0
yes
oak basin
then is there any trouble for you to solve this quadratic equation?
full forumBOT
@proper python Has your question been resolved?
vernal ruin
When tossing five, eight sided dice. What is the probability of getting a triple and two singles?
vernal ruin
So my friends and I are working on a practice quesiton but we got different results
I got 0.1025 and he got 0.20508
Which one is the correct way?
The way I solved for my answer was
by doing 8 * 7 * 6 * 1 * 1/8 * 8 * 8 * 8 * 8
pulsar sand
When tossing five, eight sided dice. What is the probability of getting a triple...
What does triples and singles mean?
sand stone
three of the same
pulsar sand
Oh.
vernal ruin
yea^
sand stone
two different
vernal ruin
guessing its like 33314
pulsar sand
Idk but I think its none of your ans is the answer.
vernal ruin
These were the MC given
A. 0.03662
B. 0.10254
C. 0.01025
D. 0.20508
E. 0.15432
deft zodiac
my friend and i are betting for the right ans
LOL
vernal ruin
lmao fr
pulsar sand
How come it isnt (1/64)(7/8)?
vernal ruin
i ran a simulation and the probability is closest to that
is there a link to the stimulator?
sand stone
by doing 8 * 7 * 6 * 1 * 1/8 * 8 * 8 * 8 * 8
did u write this wrong
vernal ruin
no
pulsar sand
Idk 7/512 is the only ans that feels right to me.
sand stone
from collections import Counter
from random import randint
yes = 0
trials = 1000000
for i in range(trials):
nums = [randint(1, 8) for _ in range(5)]
count = Counter(nums)
common = count.most_common()
if len(common) == 3:
if common[0][1] == 3 and common[1][1] == 1 and common[2][1] == 1:
yes += 1
print(yes/trials)
there might be a mistake
vernal ruin
Idk 7/512 is the only ans that feels right to me.
my brotha that answer is not on the choices
oh my lol, we all got different answers
pulsar sand
my brotha that answer is not on the choices
Exactly, From what I see, There are 8/512 chance of getting a triple, Then a 56/64 chance of NOT getting a pair.
Multiply both, 7/512. Of course simplify first.
vernal ruin
wait huh
pulsar sand
1/64 chance to roll a triple no?
YESSS!
balmy peak
what did u get in ur simulation
pulsar sand
Oh yeh, C is the answer.
vernal ruin
=calc 1/64 * 7/8 * 6/8
ye its 0.01025
sand stone
what did u get in ur simulation
close to B
pulsar sand
=calc 1/64 * 7/8 * 6/8
0.01025 dadada.
I completely missed that it is supposed to be 7/8 *6/8.💀