Oh yes
#help-27
lucid nymph
placid rover
$$ab = ba$$
$\implies$ (right multiplication)
$$(ab)(a^{-1}b^{-1}) = (ba)(a^{-1}b^{-1})$$
$\implies$ (associativity)
$$(ab)(a^{-1}b^{-1}) = b(a(a^{-1}b^{-1}))$$
$\implies$ (associativity)
$$(ab)(a^{-1}b^{-1}) = b((aa^{-1})b^{-1})$$
$\implies$ (inverse)
$$(ab)(a^{-1}b^{-1}) = b(eb^{-1})$$
$\implies$ (identity)
$$(ab)(a^{-1}b^{-1}) = bb^{-1}$$
$\implies$ (inverse)
$$aba^{-1}b^{-1} = e$$
woven radishBOT
Shuri2060
placid rover
And I can use iff sign on all lines. Then I don't need forwards and backwards.
lucid nymph
This makes much more sense. I wasn't sure if I could start it off with both a^-1b^-1, I thought we'd have to show each one by one somehow
I got the other direction
Thank you very much for the help
.close
drifting spade
how to calculate 5 - x2 = 10? i know the answer is -2.5 but i when i use the way i have learned, i got the wrong answer.
placid rover
how to calculate `5 - x2 = 10`? i know the answer is `-2.5` but i when i use th...
show us the way you learned
also what is x2
$x^2$
???
woven radishBOT
Shuri2060
drifting spade
x2 is x * 2
main gull
What was the process you did?
placid rover
This process doesn't make sense to me
What is this +5 +5
Already, on the 3rd line we have problems
restive river
```
5 - x2 = 10
+5 +5
x2 = 15
15 / 2 = 7.5
x = 7.5
```
you were supossed to subtract 5 from both sides
not add
drifting spade
undoing the 5 -
placid rover
🚫
restive river
bc if you subtract 5 on the right the 5 is gone
placid rover
$$5 - 2x = 5 + (-2)x$$
woven radishBOT
Shuri2060
placid rover
You need to realise what these things actually mean
drifting spade
oh
placid rover
'5-'
drifting spade
thanks
drifting spade
.close
hard pike
so i worked out the equation of ad
y = 5/2x + 2
and equation of ab
y = 2/5 x + 2
how would i now work out the area of the rectangle do i cut it into 2 triangles ?
supple knot
so i worked out the equation of ad
y = 5/2x + 2
and equation of ab
y = 2/5 x +...
Do you know how to find the coordinates of A, B, D?
You can use that to find the side lengths of the rectangle and then multiply the side lengths to get area
hard pike
Do you know how to find the coordinates of A, B, D?
yea so co ordinnates
A = ( 0 , 2 )
B = not sure
D = ( not sure , 0 )
how will i work out b and the rest of d?
supple knot
B has coordinates where y=0. Can you find x?
supple knot
Coordinates are usually written (x, y)
hard pike
Coordinates are usually written (x, y)
thank you for correcting my error there
so i've gotten 2 equations for lines ad , ab
how will i use those lines to find x co ordinate
supple knot
How did you find A?
B lies on the line connecting A to B
So you use that equation to find coordinates for B
hard pike
How did you find A?
both lines had an y intercept of 2
hard pike
So you use that equation to find coordinates for B
alright so i would use y = 5/2x + 2 to work out b?
im sorry if im braindead @supple knot
hard pike
alright so will i have to put 2 into the equation y = 5/2x + 2
so it will be
2 = 5/2x + 2 or
supple knot
alright so will i have to put 2 into the equation y = 5/2x + 2
It's easier to plug y=0 into the original equation and solve for x instead of yours
supple knot
so it will be ( x , 0 )
This is still wrong after your edit
hard pike
It's easier to plug y=0 into the original equation and solve for x instead of yo...
alright so i did
2y - 5x = 4 ( original eq ) ( to solve D )
2(0) - 5x = 4
i worked it out and got -1.5
for b same thing
5y + 2x = 10
5(0) + 2x = 10
worked out and got 5
/
so the co ordinates for d
( -1.25 , 0 )
b
( 5 , 0)
supple knot
Can you find the side lengths of the rectangle
hard pike
yes so i go from d to b
supple knot
AD and AB
supple knot
yes so i go from d to b
That isn't the side length, that's the diagonal
supple knot
ad length is 2
ab length is 3.75
How did you get these numbers
hard pike
How did you get these numbers
so i took away d from b
d was 1.25
b was 5
to work out the length
supple knot
Side length of a rectangle is the distance from point A to point B and A to D. You circled the diagonal of the rectangle
supple knot
How did you get 2?
hard pike
2 is the length from d to a
supple knot
Nah. You need to use Pythagorean theorem
hard pike
Nah. You need to use Pythagorean theorem
supple knot
Still not quite right. The length of AD is the hypotenuse of a right triangle. What are the side lengths of that right triangle?
supple knot
That picture doesn't show AD as a hypotenuse
hard pike
hypontenuse is the longest side tho right?
supple knot
Okay let's go back to the beginning. What is the length of OA and what is the length of OD
supple knot
OA
hard pike
2
supple knot
Now draw the triangle OAD
AD is one of the side lengths of the rectangle
It is also the hypotenuse of triangle OAD
hard pike
ohhh i see where your from from now
ok so to work out the hyp
i do this
so ad = 2.4
and u do 2.4 x 5 = 12?
which is the final answer
hard pike
AD is one of the side lengths of the rectangle
i hope this is the final answer 🤞
supple knot
Did you get length AB?
supple knot
ad length is 2
ab length is 3.75
Because this was wrong
supple knot
Are you rounding?
supple knot
I would double check all your work and don't round until the very last answer
Check length OA, check coordinates for B and D, check lengths OB and OD
hard pike
alright
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analog raft
devout snowBOT
analog raft
Can someone please explain how I can do this
main gull
Do you know what a rational number is?
main gull
But I'm asking if you know
analog raft
Yeah I do
main gull
Not by pasting a graphic
copper mango
so then what's the problem?
just find the rational numbers in that list which are the same number
analog raft
just find the rational numbers in that list which are the same number
A = 0.75
B = -0.75
C = 1.3333
D = -0.75
E = -0.75
So B D and E
copper mango
sure, though I asked for the numbers
not decimal approximations
-4/3 is not 1.3333
analog raft
O
analog raft
-4/3 is *not* 1.3333
so its -3/4, 3/-4 and - 3/4
copper mango
yes.
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rugged kraken
Hey guys, i have a function like this: f(x) = max { cos(x/2), 0 }
rugged kraken
Can i also write it as this
f(x) = { cos(x/2) when x is between (3pi/4 and pi/4) and otherwise its 0 }
Also, this should be an even function, right? Since f(-x) = f(x).
austere dust
Hey guys, i have a function like this: f(x) = max { cos(x/2), 0 }
This does not specify for what domain
austere dust
f(x) = { cos(x/2) when x is between (3pi/4 and pi/4) and otherwise its 0 }
While this does
So they are different?
rugged kraken
Hey guys, i have a function like this: f(x) = max { cos(x/2), 0 }
I was also given that f: R -> R alongside this
I think i understand your point Shuri.
placid rover
yeah I cant get the right x, but yes.
rugged kraken
is it something like i should add + 2kpi?
placid rover
f(x) = { cos(x/2) when x is between (3pi/4 and pi/4) and otherwise its 0 }
this won't be right even with 2pi
rugged kraken
Really? My logic was that i first looked where cosx > 0. If i m not wrong that is (3pi/2, pi/2). Then since i need cos(x/2) i just divided that by 2
But it seems i was wrong about that.
Especially since i don't know the domain?
placid rover
domain is
placid rover
I was also given that f: R -> R alongside this
R
rugged kraken
f(x) = { cos(x/2) when x is between (3pi/4 and pi/4) and otherwise its 0 }
I need it in a format like that
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placid rover
Draw the graph of cos(x/2)
fiery kindle
can anyone help?
devout snowBOT
can anyone help?
fiery kindle
law of indices
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rapid nest
I have found the points of A,B,C,D and E. The midpoint L is given and I found the slope of CE to be -3. How do you find the equations of the perpendiculars LO and MO? I haven't done geometry in years and just need a little guidance for this problem. And how do I use the perpendiculars to find the point of intersection which I am guessing is O?
devout snowBOT
I have found the points of A,B,C,D and E. The midpoint L is given and I found th...
@rapid nest Has your question been resolved?
restive river
Hmm
Do u know formula for midpoint
Of two points
Use that to find the coordinates of E
@rapid nest
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@rapid nest Has your question been resolved?
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@rapid nest Has your question been resolved?
rapid nest
Use that to find the coordinates of E
i already know what E is
restive river
Ok
rapid nest
please re read my query
restive river
Wut
rapid nest
i just looked at the diagram. see i'm very bad at this. if you could just tell me what i need to do, then i'll try making sense of it myself. instead of guessing answers to your small questions. i really need to understand this. my professor asks me a million questions instead of explaining exactly what i need to do
please dont do the same to me. i kinda just need it laid out to me to understand. not completely but atleast some of it
restive river
Fine fine
rapid nest
i'm willing to understand and not just jot it down
rapid nest
thank you, it really means a lot to me
slender mirage
umm
restive river
@slender mirage are u gonn explain
slender mirage
nope I'm just lurking :o
restive river
Alright first we need to show ABDE is a rectangle
For that we need coordinates of E
rapid nest
uh hm
restive river
We find that using the midpoint formula
Wait
It says find coordinates of midpoint L
rapid nest
which two coordinates do we use to find E
restive river
But they are already given
restive river
Confusion 100
slender mirage
Honestly
"Find the coordinates of the midpoint L" is probably bugged in the question lol
restive river
Yeh
rapid nest
my college is really good at making us suffer with wrong questions so not surprised
slender mirage
There's also, "draw lines OA, OE, OE, OC"
Anyways
I read your problem
The idea here is to use the fact that OM(!?) is perpendicular to AB and OL is perpendicular to CE
also notice that BM is perpendicular to BD
rapid nest
so how do i use this information to find the perpendicular of the lines
slender mirage
hmm
rapid nest
um
slender mirage
I might've over did it lol, is why I deleted those
you said you need to find equations for LO and MO right?
rapid nest
I might've over did it lol, is why I deleted those
it's okay, i've been through so many confusing questions at this point, i find it normal
rapid nest
you said you need to find equations for LO and MO right?
yes
slender mirage
what's the slope for CL?
slender mirage
Umm,
so there's this one little exercise you do while playing with straight lines
rapid nest
please dont make it hard on me with guessing questions
slender mirage
where you find the product of slopes of two perpendicular lines
rapid nest
just tell me
slender mirage
and they always end up being -1
slender mirage
so since product of slopes of mutually perpendicular lines = -1, product of slopes of LO and LC should be -1
hence slope of LO = -1/ ( -1/13) = 13
and you have the point L, so use the point-slope format to write the equation of the line
rapid nest
Point slope format? Y-y1 = m(x-x1)?
slender mirage
Yes
rapid nest
okay, one sec
slender mirage
similarly for MO
as MO is perpendicular to MB, and as for finding the point of intersection, you have equations for both MO and LO now so solve it to get O
rapid nest
is the slope for MB, 0?
slender mirage
yeah so MO would just be x = 10 lol
rapid nest
yeah so MO would just be x = 10 lol
so if we know slope for NB is 0 then that means we dont have to find the slope for MO?
slender mirage
yeah, it's intuitive that the if MB has equation y = constant then it's perpendicular would just be x = constant
x = 10 in this case passing through point M
rapid nest
is Y=13x+160 the equation for LO?
just to check
slender mirage
so, you solve the simultaneous equations :
x = 10 and (y-9) = 13(x-13)
slender mirage
is Y=13x+160 the equation for LO?
just to check
*-160
solve it with x = 10 and you get your y coordinate for O as well
rapid nest
-30? for y
slender mirage
yeah
slender mirage
lol
rapid nest
in a geometric way
lmao
of course
you've been helping really well, just a little more. i really appreciate the help i'm getting and i thank you a lot
slender mirage
honestly we're not really given much about ED
so you can only use the "midpoint" part of the question to find the coordinate of E
rapid nest
and um, how do you do that 😅
slender mirage
Umm, L is the midpoint between EC so
(26 + X)/2 = 13 ; (8 + Y)/2 = 9 - Midpoint theorem
(X, Y) = (0, 10)
rapid nest
i get it now
@slender mirage i thank you a lot. i understand this question now and I'll try solving it on my own now once. i really really appreciate the time you gave me and you were a really good helper.
again thank you a lot for your time
@restive river thank you too, you helped me too.
thanks a lot for the time you guys spent on helping me
.close
errant sage
anyone know how to find all real and imaginairy solutions to questions like
x^6 = 1
obviously u can employ difference of cubes and squares but is there any strategy that works for all powers
devout snowBOT
anyone know how to find all real and imaginairy solutions to questions like
x^6 ...
winter patrol
look up roots of unity
errant sage
k
also on a complex number line the cube root of 1 omega rotates points 120 degrees right
torpid ocean
yeah
all you do in that question is 360/6 and make it evenly spaced from the argand diagram drawned from the origin to 1
or is it finding the imaginay, you just have cis(2pi*n/6) for +- 1,2,3
and evaluate it down
restive river
anyone know how to find all real and imaginairy solutions to questions like
x^6 ...
One way of characterizing a complex number, rather than writing it as something like a+bi, is writing it as re^(it) with nonnegative real r and real t
We can look at the norms of both sides of (re^(it))^n = r^n e^(i(nt)) = x^n = 1 to find that r^n = 1, so r = 1 since we said it couldn't be negative
So it comes down to finding all t such that e^(i(nt)) = 1
Now e^(it) is a periodic function in t with period 2pi
errant sage
Pretty much tho nth root of 1 will cause a 360/n degree rotation on a complex plain
is that right
restive river
Well that's what the next step is: since 1 = e^(i * 2pi) = e^(i * (nt + 2pi k)) where k is some integer, we can just convert this to 2pi = nt + 2pi k
And solving results in t = 2pi k' / n, where k' is still just some integer
Any value of k' that "leaves" the range 0<= k' < n can be put back there, since we can pull out multiples of 2pi
restive river
is that right
so that leaves us with n n-th roots
1=2pi(0)/n, 2pi(1)/n, ..., 2pi(n-1)/n
errant sage
o
restive river
Also I leave it as an exercise to you to figure out exactly which nth roots are conjugates of each other :^)
restive river
I have a degree lol
restive river
Fun!
restive river
well obv omega has conjugates that are x^6
I think you should clarify this a little
errant sage
Well obv since +-(omega)^3 = 1.
Omega^3)^2) = will also = 1
and since u can now rerrange the real imaginary parts +- signs in any way and still be left with x^6
also it makes sense because if omega rotates a complex point 120 degrees it stands to reason that root omega and its conjugate will rotate 60 deg
right?
restive river
yes that's the same
errant sage
oh
ok
But is my reasoning sound for why omegas conjugates will equal 1 when raised to the 6th
restive river
But is my reasoning sound for why omegas conjugates will equal 1 when raised to ...
what do you mean by "omegas conjugates"?
A complex number has only one unique conjugate
errant sage
the same real part opposite magnitude of imaginairy
yeah but omega and its conjugate cubed = 1
restive river
the conjugate of that number cubed is -1 actually
so I'm still not sure what you are getting at
I think you are having a good time with these concepts and that's great!!
meager sapphire
restive river
no this cubed is 1
yeah but that's not the conjugate of $\frac{1}{2} + i \frac{\sqrt{3}}{2}$
woven radishBOT
zd
errant sage
up here i forgot - sign
restive river
$(e^{2\pi i (1/6)})^* = (\frac{1}{2} + i \frac{\sqrt{3}}{2})^* = \frac{1}{2} - i \frac{\sqrt{3}}{2} = e^{2\pi i(-1/6)}$
uh lmao what happened here
there
woven radishBOT
zd
devout snowBOT
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keen shoal
the answer is 1 right
devout snowBOT
the answer is 1 right
deft hemlock
,w ((2x^2-3x-2)/(x^2+3x)) / ((2x^2+x)/(x^2+2x-3)) / ((x^2-3x+2)/(x^2))
keen shoal
is it correct?
woven radishBOT
placid rover
lmao
keen shoal
im confused
placid rover
sure your brackets are ok there?
keen shoal
bro what happened to your input
deft hemlock
i just copied what he had written down
it has a triple diviosn
sextuple** actually
keen shoal
brackets no?
deft hemlock
brackets?
placid rover
you made a typo
keen shoal
ill try
woven radishBOT
keen shoal
you did do it correctly didnt?
keen shoal
oh right
deft hemlock
not sure how this would even be 1
deft hemlock
cuz the factors don't all cancel out
keen shoal
ill do it again
lol
wait it does cancel out
i have no idea what most of this stuff even means
oh you did the input wrong
oh wait nvm
it worked out on paper
please help
ok so
i just flipped the 2
it still works like this right
@deft hemlock
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feral scarab
How do I do these questions I’m new to them?
devout snowBOT
How do I do these questions I’m new to them?
languid ocean
How do I do these questions I’m new to them?
for a, you just find the 2 points. then you can find the slope normally.
same for b.
lemme know when you finish those
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@feral scarab Has your question been resolved?
deft hemlock
what are you confused about?
of which question?
so for the range
i would recommend completing the square and then stating what the "b" vlaue would be
in this equation
$y = (x-a)^2 + b$
woven radishBOT
Yottachad
deft hemlock
it is clear that b would be the lowest value because (x-a)^2 is always positive, so when that (x-a)^2 = 0 then b would be the min
and we know that x^2 increases to infinity
so we could say that the range is
$[b, \infty)$
woven radishBOT
Yottachad
woven radishBOT
odd elbow
Hi
odd elbow
It's been a while
Anyways
The question goes like this
And the equation goes like this
Is it fine
?
Bruh
solid trail
tag after 15 mins
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tender spade
ig noone finds this topic appealing
neither do I
sweet zinc
<@&286206848099549185>
shouldn't you be doing this on excel?
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rustic vessel
i need help
devout snowBOT
i need help
restive river
If m parallel lines are intersected with n parallel lines in a plane. Find the number of ||gm formed.
devout snowBOT
If m parallel lines are intersected with n parallel lines in a plane. Find the n...
restive river
Is it right $^mC_2 \times ^nC_2$?
woven radishBOT
!!!
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restive river
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rustic vessel
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stiff sage
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sleek nova
okay do you know y = mx+b
void harness
70 + days*45
stiff sage
okay do you know y = mx+b
yea
stiff sage
70 + days*45
i know that but I need letters n stuff
sleek nova
okay so what is the initial cost when u rent a car
stiff sage
70
sleek nova
good thats your b
stiff sage
do I just substitute then?
sleek nova
yep
stiff sage
45 x 5 + 70
sleek nova
mmmh why times 5
stiff sage
5 days
sleek nova
oh i didnt read that
sleek nova
yea u got it
stiff sage
alr thanks
sleek nova
im pretty sure you have to write the equation in the correct form tho
stiff sage
wdym
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shy kestrel
Ello! I have a few questions on statistically low powered studies.
From digging around online, I understand that 2 consequences of underpowered studies is that
- There is a higher rate of false positives. Mathematically, why does it do this? Why would a small sample size lead to more false positives?
- It can only pick up on the greatest effects and not smaller ones. How does this work? Isn't this consequence contradictory to the first one? I mean, if there are more false positives slipping in, what's preventing the samples with smaller effect sizes (dunno, p=0.049) from slipping in as well?
Thank you!
devout snowBOT
Ello! I have a few questions on *statistically low powered studies*.
From diggin...
@shy kestrel Has your question been resolved?
shy kestrel
<@&286206848099549185>
shy kestrel
😬
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@shy kestrel Has your question been resolved?
restive river
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restive river
How would I find the domain?
exotic stump
first of all, no it isn't, second, don't just give answers
quick swift
first of all, no it isn't, second, don't just give answers
Bruh, why are you so rude?
quick swift
Okay, have you never gave a wrong answer?
exotic stump
no, i don't give answers
quick swift
Okay 
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@restive river Has your question been resolved?
restive river
What have I done wrong
devout snowBOT
What have I done wrong
umbral cargo
Likely a lot of things, thanks for coming to my Ted Talk
supple knot
do you know the definition of sec?
supple knot
no one said you were stupid
restive river
Lemme walk u through
I did
2/-sqr2
Then cos 4pix = -sqr2/2
Then
I used 3pi/4 and 5pi/4 and divided them both by 4pi
I think I am correcting now
@supple knot am I right
supple knot
you can check if you plug it back into your initial equation
restive river
O
It was correct I
Thank you very much for helping whilst having not done anything in actuality
supple knot
my favorite kind of help
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@primal thistle Has your question been resolved?
lament inlet
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lament inlet
I am so confused
quasi star
let me just explain you the problem conceptually
x and y are 2 side of the rectangle
area is product of those sides
sum of all 4 sides
correct?
lament inlet
I don’t know
lament inlet
24
left gull
of a rectangle
Rectangle
quasi star
*Rectangle*
sorry
left gull
Thanks :)
lament inlet
It’s impossible to draw a rectangle with 12 square units and a perimeter of 26 units
quasi star
It’s impossible to draw a rectangle with 12 square units and a perimeter of 26 u...
no its not
we can work through it
lament inlet
Ok
quasi star
lets imagine the 2 sides are x and y
we know the formula for the area is x multiplied by y
lament inlet
K
quasi star
so we know that x multiplied by y is 12?
lament inlet
Yes
lament inlet
Yes
lament inlet
Yes
quasi star
can we write it as 2(x+y) = 26?
lament inlet
Yes
quasi star
okay so we know that some 2 numbers multiplied equals to 12
lament inlet
Yes
quasi star
can we write it as 2(x+y) = 26?
but we also have this so we know that x+y is 13?
lament inlet
Ok
quasi star
so you have to find out numbers that multiply to make 12 but when added are 13
quasi star
smart
quasi star
yeah you could
lament inlet
I’m dumb lol I’m 14 I’m in a special Ed class
quasi star
you are not dumb
lament inlet
Ty
quasi star
So I just draw a rectangle with the area of 13 square
12 block not 13 since x and y are 1 and 12
quasi star
you are not dumb
you solved the whole thing yourself
quasi star
yep
lament inlet
Thank you for your help
quasi star
you can count the side and verify your answer too
quasi star
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restive river
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floral anvil
Anyone from financial mathematics background can help me to verify the value of R here is equal to 7xx something?
The only clue is "increase his payment of R arithmetically" means R for the first year, 2R for the second year and so on.
devout snowBOT
Anyone from financial mathematics background can help me to verify the value of ...
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floral anvil
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woven radishBOT
g
neon oriole
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neon oriole
idk what to do
neon oriole
tan
feral scarab
Yep
feral scarab
Now set up an equation
feral scarab
No
Tan @ equals oppo of adjacent
We’re finding @
So tan theta is 60 divided by 600
neon oriole
oh
hexed meadow
so we know that tan of the angle is 60/600 now since tan is opposite over adjacent
you can use that to get the angle itself
exotic stump
you've already gotten which trig function it is, though i fear it was just a guess... use your knowledge of ratios to set up your equation
devout snowBOT
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neon oriole
@hexed meadow @feral scarab
ivory linden
Is there a generalized way to solve this? \
$\min{f(n)|n\in\bN\land n\geq a}$, \$f:\bN\to\bN$
devout snowBOT
Is there a generalized way to solve this? \\
$\min\{f(n)|n\in\bN\land n\geq a\}$...
woven radishBOT
Pedrosso
ivory linden
or to generalize the question further $\min{f(x)|x\in D}$ for any $f:D$
woven radishBOT
Pedrosso
devout snowBOT
@ivory linden Has your question been resolved?
warm tiger
(2+2)^2=
hardy mesa
strong pivot
hi
restive river
What's the definition of function f? I'm sure the question is incomplete. Can you share complete question?
whole sand
If 1, 2,-3 are eigen values of A then trace of A² is
None
0
36
14
restive river
it only says this
Ok, so do you know about chain rule?
heady oak
could this be a chain rule practice?
restive river
If 1, 2,-3 are eigen values of A then trace of A² is
None
0
36
14
Post in available channels.
strong pivot
kinda
whole sand
Post in available channels.
Can u pls tag em I'm kinda new sry
restive river
Can u pls tag em I'm kinda new sry
restive river
Do you what's the derivative of f(g(x)) using chain rule?
@strong pivot
strong pivot
idk how to derive f(g(x))
but i know how to derive like (3x^2+4x)^5
using chain rule
restive river
Ohh.
According to chain rule, you have to differentiate the outer function first and then multiply by the derivative of inside function. This chain continues for numerous functions.
restive river
What's the outer function?
strong pivot
f(x)?
restive river
derivative of f(x) is f'(x).
What's the inside function? Can you multiply it with derivative of inside function?
@strong pivot
strong pivot
e^2x
restive river
Yes
restive river
f
strong pivot
so its f'(x) * 2e^2x
strong pivot
isnt the outer function f(x)
strong pivot
wait whats the outer function
restive river
Outer function is f
But you have to keep inner function as it is while applying chain rule.
strong pivot
how is it f
restive river
Umm let's take another example.
What's the outer function in sin(cos(x))?
@strong pivot
strong pivot
sin
restive river
Yeah.
Can you figure out its derivative using chain rule?
strong pivot
sin'(cos(x)) * -sin x
restive river
Yeah
restive river
so its f'(x) * 2e^2x
That's why it should be f'(e^2x) * 2e^2x
It's not f(x), it's f(e^2x)
strong pivot
oh okay tysm
restive river
oh okay tysm
Did you get it?
strong pivot
yep
restive river
If you are done, you may close the channel by .close
strong pivot
.close
restive river
Hi, how would you calculate an average between two dynamic numbers? In example, i have a statistic that calculates a gain per time unit, eg income per minute, but it updates every 5 seconds and the income varies heavily from second to second so i need to get an average between a longer time span, atm the way it works is that it just extrapolates on the data it had for the past 5 seconds, i could make it just collect the data each 60 seconds instead but that makes it hard to see the fluctuations
devout snowBOT
Hi, how would you calculate an average between two dynamic numbers? In example, ...
restive river
Hope that made sense to someone
keen owl
Not to me lol
restive river
if (CurrentDeltaTime >= 5.00)
{
var expFromOld = CharCurrentExp - ExperienceOld;
if (expFromOld != 0 && ExperienceOld <= CharCurrentExp)
{
CurrentExpGainMin = expFromOld * 12;
CurrentExpGainHr = CurrentExpGainMin * 60;
ExperienceOld = CharCurrentExp;
ToNextLevelMin = (PlayerExpNext - PlayerExpCurrent) / CurrentExpGainMin;
ToNextLevelHr = (PlayerExpNext - PlayerExpCurrent) / CurrentExpGainHr;
}
CurrentDeltaTime = 0;
a snippet of my function in case it helps
basically, this works fine but because the gain updates too often and varies too heavily, i need an average of a longer period, based on the values i got
keen owl
So cant you just save 12 values over 60 seconds
Find the average of the 12?
restive river
i suppose i can do that, but i was wondering if there was another way to get an aprox without collecting the data for a longer period, but idk if that makes sense
no it doesn't nvm
keen owl
It does
But it really depends on what your doing right
Like if your tracking the position of something
Then between those 5 second intervals , you have a general idea of where it is
If that makes sense
I have no clue what your doing so idk
restive river
i'm calculating the exp gain per minute / hour
but i need a way display the data with an average that's more stable over time then only seeing what i'm getting for the past 5 seconds, cause while it's accurate it can give me like, i'm going to level up in 86 hours, while 10 seconds later it's 122 hours
restive river
yes correct~
keen owl
If the xp gain isn't extremely sparatic maybe you can find the gain in the gain and use that? Idk if that will help.
Like the second derivative if you know what I mean
Idk if thats a good idea
Otherwise I would just go with finding the average of like the last 10 values or something and then every time you get a new value, you trash the oldest one. If doing it for 10 is still all over the place you can do it for more
Now I'm sorta interested in what your making lol
restive river
If the xp gain isn't extremely sparatic maybe you can find the gain in the gain ...
i'm not sure what you mean
but i think collecting data over a longer period is the only way i currently understand, i'm terrible at math tbh 😂
keen owl
So currently your calculating the gain in xp by doing (currentxp)-(oldxp)
Something like that
restive river
Now I'm sorta interested in what your making lol
nothing special at all, it's just a exp plugin for a game
keen owl
You can calculate gain in gain in xp
Current gain - old gain
And do estimates with that
Idk homie I'm in bed just find the average lol
restive river
oh, i get what you mean
but i think the base numbers might be too erratic
so i suppose ill just end up collecting the data over a longer period instead
thanks for your help
.close
knotty jolt
on b) why is dy/dt -7/12?
flint inlet
on b) why is dy/dt -7/12?
dy/dt is calculated in part (a)
((-7)/24)x2 or -7/12
So you are substituting that in (b)
noble umbra
devout snowBOT
wintry sparrow
Corresponding sides have the same ratio
rigid cove
ye
wintry sparrow
Use that and find h
rigid cove
so
$\fac{8}{24}=\frac{h}{2}$
woven radishBOT
Mathgeek007
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rigid cove
$\frac{8}{24}=\frac{h}{2}$
woven radishBOT
Mathgeek007
wintry sparrow
I don’t know what anything is
AEB ~ CED
rigid cove
$\frac{16}{24}=h$
woven radishBOT
Mathgeek007
wintry sparrow
h = 4/6
noble umbra
0.6
rigid cove
$h=\frac{2}{3}=6.67$
woven radishBOT
Mathgeek007
rigid cove
yes
wintry sparrow
$h = 0.\bar{6}$
noble umbra
4/6 = 0.67
woven radishBOT
kirby your mom
noble umbra
I’m lost bro
wintry sparrow
4/6 = 0.67
Yes
rigid cove
I just rounded it of
winter patrol
don't round
wintry sparrow
I just rounded it of
And multiplied by 10
noble umbra
Yeah cantvround
wintry sparrow
don't round
Why not?
noble umbra
Wait so is it 0.8
wintry sparrow
You can't get something to 0.666666 places of accuracy anyways
winter patrol
why not just leave it as a fraction
noble umbra
A = .67
wintry sparrow
why not just leave it as a fraction
You could also do that
wintry sparrow
h not A
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latent root
supple knot
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ivory hedge
Can someone help me prove this identity?
devout snowBOT
Can someone help me prove this identity?
granite rover
Try changing the numerator on the left side so that it cancels out with the denominator
Start by changing 1
shut folio
it's easier than that
multiply both sides by the denominator
and then use the pythagorean trigonometric identity
granite rover
I believe usually they want you to get from one expression to the other one by modifying only one
shut folio
oh, you're right
ivory hedge
Ok I changed the 1 to sin^2x + cos^2x, but that can't cancel with the denominator can it?
shut folio
Ok I changed the 1 to sin^2x + cos^2x, but that can't cancel with the denominato...
what is (a+b)^2 ?
granite rover
No, but you know what a^2+2ab+b^2 factors into
ivory hedge
what is (a+b)^2 ?
a^2+2ab+b^2
shut folio
a^2+2ab+b^2
exactly what you have in the numerator
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merry stream
so
merry stream
for telling apart concave up/down functions
my book only says concave up skethces are ones where the graph of the function is above the tangent lines to the function
and Idk why I'm struggling with that idea
like is it possible to say concave up are graphs that just open up? like a U shape almost?
or maybe I need super exaggerated tangent lines?
thoughts?
merry stream
alright thanks @spare crypt
merry stream
concave up means it's a portion of a U shape yeah
also do you happen to know why I care about concave up/down if I know local maxima and minima?
supple knot
,wolf plot x^3
woven radishBOT
supple knot
This has an inflection point / change in concavity, but not any local extrema
merry stream
oh shoot I forgot about that
and how would that look like with y''
just like, no local extrema but y''=0 when x= (something)?
supple knot
just like, no local extrema but y''=0 when x= (something)?
Right you can probably just calculate that for this function pretty easily
merry stream
Right you can probably just calculate that for this function pretty easily
alrighty thank you : )
.close
ashen crescent
Hi
ashen crescent
How would i solve this?
I know x cannot equal 4
and I know that everything in the square root can't be negative, but idk how to find for which values the square root is negative and for which they're positive since it's a fraction
restive river
How would i solve this?
What's the actual question?
stuck field
Probably range or domain.
glossy viper
or domain maybe?
restive river
Hint: ||For the value inside square root to be negative, either numerator or denominator is negative, but not both at the same time.||
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worthy quest
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worthy quest
does anyone see what i missed here?
so i changed my answer to 90000(1/15)^t/6.7
and that's apparently correctly
so I should read "bacteria decays by a factor of 1/15 every 6.7 minutes"
stuck field
Think it like compound interest if you can relate to it.
worthy quest
as "the bacteria has 1/15 of it's initial population remaining after 6.7"
rather than it loses 1/15 of it's initial population
this doesn't seem correct
yeah if you told it me grows by 1/15 rather than decays by 1/15
i would obviously interpret that as you gain 1/15 of 90000
am i just not englishing or what?
stuck field
this doesn't seem correct
Why does it now?
It looked 1/15 of its population.
Then it again loses 1/15 of its population (the new one this time)
Compound interest formula makes perfect sense here.
worthy quest
the problem i'm having
is the "correct" answer is telling me that
after 6.7 minutes
the population is 1/15 of the initial number
not that it decayed by 1/15th
stuck field
Is that so?
worthy quest
it seems to be
90000(1/15) is 6000
so after 6.7 minutes you would only have 6000 total
rather than 6000 from 90000
stuck field
No you would have 90000-6000
That means you are doing 90000-1/15×6000
That is 90000×14/15
worthy quest
are you saying that based on the wording of the problem or off of what the program says the correct answer is?
stuck field
That's what you've written there.
worthy quest
yes but the program says 90000(1/15)^t/6.7 is correct
stuck field
1/15 or 14/15?