Pr(E&~A&T)= Pr(E&T) - Pr(E&T&A) => Pr(E&~A&T) + Pr(E&T&A) = Pr(E&T)
#help-27
lament turtle
dim halo
ah
so here's where im at
i know how Pr(P)=1-Pr(~P) works
are we going from
Pr(P)=1-Pr(~P)
to
Pr(E&~A&T)= Pr(E&T) - Pr(E&T&A)
?
lament turtle
Not as a formal derivation, but do you see the conceptual link?
Sort of let E & T become your "total" space
lament turtle
Yup, but when it's the total probability space, Pr(E & T) is 1. But to change it back you can imagine adding more to your total probability space
Hm maybe numbers would help more
dim halo
but is there any formal derivation showing Pr(E&~A&T)= Pr(E&T) - Pr(E&T&A)
or does this equation assume a certain probability space
lament turtle
It doesn't assume a probability space, but to prove it you need to step back from probabilities and think about sets instead
Oh wait might actually just be an axiom kek
point 3 here
And we know Pr(E&T) = Pr((E&T&A) or (E&T&~A)) = Pr(E&T&A) + Pr(E&T&~A), noting that E&T&A and E&T&~A are mutually exclusive
dim halo
oh yeah now u connect it all
there's one other thing here
the RHS part. theyre going from
RHS = [Pr(A&T)/Pr(T) x Pr(E&A&T)/Pr(A&T)] + [Pr(~A&T)/Pr(T) x Pr(E&~A&T)/Pr(~A&T)]
to
= [Pr(E&A&T) + Pr(E&~A&T)] / Pr(T)
not following this
(im assuming with the [] brackets, it's not explicitly stated tho)
lament turtle
,, \frac{Pr(A&T)}{Pr(T)} \times \frac{Pr(E&A&T)}{Pr(A&T)} + \frac{Pr(\neg A&T)}{Pr(T)} \times \frac{Pr(E&\neg A&T)}{Pr(\neg A&T)}
Ah heck
See how in the first fraction the Pr(A&T) cancels with the Pr(A&T) in the second fraction?
dim halo
ah i follow
woven radishBOT
ToxicFantasies
lament turtle
come learn latex :)
lament turtle
there's 1 other thign
Yup?
dim halo
Pr(E|T) = Pr(E&T) / Pr(T)
Pr(E&T) = Pr(E&T&A) + Pr(E&T&~A)
= [Pr(E&T&A) + Pr(E&T&~A)] / Pr(T)
= [Pr(A&T)/Pr(T) x Pr(E&A&T)/Pr(A&T)] + [Pr(~A&T)/Pr(T) x Pr(E&~A&T)/Pr(~A&T)]
so: Pr(E|T) = [Pr(A|T) x Pr(E|T&A)] + [Pr(¬A|T) x Pr(E|T&¬A)]
is this all formally correct
lament turtle
Yup. Is there a need to go from LHS to RHS when you already have RHS to LHS though?
dim halo
i didnt get the acrynoyms
lament turtle
RHS = Right hand side
LHS = Left hand side
lament turtle
RHS = Right hand side
LHS = Left hand side
referring to: Pr(E|T) = [Pr(A|T) x Pr(E|T&A)] + [Pr(¬A|T) x Pr(E|T&¬A)]
dim halo
yeah adding Pr(E|T) reminds me what it's equal too
lament turtle
Pr(E|T) = Pr(E&T) / Pr(T)
Pr(E&T) = Pr(E&T&A) + Pr(E&T&~A)
= [Pr(E&T&A) + Pr(E...
I guess the only issue I see potentially would be having Pr(A&T) = 0 or Pr(~A&T) = 0
lament turtle
When either are zero you're dividing by zero in the third line
dim halo
u cant cancel out the zeros?
lament turtle
I guess the only issue I see potentially would be having Pr(A&T) = 0 or Pr(~A&T)...
What you can do though is add in extra cases for this, sort of like what happens with Pr(A|B) = Pr(A&B)/Pr(B) when Pr(B) != 0, and Pr(A|B) = 0 when Pr(B) = 0
dim halo
so what would the cavet be in this case, just Pr(A&T) =! 0 and Pr(~A&T) =! 0?
lament turtle
Yeah, Pr(T) =! 0 as well now that I think about it
dim halo
i wonder if those caveats are guaranteed by the caveats of the equations on pervious lines
lament turtle
Pr(T) =! 0 by the first line I guess
The rest... no idea
You could most likely still show your final equation if either are zero though, just comes to how much is being expected
dim halo
oh it's the division & multiplication properties of equality that guarantee that
when u introduce Pr(A&T) & Pr(~A&T) via dividing both sides or multiplying both sides, it's required they're not 0
in any case, that's all
i appreciate the help & clarification
.close
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restive river
Dividing exponents with no common base:
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Dividing exponents with no common base:
restive river
No idea how to go about doing this. Please help
restive river
You can factorize 18 and 12
like find the common factor?
warped relic
Yes
restive river
then since its the same base id just add 7 + -3
restive river
Wait theres one more thing
warped relic
Oo
warped relic
Wait no
restive river
?
restive river
how would i then
warped relic
12 = 2 • 6
18 = 3 • 6
Since 12 is divided by 18
2 • 6 / 3 • 6
Cross out the 6
And you're left with 2 / 3
warped relic
Yep
It's like this hol on
$$(\frac{12}{18}) =( \frac{2 \cdot 6}{3 \cdot 6} )=( \frac{2}{3} \cdot \frac{6}{6} )=( \frac{2}{3} \cdot 1 )=( \frac{2}{3})$$
restive river
wait why would you do that
i get why 2 would go on the numerator and 3 would go on the denominator
warped relic
Simplifying
restive river
but not why 1 = 2/3
warped relic
Wait hold on
woven radishBOT
VulcanOne
restive river
which is 10
but i see in the final answer y is gone on the bottom
what made it disappear lol?
warped relic
$$\frac{7^3}{7} = 7^{3-1} = 7^2$$
woven radishBOT
VulcanOne
warped relic
Same case here
restive river
like im following everything expect why the y is gone
warped relic
$$\frac{y^7}{y^{-3}} = y^{7 -(-3)} = y^{10}$$
woven radishBOT
VulcanOne
warped relic
That's a rule when you want to simplify exponents for one base
$$\frac{a^n}{a^m} = a^{n-m}$$
woven radishBOT
VulcanOne
warped relic
restive river
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vast bison
I got some feedback on this but is this even accurate
devout snowBOT
I got some feedback on this but is this even accurate
vast bison
aside from 11 not being included does it make sense? or should it be {1,2,3} as the set i re did it and got that
woven radishBOT
Result:
false
yes, i understand im asking about the other stuff in the problem. i did a small mistake on there but im not sure if i missed the whole point
supple knot
yes, i understand im asking about the other stuff in the problem. i did a small ...
You should have divided by 3
You didn't finish all the way solving for x
vast bison
right! i think thats why i got {1,2,3}
supple knot
Oh wait
vast bison
im looking for 3x though?
woven radishBOT
Result:
3.6666666666667
Your set here is for x is correct
vast bison
So the answer was completely incorrect then?
supple knot
But like you said you're looking for {3x...}
supple knot
So the answer was completely incorrect then?
Yes
supple knot
so this makes more sense
Yes, but that's still not the final answer
vast bison
what is the final answer? or what do i do
supple knot
Your answer is in terms of x
You just need to multiply all elements by 3 to get the set in terms of 3x
vast bison
ohhh, so just plug in that set for 3x
supple knot
ohhh, so just plug in that set for 3x
Not sure what you mean
supple knot
3(1), 3(2), 3(3)?
No
I mean yes to first part
No to second
Your answer has 3 elements
vast bison
like {3,6,9}
supple knot
Yes
supple knot
thats my answer for 3x such that 3x is in Natural num
This set is infinite {3,6,9,12,15,...}
vast bison
right cause theres no bounds
supple knot
like {3,6,9}
This is all you should put
vast bison
i just cut the rest out
but okay
how about this one? i feel like i missed something here with the negative side
supple knot
Same mistake
Just multiply your set by 5
Oh and you missed the minus sign
-(a+b) = -a-b
vast bison
but this time im only looking for x? i think
supple knot
but this time im only looking for x? i think
You're asked for 5x
That's the first part
vast bison
okay
supple knot
Everything after the : is conditions that 5x must satisfy
vast bison
so i just need to find an x that is in integers?
supple knot
so i just need to find an x that is in integers?
Plural conditions
vast bison
eh?
so like for example the solution for this is x <2 it seems but im unsure even with the steps if thats correct?
because i got full credit for the question like this
im so confused
supple knot
so like for example the solution for this is x <2 it seems but im unsure even wi...
That's some garbage you sent
supple knot
because i got full credit for the question like this
This is right
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hushed cedar
bit confused on what to do
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bit confused on what to do
quaint hearth
how can you get a parabola with the turning point on the origin
quaint hearth
give me an equation that has the turning point on the origin
better stated like this
hushed cedar
y=3x^2
quaint hearth
a simpler way to think about it is, when you plug in x=0, you get out y=0
hushed cedar
yup
quaint hearth
so try to think how you can get a number that when plugging in 0 for x, you get out y=0
thats how i see it
hushed cedar
so try to think how you can get a number that when plugging in 0 for x, you get ...
so sub in x=0 and y=0 and solve for b?
quaint hearth
bad question ngl
im not sure the correct way to solve this ngl either. intuitively you want it to be close to the origin, and you want to find which point is closest to the origin, which also needs distance
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jaunty mantle
I feel like you can find the derivative then the turning point in terms of b
Then graph the distance between the turning point and origin vs value of b
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maiden igloo
Id like to learn how to calculate the intersection of 2 lines as such
upper schooner
Set them equal to each other...?
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quasi rover
Are 2^aleph_0 and 3^aleph_0 equal?
devout snowBOT
Are 2^aleph_0 and 3^aleph_0 equal?
zenith jacinth
,w 2^{\aleph_0}
woven radishBOT
zenith jacinth
,w aleph zero
woven radishBOT
zenith jacinth
,w 3^{\aleph_0}
uncut crow
it's the number of functions from N to {1,2,3}
woven radishBOT
uncut crow
anyway... yes they are
if you know some things about decimal numbers, a helpful way to look at is that one is the set of infinite sequences of 0s and 1s, the other is the set of infinite sequences of 0s, 1s, and 2s
so they can be thought of as base 2 and base 3 representations of numbers in [0,1]
or... since $3\leq 2^{\aleph_0}$, $$3^{\aleph_0}\leq (2^{\aleph_0})^{\aleph_0} = 2^{\aleph_0\cdot \aleph_0}= 2^{\aleph_0}$$
woven radishBOT
💜𝓁𝒶𝓎𝓁𝒶💜
uncut crow
assuming some cardinal arithmetic stuff ^
inequality the other way is a lot easier
by that i mean showing $2^{\aleph_0}\leq 3^{\aleph_0}$ is a lot easier
woven radishBOT
💜𝓁𝒶𝓎𝓁𝒶💜
true granite
How to perform questions based on inclusion and exclusion principle like what's the method to perform it for example there is a question - there are 20 diff book , 5 students each students get at least 1 book
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How to perform questions based on inclusion and exclusion principle like what's ...
@true granite Has your question been resolved?
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@true granite Has your question been resolved?
topaz axle
suppose we did (5C1) * 1^20, we would count ways where 1 student gets 20 books
then we do (5C2) * 2^20, some of it would account for the outcomes where 2 students have all the books, and the rest would look like 1 student gets 20, repeatedly
specifically 4 times for each student
1 × e2 + 4 × e1
then we would get 1 × e3 + 3 × e2 + 6 × e1 if we do (5C3) * 3^20
then 1×e4 + 2×e3 + 3×e2 + 4×e1
finally 1×e5 + 1×e4 + 1×e3 + 1×e2 + 1×e1 when we do (5C5) * 5^20
and for some reason if you add and subtract all of this
1×e5 + 1×e4 + 1×e3 + 1×e2 + 1×e1 −
(1×e4 + 2×e3 + 3×e2 + 4×e1) +
(1×e3 + 3×e2 + 6×e1) −
(1×e2 + 4×e1) +
1×e1
you end up with 1 × e5 which is the objective, all ways where exactly 5 students get some amount of books
it's not intuitive
true granite
suppose we did (5C1) * 1^20, we would count ways where 1 student gets 20 books
thank you :))
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finite inlet
\begin{align*}
\sum_{n=0}^\infty \left(\dfrac{1}{3}\right)^{n+3}
&= \sum_{n=0}^\infty \left(\dfrac{1}{3}\right)^{n} \cdot \left(\dfrac{1}{3}\right)^{3}\
&=
\end{align*}
woven radishBOT
madmike
finite inlet
I can't use the geometric series here I don't think?
or can I just pull out the (1/3)^3 out of the sum?
multiplying each element of the sum with a constant should be equivalent to multiplying the result of the sum with the constant, right?
yeah
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lone ravine
multiplying each element of the sum with a constant should be equivalent to mult...
Yes
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Available help channel!
finite inlet
$\left(\dfrac{1}{3}\right)^{3} \cdot \sum_{n=0}^\infty \left(\dfrac{1}{3}\right)^{n}
= \left(\dfrac{1}{3}\right)^{3} \cdot \dfrac{3}{4}$
devout snowBOT
$\left(\dfrac{1}{3}\right)^{3} \cdot \sum_{n=0}^\infty \left(\dfrac{1}{3}\right)...
woven radishBOT
madmike
finite inlet
This seems to be wrong, any idea why?
I got the 3/4 with the geometric series like this
woven radishBOT
madmike
restive river
$S_{\infty} = \frac{u_1}{1-r}$ where $r = \frac{1}{3}$ and $u_1 = 1$
woven radishBOT
45
restive river
so yes it's wrong
restive river
finite inlet
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maiden pulsar
what does an integration sign, with the lower limit as l and no upper limit imply?
devout snowBOT
what does an integration sign, with the lower limit as *l* and no upper limit im...
long kettle
Send a picture
maiden pulsar
Send a picture
Oops my bad
maiden pulsar
surface integral or something
What is surface integral?
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maiden pulsar
<@&286206848099549185>
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stone stump
yes
but it's not like this is a super precise definition anyway
maybe they are just talking about functions defined on an interval?
sonic smelt
fringe olive
how to divide guys
devout snowBOT
how to divide guys
long kettle
It's generally illegal to divide people
fringe olive
oh
torn wave
some goofy people will pay you to send a vid of u doing it on an obscure reddit server tho
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restive river
It's generally illegal to divide people
unless 👀
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halcyon plover
why did they divide it, instead of cancelling both sides ?
how do i know if you will divide it or cancel both sides?
devout snowBOT
why did they divide it, instead of cancelling both sides ?
how do i know if you ...
zenith jacinth
wdym cancelling both sides
halcyon plover
it'll be x = 8 instead of x = 3
zenith jacinth
now 4 x 8 = 12
pog
4x = 12
which means 4 multiplied by some numbers we dont know yet, give 12 and we need to find this number
and since we want x alone equal to something
we need to get rid of that 4 on the front
we have an equality, so they are subjects to the same operation
if a = b, then ac=bc
so here we divide by 4 on both sides
wide leaf
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wide leaf
I cant figure the formula
What i have so far is 14000(1+(0.062/n))^nt
<@&286206848099549185>
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wide leaf
<@&286206848099549185>
wide leaf
Alright
restive river
well first of all is it compund or simple interest
wide leaf
What i have so far is 14000(1+(0.062/n))^nt
restive river
What i have so far is 14000(1+(0.062/n))^nt
let me work it out and get back to u
wide leaf
Alright
restive river
bc i got the same thing
wide leaf
let me work it out and get back to u
I figured out the answer
What i have 14000(1+(0.062/12))^12t
If its compounded monthly then the n is 12
<@&286206848099549185>
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fluid solar
how do you solve this?
fluid solar
<@&286206848099549185>
brisk totem
draw a diagram
in this case you might want more diagrams
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restive river
Let g(x) = 16 - 8x and h(x) = 1/4x - 6. Find g(h(x)). Simplify the expression
flat marlin
So the g(h(x)) is the g of h(x).
We know that h(x) = 1/4x - 6, so all we need to do is evaluate $$g(\frac{1}{4}x-6)=$
@restive river does this make more sense?
woven radishBOT
Derpy
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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restive river
<@456226577798135808> does this make more sense?
not really
im still kinda confused
flat marlin
So when you put an x value something like g(x), it simply just means that you’re using that x value. So the g(x)=30x-5 as a function, we want to find when x=1, so g(1)=30(1)-5, that equals 25
So basically what I told you to evaluate is $g(\frac{1}{4}x-6)=16 - 8(\frac{1}{4}x-6)$
woven radishBOT
Derpy
restive river
oh
flat marlin
So the concept is essentially working your way inwards from the x. if it says the g(h(f(x))) you would find the f(x), plug that into the h(x), then plug that into the g(x).
flat marlin
No problem!
restive river
hold on
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muted reef
i have no idea where to start or how to do the question
devout snowBOT
i have no idea where to start or how to do the question
muted reef
oh wait it should have two parts to it
devout snowBOT
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muted reef
<@&286206848099549185>
lusty sapphire
what are the two parts?
muted reef
literally the top and bottom
I didn't realise I chopped off the question number and part
brisk totem
i guess it's manipulating generating functions
lusty sapphire
Oh so, find the sum of both of those series? It's two separate problems
muted reef
Oh so, find the sum of both of those series? It's two separate problems
it's two separate problems
lusty sapphire
Well if it were me, I don't remember all my taylor expansions. So I would look up the standard ones and see which ones the series look close to.
It may be something like f(2x) or f(x^2) or something, so I'd try to keep that in mind while looking
muted reef
hmmm
lusty sapphire
edit: I'd look up the standard ones like trig functions, hyperbolic, exponents, etc.
Just an approach, can't guarantee it'll work
muted reef
I feel like I need a more solid approach i'm afraid
dim grove
For the first one. Try taking derivative of the power series for 1/(1-x)
brisk totem
oh right this is formal power series
then starting from that you can solve both problems
lusty sapphire
Oh that's cool stuff! Better than my "stab in the dark" approach
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muted reef
wym?
woven radishBOT
half minnow
but where does c feature?
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@muted reef Has your question been resolved?
dim grove
On the second problem, I have found something that looks very similar.
You can start with this equality and manipulate the RHS to get the series in the question, then see what's on the LHS.
I don't think c is necessary.
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tired junco
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tired junco
Not quite sure how to approach this problem
wooden wraith
You can just let $ \vec x = \begin{bmatrix} x_1 \ x_2 \ x_3 \end{bmatrix}$. Then compute $\vec v \times \vec x$ and $[L]\vec x$ and show that they give the same result
woven radishBOT
tatpoj
tired junco
but can't you multiply a 3x1 vector with a 3x1 vector
wooden wraith
Interpret them as vectors, not matrices
You can take the cross product of two 3-dimensional vectors
wooden wraith
Yes
tired junco
Oh i see
and if I multiply that matrix by x, I get the same as the cross product of v and x
wooden wraith
You have to show that
$$\begin{bmatrix}
0 & 1 & 0 \
-1 & 0 & -1 \
0 & 1 & 0 \end{bmatrix}
\begin{bmatrix} x_1 \ x_2 \ x_3 \end{bmatrix} =
\begin{bmatrix} 1 \ 0 \ -1 \end{bmatrix} \times
\begin{bmatrix} x_1 \ x_2 \ x_3 \end{bmatrix}$$
woven radishBOT
tatpoj
tired junco
wait
for the second row
<-1, 0, -1> * <x1, x2, x3>
that makes -x1 -x3
but the cross product is x1 + x3
wooden wraith
um wait let me see, I didn't actually do the computation, I just trusted your prompt that it was true lol
No, they should both be -x1-x3
The second entry from the cross product is (-1)(x1) - (1)(x3)
tired junco
hmm
wooden wraith
Sorry got the terms backwards, I fixed it
tired junco
I'm getting 1(x3)-(-1)(x1)
wooden wraith
but still it's true
tired junco
wooden wraith
Ah, you're calculating it by determinants?
You negate the second one, then, right?
check your formula, the middle one is the opposite
tired junco
of what?
wooden wraith
Can you show me the formula you're using for the cross product?
wooden wraith
dat negative sign
wooden wraith
Looks good
wooden wraith
hm, sorry, not sure I'm gonna be able to help with this one
I might be able to figure it out but I'm not confident enough to help
There are much smarter people here than me though
tired junco
I'm wondering if this could be the first step
I've done a similarish question
<@&286206848099549185>
hazy quail
wtf are you using e and pi for vectors
wooden wraith
wtf are you using e and pi for vectors
e_1 is the first column of the 3x3 identity matrix
1
0
0
i assume
tired junco
heres the similarish question
context
but I can't see how they're related
so back to square one
no clue how to approach my question
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sage mural
how do i find the lower and upper bounds🙏
devout snowBOT
how do i find the lower and upper bounds🙏
uncut crow
how do i find the lower and upper bounds🙏
of what haha
sage mural
Honestly. I don’t know I am so desperate and I have a math final I cannot do this anymore
I don’t even knkw what Im doing in class.
but umm
uncut crow
:c
sleek estuary
I don’t even knkw what Im doing in class.
me too 😦
sage mural
on the instructions it says “use your highest residual to write the equation of your upper and lower boundary for this scatter plot” (i’m pretty sure the highest residual would be 1, -22.186) so i did 89.83-22.18 and got liek 97 or something. the answer key says it’s wrong though. THAT WAS AN AWFUL EXPLANATION
sleek estuary
what is that, is that algebra
sage mural
i think so? idk it’s called integrated math 1
worn flax
devout snowBOT
worn flax
H is not a subgroup of G right?
Because it is not closed under multiplication, where (log a)(log b) cannot be represented in a form log(Q)
hazy quail
Because it is not closed under multiplication, where (log a)(log b) cannot be re...
why does it need to be closed under multiplication?
worn flax
oh
i got my definitions wrong
or rather
I saw G as <R, x> which is different from <R, +>
hazy quail
yea the operation is addition
worn flax
and log a + log b can always be represented as log ab, where ab is always an element of Q since the product of two rationals is rational
so it is closed under addition
then we have to check for closure under negatives
hazy quail
that is correct im just thinking about identity and inverse
hazy quail
then we have to check for closure under negatives
a>0 bro
log a is always positive anyways
violet wind
log a isn't always positive
hazy quail
in this case it is
violet wind
,w log(0.5)
hazy quail
right?
woven radishBOT
violet wind
lol
hazy quail
wait non astral you forgot too
ok whatever
um
ok identity element is log(1)
loga+log1=loga for all a
and if we have log a choose log 1/a so that log a + log 1/a = log 1
and we're done its a group
subgroup to be exact
worn flax
yes
spark pewter
violet wind
it be like that sometimes
devout snowBOT
violet wind
np
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grave void
How can one show that the Barnes G-function is an extension of the superfactorials to the complex numbers?
devout snowBOT
How can one show that the Barnes G-function is an extension of the superfactoria...
grave void
and does it involve first showing that the K function is a generalization of the hyperfactorial to the complex numbers?
cause wikipedia only gives some 20 page reference from 1860 in german
maybe i should ask in advanced analysis?
stone stump
probably
wikipedia also references this
(in fact I don't see any source from 1860)
grave void
the 1860 one is one the K function page
and this one looks promising imma look through it briefly thank you
right so
stone stump
I don't see a source from 1860 in the article of the k function either
grave void
oh you're right it was on the hyperfactorial page, reference 3
Kinkelin, H. (1860), "Ueber eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechung"
this is the title
right so it seems like this is unintelligible to me if studied briefly imma need to take some time to digest what barnes wrote
thank you again ill study this and see if i can understand how it's shown
.clsoe
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still summit
Guys question how do you do this :'D
devout snowBOT
Guys question how do you do this :'D
open laurel
You got area of what
still summit
I got the area of the triangle I think
I did 60 + 60 = 120
and then I misused 120 to 180
and I got 60
so all three angles are 60
so that means all sides ar 24
junior sun
fiery seal
"You want to cut out the largest possible rectangle from the leftover piece shown. How must the lateral positions be selected?"
devout snowBOT
"You want to cut out the largest possible rectangle from the leftover piece show...
regal torrent
U know derivatives?
fiery seal
No
hushed wraith
Complete the rectangle and u can find a triangle
Ucan call one of these lengths x, and then find the other in terms of x using similrr triangles
Can u try that
fiery seal
Dont really know what U mean
hushed wraith
Wait
fiery seal
Idk If that Info helps but my teacher Said we have to use A=x*y and y=mx+t and find out m
hushed wraith
try extending that line labeled x until it meets BG
and extend HE until it meets BF
crimson tiger
long kettle
Don't give answers
fiery seal
and extend HE until it meets BF
OK and now?
hushed wraith
do u see some similar triangles
fiery seal
Yeah
fiery seal
hushed wraith
no like can u also mark those places where HE meets BF and the other line meets BG?
and send
fiery seal
Like that?
hushed wraith
yeeah okay now what is EJ equal to
fiery seal
EJ=EI
hushed wraith
no...
hushed wraith
yeah what is IB again equal to in terms of x
what is EJ equal to in terms of x basically
what is the length of the entire line that goes from one end of the page to the other
fiery seal
90 cm
hushed wraith
yeah and the beginning of this line is x cm
fiery seal
Yes
hushed wraith
then the remaining part EJ is how long
fiery seal
90-x
fiery seal
Yeah EGJ and EFI
hushed wraith
can u use their similarity to find the length of IE in terms of x?
i guess it might be easier if u can use the triangles BFG and EFI instead idk
fiery seal
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frosty mesa
PLEASE HELP I ONLY HAVE 1 MINUTE
devout snowBOT
PLEASE HELP I ONLY HAVE 1 MINUTE
frosty mesa
craggy dagger
we aren't giving answers away directly
pastel belfry
Loool
frosty mesa
please help me understand then
pastel belfry
@frosty mesa tell us what u have done
pastel belfry
please help me understand then
If harley has 6 pints
Then rosie has 11/3 of them ie 22
And for b part just subtract thr number of pints
somber shore
hi
somber shore
,tex $f(x-1)+2f(1-x) = 3x \newline f(1)=?$
woven radishBOT
AbJoe
somber shore
I solved this question but I'm not sure about the answer
,tex $f(x) = a{n}x^{n} + a{n-1}x^{n-1}+\dotsb + a{1}x+a{0} \newline f(t)+2f(-t)=3t+3 \newline (a{n}t^{n} - 2a{n}t^{n-1}) +(a{n-1}t^{n-1}-2a{n-1}t^{n-1})+ \dotsb + a{1}t - 2a{1}t + 3a{0} = 3t + 3 \newline \rightarrow a{n}=a{n-1}=\dotsb=a{2} = 0, a_{1} = -3, a_{0}=1$
woven radishBOT
AbJoe
somber shore
is this correct? ( f(1) = -2 )
long kettle
Yes
Though there's an easier way
Plugging in x = 0 and x = 2, you get a system of equations
magic agate
Ok so what do I look at to determine wether they are Pharrell perpendicular or neother
devout snowBOT
Ok so what do I look at to determine wether they are Pharrell perpendicular or n...
hushed wraith
two lines are parallel if they have the same gradient
two lines are perpendicular if the product of their gradients = -1
craggy dagger
- some caveats for vertical lines
hushed wraith
Ok so what do I look at to determine wether they are Pharrell perpendicular or n...
whats with line 3
magic agate
Idk
quaint citrus
Maybe it’s y = -1
magic agate
Wait so the gradient is the slope right
hushed wraith
Wait so the gradient is the slope right
yes
sometimes u cant find the slope...in times like that the line is vertical
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@magic agate Has your question been resolved?
restive river
I'm gonna start again
restive pulsar
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restive pulsar
Hey, looking for some reassurance
this would be 4(3) - (-5/10), yeah?
Whatever that number comes out to be
stone stump
yes
restive pulsar
Thanks!
round canyon
How do i fdind the gradient?
devout snowBOT
How do i fdind the gradient?
round canyon
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high chasm
Why do you write the answer in the start?
?
polar bolt
Why is that not the last thing on your working?
polar bolt
What is the answer to the original question?
high chasm
so i restrict the domain first
polar bolt
I mean just a weird order
high chasm
how
polar bolt
Then say we restrict it to [0,inf) and show it works
Now its unclear what the answer even is
high chasm
normally when u find the inverse u restrict the domain
and then find the inverse
and thats what ive done
high chasm
well is everything correct there anyway
polar bolt
Sure but you should make it clear what your answer is
high chasm
Sure but you should make it clear what your answer is
0 inf
polar bolt
Either you find inverse then show [0,inf) works
Or you say [0,inf) works
And show it
high chasm
^
polar bolt
Yes
languid sierra
hi
knotty bolt
can someone help me plz
just ask the question
languid sierra
languid sierra
@knotty bolt
knotty bolt
what is the question here
wheat pebble
what is the question here
basically she needs to find a set boundry for x
which is very weird question
languid sierra
yes thank u
knotty bolt
I can see that
languid sierra
idk how to do it
languid sierra
then how do i solve
devout snowBOT
@languid sierra Has your question been resolved?
vernal monolith
i would try law of sine but dunno if it works (since it requires a calculator)
since they share 2 equal sides
you can say for sure that x is less greater than 10 (11x-33 <77 => x<10) but dunno if its the lowest upper bound
devout snowBOT
@languid sierra Has your question been resolved?
hollow hollow
calc question
devout snowBOT
calc question
hollow hollow
i know i have to find critical numbers and interval tewst to see whats a max or min, but my critical numbers come out to 0
so idk if its increasing or decreasing
im assuming i did something wrong
torn vessel
there should be two other critical values
hollow hollow
lemme send my work
i got 3 CN's
0, and plus or minus root2
if i plug in the roots i get a zero
torn vessel
right.... you should be plugging in values around the roots
hollow hollow
cuz they DNE?
torn vessel
the roots give you intervals of increasing/decreasing, you plug in points in those intervals to determine where the derivative is positive/negative which gives you the function is increasing/decreasing on that interval
hollow hollow
no i know that
but if i
OHHH SHIT\
your right i was just brainfarting
thanks man
clever silo
devout snowBOT
devout snowBOT
@clever silo Has your question been resolved?
supple knot
,calc 1075/(1.08)^15
woven radishBOT
Result:
338.88483283833
my guess is 957.2 is the sum of column (3)
clever silo
@supple knot Is there another way of calculating the 338.88 instead of using the algebraic way
Also, I did the sum of column 3 and I got $618.31 and not $957.20
supple knot
<@261933205387477002> Is there another way of calculating the 338.88 instead of ...
no
clever silo
My friend said the other way is: the 338.88 is because its the last payment - so you add the 75 + the principle (1000) = 1075
But I don’t understand her explanation
supple knot
My friend said the other way is: the 338.88 is because its the last payment - so...
yea your friend has information i don't
supple knot
But I don’t understand her explanation
then just ask her
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@clever silo Has your question been resolved?
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shy willow
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Available help channel!
meager kraken
For this problem, would I add the total of fruits and use the combinations to find the probability of having each fruit? or am i doing this wrong
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For this problem, would I add the total of fruits and use the combinations to fi...
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patent marsh
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restive river
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restive river
Can someone explain my teacher’s notes?
Just looking for how he went from the first line to the second line
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
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@restive river Has your question been resolved?
hazy quail
@forest olive
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<@1023865295112245288>
hazy quail
send the integral here
forest olive
hazy quail
send working
forest olive
Ok
I can do it algebraically
This was the original question
And I can't do the first integral geometrically
forest olive
In the working, they did the area of the sector minus the area of the triangle
hazy quail
ignore that
hazy quail
ignore that its wrong
forest olive
Oh, ik what they've done, nvm
hazy quail
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restive river
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restive river
was evaluating under the curve with integration and got -32/3
i know its 32/3
did I do something wrong
worn flax
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worn flax
I think I get this conceptually but have no clue how to put it in jargon. My current idea is that we check the base case n=2, where clearly $a_1 * (a_2 * a_3)$ is equivalent to $(a_1 * a_2) *a_3$ since by definition operations in groups are associative
woven radishBOT
astral
worn flax
So we can (somehow) use this to show that every a series of n terms with parantheses around two elements in the front can be written as a series of n terms with parantheses around the two elements at the back
and idk we can apply this principle to n terms with multiple sets of parentheses by doing this to each group of elements in each set of parentheses and then combine them tgt
idk how to explain it
:circlethink:
torn vessel
Like it says, use induction.
You just explained your base case.
Now assume it's true for k < n elements, and show it's true for n elements
worn flax
So the statement for n-1 elements would look like "Suppose $a_1 * a_2 * a_3 * ... a_(n-1) = (((... a_1 * a_2) * a_3) ... * a_(n-1)$
woven radishBOT
astral
worn flax
i chan show the n case for that
torn vessel
sure
worn flax
But how do I deal with say, things like $(a_1 * a_2) * (a_3 * a_4)$
woven radishBOT
astral
torn vessel
(a1 * a2) = a for some other a in the group,
so that's equal to a * (a3 * a4) which is n-1 elements. So by induction it works.
arctic field
i think the intention is that any bracketing results in the right-associative bracketing
worn flax
(a1 * a2) = a for some other a in the group,
Oh, by definition of how a group is self-contained?
worn flax
i think the intention is that any bracketing results in the right-associative br...
how would you express this in formal proof-language
arctic field
well its just like
woven radishBOT
arctic field
and what you have to show is like
for an arbitrary bracketing of n+1 terms, you can rearrange the brackets into the right-associative one
torn vessel
pick any placement of parenthesis, then you have the product of k < n elements (by closure of a group), so by induciton.....
woven radishBOT
woven radishBOT
worn flax
can you just explain the first step please, i dont see how it follows from the assumption
I get the rest
arctic field
every step is using associativity
woven radishBOT
arctic field
the main idea is
arctic field
with something like this
you can rearrange both large brackets on the left into the right associative bracketing
by induction assumption
and then using just the 3 term associativity
you can progressively "eat" terms from the right bracket into the left bracket
worn flax
👍
i think i get it
gonna try and express it fomally later, which i think i should be able to
thanks a bunch, appreciate it
.close
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Available help channel!
tawny coral
yow same question again but different answers
devout snowBOT
yow same question again but different answers
tawny coral
$F(x)=\displaystyle\int_{1-2x}^1\frac{t^2+1}{\sin^-1(t)\pi^t},dt$ at x=0
woven radishBOT
wowowin123
tawny coral
this is what i did
$y_0 = F(0)=\displaystyle\int_{1}^1\frac{t^2+1}{\sin^-1(t)\pi^t},dt=0$
woven radishBOT
wowowin123
tawny coral
$F'(x)=\displaystyle -\int_{1}^{1-2x}\frac{t^2+1}{\sin^-1(t)\pi^t},dt$
$F'(x)=-\frac{(1-2x)^2+1}{\sin^{-1}(1-2x)+\pi^{1-2x}}*[-2]$
woven radishBOT
wowowin123
tawny coral
thus
woven radishBOT
wowowin123
tawny coral
the question is from a text book but the answers are not given only for odd numbers lol
tawny coral
**wowowin123**
equation of the tangent line to the graph of this func at x=0
woven radishBOT
wowowin123
tawny coral
$F'(0)=-\frac{2}{\frac{\pi}{2}+\pi}*[-2] \rightarrow \boxed{y=\frac{8}{3\pi}(x)}$
woven radishBOT
wowowin123
devout snowBOT
@tawny coral Has your question been resolved?
tawny coral
<@&286206848099549185>
devout snowBOT
@tawny coral Has your question been resolved?
hushed wraith
What is ur problem exactly?
devout snowBOT
@tawny coral Has your question been resolved?
remote gust
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thin epoch
the x-intercept is the point at which y = 0, so solve for x
the y-intercept is the point at which x=0, so solve for y
then pick points for x between those points and solve for y in those so you can graph them
remote gust
you see that's what I was thinking but I wasn't quite sure