I did it like 3 diff ways but idk how I should’ve acc done it
#help-17
trail seal
vocal sleetBOT
@trail seal Has your question been resolved?
trail seal
<@&286206848099549185>
vocal sleetBOT
@trail seal Has your question been resolved?
vocal sleetBOT
@trail seal Has your question been resolved?
vocal sleetBOT
@trail seal Has your question been resolved?
vocal sleetBOT
@trail seal Has your question been resolved?
mighty stone
We can model a standard 12 ounce soda can as a cylinder with a volume of 410.5 cubic centimeters, a height of about 12 centimeters and a radius of about 3.3 centimeters.
How do its dimensions compare to a cylindrical can with the same volume and a minimum surface area?
How do i begin?
vocal sleetBOT
We can model a standard 12 ounce soda can as a cylinder with a volume of 410.5 c...
@mighty stone Has your question been resolved?
sterile rune
Is there any more text that explains the ex or something related to it beacuse at my view point I dont think we can do much with only this part
mighty stone
Is there any more text that explains the ex or something related to it beacuse a...
so we have volume 452 of cylinder and want to find the height so our formula is 452/pi*r^2=H
@sterile rune
.close
tepid path
why is -8 an extraneous solution?
vocal sleetBOT
why is -8 an extraneous solution?
tepid path
-9 is a square root of 81
along with 9
but its not counted?
wolfram alpha and symbolab and mathway are telling me the same thing because they arent taking into account the negative root
am i going nuts
drifting jackal
coarse ridge
but its not counted?
The square root function only outputs positive roots
vast shale
-9 is a square root of 81
$-9$ is a solution to the equation $x^2 = 81$, not a square root of $81$.
twin meteorBOT
maxim
late ingot
alternatively, $|x| = 9$
twin meteorBOT
b0ngl0rd
tepid path
$-9$ is a solution to the equation $x^2 = 81$, not a square root of $81$.
what
does square root only positive
vast shale
the square root func outputs only real numbers yh
tepid path
why only positive
vast shale
and takes in $\mbb{R}^+ \cup {0}$
twin meteorBOT
maxim
tepid path
but wouldnt it go like this:
x^2 = 81
x = sqrt81
x = 9, -9
vast shale
nope
tepid path
what
vast shale
$x = \pm \sqrt{81}$
twin meteorBOT
maxim
vast shale
because x^2 gets rid of the negative sign
tepid path
so it needs to be the plus minus to have the negative root?
vast shale
yep
vast shale
so it needs to be the plus minus to have the negative root?
yes
tepid path
wait
so if
sqrt 4 = x
then x^2 = 4
and both -2 and 2 satisfy that
wait im confused again
late ingot
think about the graph of x^2
its even, so f(x) = f(-x)
f(2) = 2^2 = 4
f(-2) = (-2)^2 = 4
vocal sleetBOT
@tepid path Has your question been resolved?
tepid path
<@&286206848099549185>
peak wharf
ye?
vocal sleetBOT
@tepid path Has your question been resolved?
lime kraken
vocal sleetBOT
lime kraken
why did the e just disappear
median crane
One sec
lime kraken
shouldnt it be e^-x and derivative of -x
twin meteorBOT
Pure
median crane
It’s the logarithm of the base law
tame hound
coming up as wrong though, anybody have an idea?
vocal sleetBOT
coming up as wrong though, anybody have an idea?
vocal sleetBOT
@tame hound Has your question been resolved?
twin meteorBOT
..,,
gaunt sparrow
Integrate it and use sin(x+pi) = -sin(x) and cos(x+pi)=-cos(x)
twin meteorBOT
..,,
soft walrus
mmm that might work let $\theta=x-\phi$ this gives $\cos^{2}\phi\int_{0}^{\pi}\sin^{2}\theta\dd\theta-2\cos\phi\sin\phi\int_{0}^{\pi}\cos\theta\sin\theta\dd\theta+\sin^{2}\phi\int_{0}^{\pi}\cos^{2}\theta\dd\theta$
twin meteorBOT
PajamaMamaLlama
soft walrus
idrk tbh might be better off doing it the usual way, just by integrating 
well it simplifies nicely if it helps any
$\cos^{2}\phi\int_{0}^{\pi}\sin^{2}\theta\dd\theta+\sin^{2}\phi\frac{\pi}{2}$
twin meteorBOT
PajamaMamaLlama
soft walrus
^ this could also work
karmic mica
(phi + pi) - phi = pi
you dont have to integrate anything
the two integrals have the same interval
you can integrate sin²x with the fact that cos2x = 1-2sin²(x)
what
thats even worse than just integrating
get the value of the second integral first
and maybe we can use substitution to solve it
twin meteorBOT
..,,
vocal sleetBOT
@waxen relic Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
toxic cedar
Hi,
I need help with this following problem where we need to find the value of c_n where n is an odd number represented by 2k + 1. I am confident in my answers for c_n where n is an even number is equal to 0 and m = 3, but i have no idea how to approach this problem. I have tried various different methods using the series definition of y and findin the derivatives and plugging it back into the original differential equation to find a number of c_n but i keep getting a recursive function for c_n which is dependent on x and n which does not not converge. Any idea on how i can solve this problem. The answer has to dependent on k only.
vocal sleetBOT
Hi,
I need help with this following problem where we need to find the value of ...
@toxic cedar Has your question been resolved?
toxic cedar
<@&286206848099549185>
vocal sleetBOT
@toxic cedar Has your question been resolved?
toxic cedar
can someone please help with this
toxic cedar
<@&286206848099549185>
vocal sleetBOT
@toxic cedar Has your question been resolved?
vocal sleetBOT
@toxic cedar Has your question been resolved?
elder scaffold
how does gravity affect circular motion?
vocal sleetBOT
how does gravity affect circular motion?
vast shale
how does gravity affect circular motion?
Tension at topmost position when spinning vertically
It should be a derivation
elder scaffold
we are spinning it horizontally
vast shale
Hm
There must be something in the question
Usually the y axis is ignored, centripetal and centrifugal forces are calculated on the x axis
vast shale
how does gravity affect circular motion?
uniform?
elder scaffold
well its meant to be uniform
vast shale
uniform?
I would assume, if he knew how to calculate non uniform motion he would probably know what gravity does
He or she or they
twin meteorBOT
Galaxy
elder scaffold
.close
vocal sleetBOT
@wary mantle Has your question been resolved?
vocal sleetBOT
@wary mantle Has your question been resolved?
rancid notch
vocal sleetBOT
rancid notch
Why c an we replace it like so in the second part?
vast shale
Can someone please help me make this in Nspire
vocal sleetBOT
Can someone please help me make this in Nspire
waxen hawk
vocal sleetBOT
waxen hawk
This is a column matrix
And a,b are entries of that column matrix
Yet I wanna if I can call the element “a” as a top entry
While the “b” as the bottom entry
Or should I just name them numerically? Like the first and second entry
sweet birch
I'd say calling them the top and bottom elements or x_1 and x_2 or something would be clearest
waxen hawk
I'd say calling them the top and bottom elements or x_1 and x_2 or something wou...
Sounds terrific
Thank you so much for answering my question
vocal sleetBOT
@waxen hawk Has your question been resolved?
quaint wolf
is that statement correct? sorry for the bad drawing, had to use paint
dim quail
no or maybe
vocal sleetBOT
@quaint wolf Has your question been resolved?
vast shale
is that statement correct? sorry for the bad drawing, had to use paint
what's that "U" shaped symbol beside AB/CD?
quaint wolf
what's that "U" shaped symbol beside AB/CD?
the symbol for arc
like the arced length between a and b
vast shale
hm
vast shale
is that statement correct? sorry for the bad drawing, had to use paint
i don't think so
vast shale
i don't think so
i think the ratio of the lengths of the two chords doesn't always mean it's equal to the ratio of the arc lengths
for example, if two chords have the same length but subtend different angles then their arc length is different
quaint wolf
that makes sense, thanks !) Its nowhere to be found on google too, so you are probably right
vast shale
that makes sense, thanks !) Its nowhere to be found on google too, so you are pr...
you're welcome
quaint wolf
.close
woeful widget
i think the ratio of the lengths of the two chords doesn't always mean it's equa...
But Chords having same length subtend same angles?
vocal sleetBOT
But Chords having same length subtend same angles?
woeful widget
vast shale
Lmao
woeful widget
?
vast shale
back
vast shale
But Chords having same length subtend same angles?
then it means the ratio of two lengths of the chords is equal to the ratio of the two arc lengths, considered with the same subtended angles
woeful widget
then it means the ratio of two lengths of the chords is equal to the ratio of th...
Wait ill draw what im trying to say
woeful widget
then it means the ratio of two lengths of the chords is equal to the ratio of th...
You cant say that just because it holds true for the case in which the lengths are equal, youd have to prove it using trigo
vast shale
You cant say that just because it holds true for the case in which the lengths a...
hm
i dont know trigo but i could try using basics
what ive learned is that the arc length is proportional to both the chord length and the central angle. for example, if the chord length of AB and CD is 10cm and the central angle of AB and CD is 45°, then the arc length of AB and CD is 10 * 45/180 * π ≈ 7.85: the ratio of the arc length is 1
woeful widget
old niche
I wrote a proof for this
vocal sleetBOT
I wrote a proof for this
old niche
but im not sure if its correct
im gonna show it
i would appreciate feedback or some type of point in the right direction if im very incorrect
hard atlas
why is the supremum of the set of lower bounds also itself a lower bound?
oh and I noticed you didnt even use the word supremum for that one
old niche
uhhh maybe i did this bad
autumn oyster
This won’t change the content of your proof of part (a), but you claim that the lower bound b is in the set A which isnt necessarily a requirement on a lower bound
autumn oyster
The inequality will hold just as real numbers, you won’t need both a and b in the set A for a lower bound to make sense, for example of A was the set of all strictly positive real numbers, then -1 would be a lower bound because we have -1<=a for each a, even though -1 is not actually on the set A
autumn oyster
For part A your your solution is good, you should just say there exists a b in R instead of a b in A
old niche
so like this?
autumn oyster
Mostly, you should still have a in A in the first line
But also the last step in this is not necessarily clear, why does having a lower bound guarantee the will be a greatest lower bound?
old niche
But also the last step in this is not necessarily clear, why does having a lower...
could I use the completeness axiom
autumn oyster
could I use the completeness axiom
old niche
The Completeness Axiom states that every non-empty set of real numbers that is bounded below has a greatest lower bound, this holds for the real numbers
the set of real numbers
autumn oyster
The Completeness Axiom states that every non-empty set of real numbers that is b...
Hmm, isn’t this what it is asking you to prove in part (a) anyway though?
So I guess it depends on which version of completeness you have proven already
If you have proven that every set of reals bounded above has a lowest upper bound then you can apply this the the set of lower bounds
old niche
this is from class
autumn oyster
this is from class
Yep
This version works
Since in the last line of part (a) you are claiming that the collection of lower bounds has a supremum
And you already know it is non empty and bounded above by a
And then yeah, you would probably need a bit more detail on why the supremum of all lower bounds is really the infinimum of the set A
old niche
i think im sorta getting confused with the mix of upper and lower bound snow
autumn oyster
Yeah, it’s very confusing the first few times when defining completeness, but essentially what you have done is that you want to show that A has an infimum, and your how is to do this by showing that the supremum of the set of all lower bounds is really the infimum of the set
Which you may be able to take for granted depending on if you’ve proved it before since in some sense this is really saying the the infimum IS the greatest lower bound
But the subtly comes from the fact that if you take a supremum of a set, it’s not guaranteed to be an element of the set itself
So you need to argue that the supremum of all lower bounds is still a lower bound
old niche
right because the surpreumum of the set is the greatest lowest bound, so therefore its the infimum of A by definition
autumn oyster
Yeah
old niche
thank you for your patience also
autumn oyster
no problem! I like doing math
old niche
i dont think its as simple as citing the axiom and saying that then the supremium of the bounds by definition is the infamium of a?
autumn oyster
right because the surpreumum of the set is the greatest lowest bound, so therefo...
The subtle problem with this is that depending on what you have already proven before, it’s not necessarily obvious that there even is a greatest lower bound, by completeness, you know that there is a supremum of lower bounds, but in order for this supremum to be the greatest lower bound, it would also need to be a lower bound itself
autumn oyster
i dont think its as simple as citing the axiom and saying that then the supremiu...
Yeah, it’s not quite that simple because of this issue
Like for example
If the set of all lower bounds was (-infinity,3)
Then the supremum of this would be 3
Which isn’t in the set anymore
So it’s not clear that 3 is still a lower bound
But really this kind of case cannot happen
old niche
oh because (-infinity,3) --> doesnt include endpoints?
old niche
The subtle problem with this is that depending on what you have already proven b...
I guess I dont know what to think of this
I never really ever thought of this to be honest
autumn oyster
You can show this directly by expanding definitions , though it’s not really obvious
So
If L is the set of all lower bounds, we want to show that sup(L) is still a lower bound
What does it mean for a real number l to be a lower bound on A?
old niche
it must be the sepremium of L?
autumn oyster
Not quite, we don’t really know anything about the supremum of L yet, but we are hoping to provide something about it by looking at the terms l in L
Which is to say that if l is a lower bound, then for every a in A, we have that l<=a
old niche
right yest
that makes sense
even if its not the supremium, it holds that
l is still less than a
okay I see
autumn oyster
Exactly!
But supremums preserve this fact
Since they preserve ordering
We know that l<= a for every l
Which means that sup(L) <= a
old niche
why do surpremums presevere ordering?
autumn oyster
Let’s suppose by way of contradiction that they didn’t!
Which would mean, suppose by way of contradiction that a<sup(L)
But by the definition of supremum, we know that this means there will be an l which is arbitrarily close to sup(L)
old niche
arent sets always ordered tho?
autumn oyster
Which means that a<l< sup(L)
autumn oyster
arent sets always ordered tho?
Yeah, these sets all have an order , but we basically are using the fact that even if the supremum isn’t in the set we are looking at, it will be at least very close to it
autumn oyster
Which means that a<l< sup(L)
Because this inequality has a problem!
We know that l is a lower bound on A
But a<l for some a in A
(Which contradicts l being a lower bound)
Do you see how this shows that sup(L)<= a for each a in A?
old niche
right yes
autumn oyster
So since sup(L)<= a for every a, what does this say about sup(L)?
autumn oyster
Yep!
So now we have found a greatest lower bound on the set A
Which is to say that A has an infimum!
Does this make sense?
autumn oyster
Looks great to me
If you want more detail you can prove why the supremum preserves ordering, but if you don’t need full detail, then the claims you made here are all true
old niche
thanks so much, you really helped me understand some things I was confused about
old niche
If you want more detail you can prove why the supremum preserves ordering, but i...
probably not
is it worth it changing some of the wording I used in part b)
like to not use upper and lower bound but instead supremum and infamum
autumn oyster
is it worth it changing some of the wording I used in part b)
Your wording in part b looks good to me
Though you maybe want more detail for what sup(A)>inf(B) implies there is an a>b
Since this is really doing two steps at once
It may be clearer if instead you have something like sup(A)>inf(B) implies there exists an a such that a>inf(B) by definition of supremum, and by definition of infimum this means there is a b such that a>b
But this is just a level of detail thing
autumn oyster
was proof by contradiction the correct way to go
Yeah, it makes it much easier in this case
When doing a proof by contradiction all of the less than or equal to symbols just become greater than symbols
And strict inequality’s work well with the properties of inf and sup
old niche
right and this is a contradiction because earlier we still assumed that for all elements in A and B, A's elements should always be less than B's elements?
old niche
thanks! is there anything else I should add in the proof or is this sufficient detail
old niche
Thanks so much for your help
autumn oyster
Your welcome 
good luck with your studies
vocal sleetBOT
autumn oyster
🤡 im so confused
Open up a new thread
velvet knoll
kk
vocal sleetBOT
Available help channel!
craggy hamlet
For the function f(x)=x^2-4x+3, the area bounded between the function and the x-axis is 0 over the interval [0, 3]
What does this mean for the area to be zero ? Please include a sketch of the graph as part of your explanation
vocal sleetBOT
For the function f(x)=x^2-4x+3, the area bounded between the function and the x-...
craggy hamlet
i dont know where to start
magic wasp
It's a signed area
Above the x-axis is positive, below the x-axis is negative
Add the two parts, you should get zero
vast shale
When the area bounded between a function and the x-axis is zero, it means that the function and the x-axis intersect and create a closed shape without any area between them.
vast shale
The graph of f(x) = x^2 - 4x + 3 is a parabola that opens upward. It intersects the x-axis at two points: (1, 0) and (3, 0).
magic wasp
how do i sketch the graph
Just like any quadratic
vast shale
If the area is zero, it means that the positive (above the x-axis) and negative (below the x-axis) areas cancel each other out.
vocal sleetBOT
@craggy hamlet Has your question been resolved?
normal tulip
vocal sleetBOT
vocal sleetBOT
@normal tulip Has your question been resolved?
crisp saddle
Try to draw a matching for n and f(n) = 1,2,3,4,5,6. You may get a better "feel" for the inverse.
normal tulip
Try to draw a matching for n and f(n) = 1,2,3,4,5,6. You may get a better "feel"...
I “feel” impossible
normal tulip
Try to draw a matching for n and f(n) = 1,2,3,4,5,6. You may get a better "feel"...
do i do the inverse of the conditions?
normal tulip
Try to draw a matching for n and f(n) = 1,2,3,4,5,6. You may get a better "feel"...
can i say 3 not divides n
<@&286206848099549185>
peak root
Remember that this is a function; a single input cannot correspond to two different outputs.
normal tulip
Remember that this is a function; a single input cannot correspond to two differ...
yh
normal tulip
Remember that this is a function; a single input cannot correspond to two differ...
would it be 3|n+2
@open sundial xD can you help me
peak root
would it be 3|n+2
yes, one condition will be 3|(n+2), the inverse is also a function with conditions
normal tulip
yes, one condition will be 3|(n+2), the inverse is also a function with conditio...
alright thanks.
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
karmic epoch
Someone can help?
vocal sleetBOT
Someone can help?
karmic epoch
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
faint jetty
Hello, I need help finding x and y in this diagram. I am new to doing sides and trying to learn
vocal sleetBOT
Hello, I need help finding x and y in this diagram. I am new to doing sides and ...
vast shale
in left triangle, all angles are equal, so all sides are equal too, then 4x = 5y + 4
in right triangle, two angles are equal, so the sides adjacent to these angles are equal, then, 4x = 5y + 4 and 4x = 6x - 13
solve second equation:
4x = 6x - 13
-2x = -13
x = 7.5
then, solve first equation:
4x = 5y + 4
4 * 7.5 = 5y + 4
30 = 5y + 4
-5y = 4 - 30
-5y = -26
y = 5.2
vocal sleetBOT
vocal sleetBOT
Available help channel!
plush roost
vocal sleetBOT
plush roost
i calculated for the gradient: <x/(x^2 + y^2)^.5 , y/(x^2 + y^2)^.5 >
and now im stuck
because setting that to 0 gives the point (0,0) but that's clearly undefined for the gradient
vocal sleetBOT
@plush roost Has your question been resolved?
plush roost
<@&286206848099549185>
plush roost
.close
vast shale
Please help me solve this. I am not sure how.
vocal sleetBOT
Please help me solve this. I am not sure how.
outer warren
are you able to determine the slope of the line?
vast shale
are you able to determine the slope of the line?
yes. the slope is -1/3
vast shale
(-6,-6)
outer warren
do you know what point-slope form refers to?
vast shale
y-(-6)=m(x-(-6)
outer warren
your slope too
vast shale
into the first x and y?
outer warren
no
vast shale
oooohhh as m?
outer warren
slope into slope, m yes
vast shale
ok
outer warren
then clean up those
-(-6)
outer warren
no
you're doing stuff that you shouldn't be doing
then clean up those
-(-6)
what do you have after doing that?
vocal sleetBOT
vocal sleetBOT
Available help channel!
jaunty bobcat
how would i like simplify this into 1 logarithm 😭
vocal sleetBOT
how would i like simplify this into 1 logarithm 😭
twin meteorBOT
Azyrashacorki
gaunt sparrow
$$\log_b(x) + \log_b(y) = \log_b{xy}$$
twin meteorBOT
Azyrashacorki
worldly adder
Hey can someone help me
vocal sleetBOT
Hey can someone help me
worldly adder
Hey can someone help me
<@&286206848099549185>
vast shale
this is math?
vocal sleetBOT
@worldly adder Has your question been resolved?
worldly adder
whats the total resistance of the circuit
I found 3,2 ohm
worldly adder
I found 3,2 ohm
@pale perch
pale perch
show your work
worldly adder
R12 = 2*3/2+3= 1,2 ohm
R total = 2+1,2 = 3,2 ohm
I total
V total/Rtotal = 3/3,2 = 0,9375
Only find R and I @pale perch
pale perch
youre saying the resistance across the parallel part is 1.2?
pale perch
nice
worldly adder
Hey can someone help me
May i ask how to solve point b? Potential difference
pale perch
the parts have equal resistance so it just splits equally between them
you can verify by using V=IR
worldly adder
0,75*4?
pale perch
not quite
thats just the emf
0.75*2
each part, R1 and the combo of (R2 and R3), has 1.5V across them each
oops
sorry was writing an email for my friend earlier
worldly adder
So R1= 1,5v and R23= 1,5v , right?
pale perch
yup
V1=1.5V and V2,3=1.5V
do you know how to calculate how current splits at a junction?
for c
pale perch
it splits in the ratio of said resistor to the total of the branches
worldly adder
Just guessing, maybe
I2= 1,5/3?
I3= 1,5/6?
pale perch
not quite
you can tell when youre wrong because it should be the case that I2+I3=0.75
oh wait
maybe just maybe
,calc 1.5/3+1.5/6
twin meteorBOT
Result:
0.75
Result:
0.33333333333333
,calc 6/(3+6)
twin meteorBOT
Result:
0.66666666666667
checks out
vocal sleetBOT
worldly adder
.reopen
vocal sleetBOT
✅
pale perch
wait
worldly adder
checks out
So
pale perch
how did you get those actually
worldly adder
Which one
pale perch
both, what was your process
twin meteorBOT
pale perch
yeah, okay
what you need to do is:
for example with I2, what i just did is
$I_2=I\left(\frac{R_2}{R_2+R_3}\right)$
twin meteorBOT
AℤØ
pale perch
I is the 0.75 entering the junction
for I3 just replace the numerator with R3
you can extend this to however many branches there may be in a parallel circuit
worldly adder
But, If we do I2+I3 the ans not 0,75
pale perch
,w 0.75*(6/9)
twin meteorBOT
pale perch
0.5+0.25=0.75
I3=0.5 I2=0.25
which makes sense since R3=2R2
so in the ratio, I3=2I2
vernal estuary
icy moth
For the first one, the y-intercept is when the function crosses the y-axis. The second can be solved using factoring (Hint: factor out -2 to make factoring easier). The last one is solved using -b/2a.
tropic schooner
This might be a bit unconventional for this Discord, but I don't know where else to ask. Today at work, we had a spin the wheel thing for prizes and there were 6 spins. The first three spins were out of 222 outcomes (names) and there could be multiple entries for each name so that chance wasn't always 1/222 for a person to win. The next three spins were out of 92 outcomes and again names could appear more than once. My team is a small one (4 of us) and three of us won 3 of the 6 spins. We thought it would be fun figure out the chances of that happening.
One of us won Spin 3 with a chance of 3/222. The other two won Spins 4 and 6, each with the same chance of 2/92. Since these were independent probabilities (none of the spin outcomes were affected by previous spins), I figured it would be as easy as multiplying these three probabilities together. But I don't think it's as simple as that. Don't I have to get the probability of the sequence of wins and losses or something?
My question is, what is the probability of this outcome (that the three of us each won a spin out of 6 spins)? I'm old as dirt and haven't done math in ages, so I don't know how to show my work. I've looked up formulas for probability but don't know how to account for all these variables. Thanks in advance for any help you can give.
vocal sleetBOT
This might be a bit unconventional for this Discord, but I don't know where else...
lime gorge
Since they’re independent, I think we can look at each spin separately. For the first spin, out of the 222 names, how many of them belonged to you and your team?
tropic schooner
For Spins 1, 2, and 3 the number of entries we had were 4, 4, and 3 out of 222.
For Spins 4, 5, and 6 the number of entries we had were 2, 2, and 1 out of 92.
So 11 for Spins 1, 2, and 3 and 5 for Spins 4, 5, and 6.
What started to break my brain was thinking about the odds of the three of us winning 3 out of those 6 spins.
Since the number of outcomes varied and our individual chances.
And I figured the odds of none of us three winning on three of the spins was relevant, too.
lime gorge
What started to break my brain was thinking about the odds of the three of us wi...
The probability of winning spins 3, 4, and 6 like u guys did or the probability of winning any three spins? I’m guessing it’s the former
Slowly narrowing down the permutations haha
tropic schooner
I appreciate it so much! It's not so much the order of the spins since we were each entered for all 6 spins but the order matters in the sense that our chances and the outcomes were different between the first 3 spins and second 3.
So my question is, of us 3 people who were entered in 6 spins, what are the odds that we won 3 out of 6 of them?
So, like, Spin 1: 4/222, 4/222, 3/222
Spin 2: 4/222, 4/222, 3/222
Spin 3: 4/222, 4/222, 3/222
Spin 4: 2/92, 2/92, 1/92
Spin 5: 2/92, 2/92, 1/92
Spin 6: 2/92, 2/92, 1/92
In Spin 3, the winner was 3/222
In Spin 4, the winner was 2/92
In Spin 6, the winner was 2/92
lime gorge
So there’s 4 people in ur group, but only 3 of u participated in the spins?
tropic schooner
Ah, I meant to clarify. The total number of outcomes was based on the number of knowledge quizzes we completed for a new product rollout the company is doing. So our names appeared as many times as we completed the quizzes.
Two of my colleagues completed 4 and I completed 3.
The second three spins were a count of how many of the quizzes we got 100% on. Two of my colleagues got 2 perfect scores and I got 1.
And I guess they wanted to give staff 3 chances to win in each category, so they did the first three spins and then the second three for a total of 6.
The embarrassing part is I'm on the analytics team. I just haven't done probability in this way in so long that what I thought would be an easy calculation has turned out to be complex.
lime gorge
Yea this kind of stuff gets real tricky real fast
tropic schooner
Right?
I was all excited to post it to the general Slack (they did this at a Town Hall and people were joking that the Analytics team must have rigged it). But then I was like, how do I calculate this?!
lime gorge
Lol that’s funny
lime gorge
So my question is, of us 3 people who were entered in 6 spins, what are the odds...
So here when you say that “what are the odds that we won 3 out of 6 of them”, are you asking the probability that the team won 3 spins total, or the probability that each person from ur 3-person team won 1 spin (aka 50% of all spins)
tropic schooner
I think it's the latter.
Like, "What are the odds that you three won half of those spins?"
Although I'm not opposed to the solution to the former also just because this is interesting to me.
But you're also kind enough to help for free, so no obligation of course.
I'm just an old math nerd with way rustier skills than I thought.
lime gorge
Ok let’s see
So three people
Person X, Person Y, Person Z
Potential events that satisfy this question are:
X wins spin 1, Y wins spin 2, Z wins spin 3
X wins spin 1, Y wins spin 2, Z wins spin 4
X wins spin 1, Y wins spin 2, Z wins spin 5
X wins spin 1, Y wins spin 2, Z wins spin 6
These are just a few
These events satisfy ur question right?
tropic schooner
I think so. Of six spins, I guess we'd be calculating the probability of all the combinations of three wins (one per person). Is that right?
tropic schooner
Yeah. I guess the complexity comes from the chances over possible outcomes varying a bit by person and by spin set (first vs. second 3 spins).
vocal sleetBOT
@tropic schooner Has your question been resolved?
lime gorge
Yes
tropic schooner
I'mma need some popcorn. This is exciting. lol
lime gorge
Ok I think this may be a bit tougher than it seemed at face value. To find the probability that each member of your group won exactly 1 out of the 6 spins, we need to find every combination of each member of your group winning 1 spin. Once you do this, you then plug in the probability of each win, then multiply them together and add every row in the table up. Ultimately, I think there will be 6! / (6-3)! = 120 different ways to “arrange 3 people among 6 different chairs”. Thus we will have 120 rows in our table. Here’s a sample table
this is just the first 16 rows
tropic schooner
With you so far.
lime gorge
but for example, to calculate the probability of combination 1
itd be
4/222 * 4/222 * 3/222
<@&268886789983436800>
wow eric ur perfect for this considering ur name
but ok lets continue
tropic schooner
Ha.
tropic schooner
Got it.
lime gorge
and so we'd have to add all 120 of these products up to find our probability
tropic schooner
Ok, so we multiply the probability of win combinations for every combo and then adding those products gives us the cumulative probability.
of the three of us winning 3 of 6 rolls
er, spins
I keep thinking dice.
lime gorge
of the three of us winning 3 of 6 rolls
of "each member of the 3-person team winning 1 spin", yes
im not tryna be pedantic, just making sure we're clear that its not about the team winning 3 spins in total
tropic schooner
This is one place where I think pendantism is warranted (and appreciated).
*pedantism
I'm sure that's not a word. lol
Ok, the odds of each member of the 3-person team winning one spin.
That's what I wanted to know! I'll build out a spreadsheet like the example you shared and look forward to finding out the answer.
tropic schooner
Well, I'd have to figure out the logic of setting up, but I imagine I can do so in R, yeah?
Define all the conditions and then have it iterate and produce all the rows?
And then it could get the products by row and sum them.
lime gorge
honestly im not all that familiar with R (i only know basic functions cuz i just started using it this semester), but yea that sounds good. for column 2(wheel won by person X), if theres a "1", "2" or "3" , code it to replace the value with 4/222. if theres a 4, 5, or 6, replace the value with a 2/92. Do the exact same for column 3. then do column 4 according to its probabilities. then you can make a new column which is the product of each row. then you can sum that new column to get the probability
this is pretty funny considering i literally have a data science project due in a few days with a process similar to this
tropic schooner
Ok, awesome!
It's wild how much time I spend every day writing SQL, R and Python scripting, running inferential models... yet this stumped me.
If you're at it this young, you'll do great.
I was always better at quant in social science settings. Less pure math.
lime gorge
If you're at it this young, you'll do great.
lol thanks, it was an interesting puzzle
lime gorge
I was always better at quant in social science settings. Less pure math.
ahh yea
no pure math for me either, i dont think i'd enjoy all that proofwriting haha
tropic schooner
Well thanks so much for your help, and all the best with your studies! This was a blast.
lime gorge
i had a lot of fun too, thanks for sticking around haha. no problem and thanks for the well wishes
have a good night
vast bridge
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vast bridge
i photo math to get iit right
but
i dont know how you get 2/3 rather than 3/2 like i did
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stuck girder
Can someone help me
vocal sleetBOT
Can someone help me
stuck girder
I had my report card and well it’s bad
I know this is a math serve
Server
But I’m DESPERATE for help
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thin root
Can someone help me recall how to get these from the
sum identities
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
cos(A+B) =cos(A)cos(B)+sin(A)sin(B)
thin root
I don't wanna memorize all of this
lime basin
Can someone help me recall how to get these from the
sum identities
sin(A+B) =...
Yeah so if you get cosa*cosb just remember 2 cos or 2 sin terms together are only in cos(a+b) or cos(a-b)
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mortal cloud
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mortal cloud
how did itg go from 1/3 to 1/9
outer warren
chain rule, due to the 3x in tan(3x)
gleaming sluice
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gleaming sluice
this ratio gives EXACTLY 3
how in the world do you come up with those boundaries
This is correct but it doesn't get me any closer to an explanation
viral copper
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simple urchin
how..?
graceful marlin
Hi! probability question. I'm really unsure how to approach this question, what formula to use and which values do I need to take?
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Hi! probability question. I'm really unsure how to approach this question, what ...
@graceful marlin Has your question been resolved?
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dark kiln
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spring tapir
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charred oriole
I was wondering if I could be given an idea where to start. I’m not sure how to get started solving the problem.
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pallid wren
covert granite
i mean u domt have any if the lengths
so u can only find x in terms of AB
oh wait x is also the angle
i see
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fiery oriole
I need help solving this question, I dont know where to go or start. This is my attempt but I dont think it is going in the right direction
vocal sleetBOT
I need help solving this question, I dont know where to go or start. This is my ...
vast shale
try expressing the fraction where the dominator is the real part ?
fiery oriole
do you mean from the original question?
vast shale
ye
fiery oriole
okay
hushed pewter
@fiery oriole I think you made a mistake here
fiery oriole
as far as I can see everything looks substituted properly, where is the mistake?
hushed pewter
Oh, the book made a typo here
hushed pewter
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fiery oriole
try expressing the fraction where the dominator is the real part ?
I did this
vast shale
compare the coefficients?
fiery oriole
could you elaborate on that
vast shale
i think u should have left the 34 + 34i on the right hand side
then simplified on the left hand side
and compared the real part and the imaginary part on the left hand side to the rhs?
fiery oriole
im trying to find an x and y right
wouldnt that be to prove that both sides are equal
wait
okay lemme try
vast shale
cz iirc ull form two simultaneous equations i think
and then u can solve for x and y?
vast shale
wouldnt that be to prove that both sides are equal
yes but ull get x and y terms on the LHS
which u can then use to make simultaneous equations comparing the imaginary and real parts
fiery oriole
i see I think i understand what you mean
vast shale
ye
fiery oriole
tys,
tysm
I finally got an answer lol
x=1 y=11
is there a way I can double check my answer?
nvm, tysm again!
.close
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plain aurora
Can I make the following claim?
vocal sleetBOT
Can I make the following claim?
hushed pewter
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Expand on this
plain aurora
median crane
Then post your solution
plain aurora
well
just decompose b via FTA
then we must have a and c as factors
i.e. a,c = product of finintely many primes in the prime factorisation of b
but then it follows that ac must also be a factor
i.e., just group together their constituent primes
hushed pewter
but then it follows that ac must also be a factor
How does this follow?
median crane
a=b=c=2
magic wasp
a=4, c=6, b=12
plain aurora
wth where is the hole in my argument then
ah it's because they can share prime factors aye
hushed pewter
but then it follows that ac must also be a factor
How does this follow?
plain aurora
$4=2^2$ and $6=2\cdot 3$ share the same 2
twin meteorBOT
Kalgar
magic wasp
Very restrictive
plain aurora
Very restrictive
you mean my claim is too restrictive to be useful?
well, this is the original motivation behind making the claim
I used inclusion exclusion
for multiples of 3,4,5,7
but then I need to take into account the intersections
so sets of numbers that are multiples of 3 AND 5 etc
i.e. 15
but 3 and 5 are coprime, so my claim applies right? >
Otherwise, how else could I have seen it
and done this question
magic wasp
Not sure how your claim would help tbh
plain aurora
Not sure how your claim would help tbh
Let |A| := {set of numbers that are multiples of 3}
|B|:={set of numbers that are mulitples of 4}
and so on
then, to answer the question, we require |A⋃B⋃C⋃D|
By the principle of inclusion exclusion, we have |A⋃B⋃C⋃D|=|A|+|B|+|C|-|A⋂B|-|A⋂C|-|B⋂C|+|A⋂B⋂C|+|A⋂B⋂D|+... and so on
Thus, we must consider each of the n-way intersections of sets,
i.e. |A⋂B|
magic wasp
By the principle of inclusion exclusion, we have |A⋃B⋃C⋃D|=|A|+|B|+|C|-|A⋂B|-|A⋂...
You're missing |D|
plain aurora
You're missing |D|
yeah I missed the three way intersetcions too
but you get the idea
cbb typing it out
twin meteorBOT
Kalgar
plain aurora
Right, and A⋂B are just the numbers divisible by the LCM of 3 and 4
yes, but why can you do this?
plain aurora
if a|b and c|b, then ac|b
because of this claim right?
hence why I asked in the first place
magic wasp
Yeah
magic wasp
Sure
plain aurora
wait, but technically my claim above could also be applied
just that, it's ... extra lol
magic wasp
Limiting a and c to be coprime makes your claim a "subset"
magic wasp
4|12 and 6|12, so LCM(4,6)=12 | 12
Yet 4 and 6 aren't coprime
I just mean your claim is less general
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lavish oriole
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haughty tusk
that one right too
haughty tusk
np
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fair prawn
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fair prawn
is the answer c?
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river minnow
is the answer c?
Yes
solemn ice
help
spiral inlet
The independent variable is x, you plug that into the equation to find the dependent variable, y
In fact, they already did the first one for you
solemn ice
they did??
spiral inlet
In the first row, see how they plugged in 3 for x, and got a value for the independent variable, y
spiral inlet
it's the thing you plug in, we often call it x
so in the first row, your equation was y = 2x+2
and they gave the independent variable the value of 3
so they plugged in 3 for x, and showed all the work in that middle box
y = 2x+2
y = 2(3)+2
y = 6+2
y = 8
spiral inlet
tbh I think the reason you're confused is because they showed the work in the first one RIGHT in the middle of the table, which is weird
so let's do the second row
spiral inlet
well let's take that equation from the second row
y = 3x-4
if we choose some value of x, that will determine the value of y
so like, take the equation:
y = 3x-4
and let's say, x=8
see how we can replace the x with 8
and get
y = 3(8)-4
solemn ice
why do you put the 8 there??
spiral inlet
because if x=8, that means x and 8 are equal. wherever you have x, you can replace it with 8
spiral inlet
yeah, x is a variable, so it "can" be anything, but in the second row, we're told that it's 8
so
y = 3x-4
becomes
y = 3(8)-4
solemn ice
so how do you solve it
solemn ice
how did you get 24?????
spiral inlet
yes
spiral inlet
this one?
twin meteorBOT
tatpoj
spiral inlet
We just do the calculation
see, you have 9 divided by 3?
and then you have 7.8 + that
spiral inlet
yep, same thing
solemn ice
oh
spiral inlet
man, I don't know how to write the oldschool divide sign in tex lol
but yes it's the same as 9 divided by 3
spiral inlet
what's 9/3?
solemn ice
10.8?
spiral inlet
yep 👍
solemn ice
oh sick thank you
spiral inlet
sure thing 👍
solemn ice
im really bad at math if u cant tell
spiral inlet
no worries lol
solemn ice
do i do the same for the others or are they different
spiral inlet
np 👍
solemn ice
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slow atlas
Hi can someone help me with some calc 3 problems
vocal sleetBOT
Hi can someone help me with some calc 3 problems
slow atlas
If someone could hop in call and let me stream and exam and explain some things it would be nice
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thin vale
If someone could hop in call and let me stream and exam and explain some things ...
That’s not the purpose of this server. You can post your question in this channel if you have one. Otherwise close it
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night beacon
anyone help me with factor bionomial