that
#help-13
dire geode
what are the numbers
lunar mica
for what n?
dire geode
.
lunar mica
n=1 , t(1) = 1
n=2, t(2) = 2t(1)+2 = 4
n=3, 3t(2)+3 = 15
n =4, 4t(3)+4 = 64
is this what you mean?
lunar mica
bro... i cant do that for exam later
dire geode
Oh
You're just looking for big Theta. Since you're multiplying the previous number by n, it grows as factorial
The +n is negligible
dire geode
You're just looking for big Theta. Since you're multiplying the previous number ...
do you know what factorial means?
lunar mica
yes
dire geode
but how do I prove it mathematically?
repeated substitution and/or induction could work. similar to mergesort solution here:
Analysis of Mergesort
https://web.njit.edu/~nassimi/cs610/notes/3 Recursive Algorithms.pdf
hollow niche
My professor doesn't have lectures. This is for calc 2 and im very lost. Does anyone understand this?
hollow niche
<@&286206848099549185> can anyone help?
dire geode
read
cedar kilnBOT
@hollow niche Has your question been resolved?
cedar kilnBOT
@hollow niche Has your question been resolved?
tulip river
Hello guys, why does sinx=-1/10 have 2 results in 0 <= x <= 2pi? shouldnt it be only 1?
sharp lotus
sin (x) = -1/10?
flint plinth
sen is sine?
tulip river
Yes
flint plinth
plot the function, there are two points corresponding -1/10, or to any y value with -1 < y < 0
indigo warren
This is the formula I used to find the percentiles and I'm confused where would the 1st - 4th and 96th - 99th percentile fall in?
cedar kilnBOT
This is the formula I used to find the percentiles and I'm confused where would ...
@indigo warren Has your question been resolved?
cedar kilnBOT
@indigo warren Has your question been resolved?
cedar kilnBOT
@indigo warren Has your question been resolved?
cedar kilnBOT
@indigo warren Has your question been resolved?
indigo warren
No it hasn't
cedar kilnBOT
@indigo warren Has your question been resolved?
indigo warren
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
elfin wedge
wouldn't applying bayes thm give P(E intersect F |A)p(A)?
cedar kilnBOT
wouldn't applying bayes thm give P(E intersect F |A)p(A)?
elfin wedge
why is the intersection with A and F instead?
cedar kilnBOT
@elfin wedge Has your question been resolved?
elfin wedge
<@&286206848099549185>
crimson sedge
P(E ^ F | A) * p(A) = P(E | A ^ F) * p(A ^ F)
cedar kilnBOT
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cedar kilnBOT
cedar kilnBOT
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delicate ember
does (-1)^x have a graph? I tried plugging it into desmos but it's plotting nothing
slow thorn
try y= (-1)^x
delicate ember
nothing
I was expecting at least some points like (1, -1), (2, 1) but they aren't even plotted
is the domain of (-1)^x = Z?
tropic oxide
most graphing tools are not designed to handle functions which could only be plotted on a set of isolated points
slow thorn
i got (0,1)
delicate ember
so they don't plot discrete functions?
tropic oxide
if by "discrete function" you mean "a function whose domain is discrete in the topological sense" then yes
delicate ember
probably that yeah
tropic oxide
there are ways to plot individual points and even lists of points in desmos tho
delicate ember
so this is undefined?
fair hare
does (-1)^x have a graph? I tried plugging it into desmos but it's plotting noth...
it does plot
delicate ember
but it would be possible if I substituted e^ipi = -1?
fair hare
desmos looks at real numbers lol
delicate ember
yes ik
tropic oxide
well if you wanted to do $\int_0^1 e^{i\pi x} \dd{x}$ then this is perfectly valid and can even be integrated without much trouble
wraith daggerBOT
Ann
delicate ember
yeah I got $\frac{-2}{i\pi}$
wraith daggerBOT
ホタル
tropic oxide
good for you.
quiet tusk
So I have a friend group of 4 or 5 and we need to choose 5 people to be in next tutor group, and it is optional to write how many person. But I think the teacher will be suspicious if we have all 100% and making a big chain, so I am trying to think of a way to get all of us to be in the same tutor group. But idk how, so I need help thx !
quiet tusk
I want to get it close as possible to 100% if 100% is not achievable
cedar kilnBOT
@quiet tusk Has your question been resolved?
quiet tusk
<@&286206848099549185>
zenith sail
What is your question? I dont understand
cedar kilnBOT
@quiet tusk Has your question been resolved?
delicate ember
How do I remember these 💀
cedar kilnBOT
How do I remember these 💀
crimson sedge
How do I remember these 💀
💀
It generally becomes a habit
The more problems u solve
tropic oxide
well the sin and cos ones are more crucial to commit to memory than the others imo
crimson sedge
I only used to remember cos and sin when I started
tropic oxide
for the other four named functions just think of them as reciprocals and ratios of cos and sin and you can recover the same identities
crimson sedge
for the other four named functions just think of them as reciprocals and ratios ...
Ya like the trig table
tropic oxide
and for sin and cos remind yourself of the unit circle
delicate ember
ic, I guess with practice I'll be able to remember them, but I do notice a pattern that if its odd multiple of pi/2 +- x then the original function changes to the co function 
and for even multiples the function is the same
cedar kilnBOT
@delicate ember Has your question been resolved?
dusky gate
cedar kilnBOT
cedar kilnBOT
Available help channel!
umbral sparrow
cedar kilnBOT
umbral sparrow
I did 0.6*0.0.3 and got 1.8 percent but the teacher answer says 4.5 percent
am i wrong or is the teacher
wanton minnow
I believe 4.5 percent is the correct answer
The key to solve this is in this part of the question: “Given that the patient tests positive for the disease, …”
umbral sparrow
The key to solve this is in this part of the question: “Given that the patient t...
but how would we go in reverse?
wanton minnow
idk :[
umbral sparrow
aw, im a bit confused but im trying to put it in a 2 way chart rn
glacial pollen
its not 0.6*0.03
its (0.6*0.03)/((0.6*0.03) + (0.4*0.95))
,calc (0.60.03)/((0.60.03) + (0.4*0.95)) * 100
wraith daggerBOT
Result:
4.5226130653266
which is 4.5 percent
umbral sparrow
its `(0.6*0.03)/((0.6*0.03) + (0.4*0.95))`
where would the 0.4*0.95 come from?
glacial pollen
You are tasked to find $P(A | B)$ and you know that $P(A | B) = \frac{P(A) \cup P(B)}{P(B)}$
wraith daggerBOT
jixana
umbral sparrow
mhm
glacial pollen
where would the 0.4*0.95 come from?
you want P(B) now, but you need to total up the probability for P(B)
$P(B) = P(B)P(A) + P(B)P(A^c)$
wraith daggerBOT
jixana
umbral sparrow
mhm but how would i find the P(b) if thats in the equation
glacial pollen
you are already given P(B)P(A) and P(B)P(A^c) from the tree diagram
you add them together
cedar kilnBOT
umbral sparrow
tysm btw
cedar kilnBOT
Available help channel!
quiet shadow
Hey I asked this before but cant find it and I can't remember the reason
rustic siren
quiet shadow
That doesn't really help me, I know they are the same numbers, I just wanna know when I can do this, or why
Doesn't seem intuitive
whole ember
if you mean why you should write it like that, then we'd need more context
lament sonnet
That doesn't really help me, I know they are the same numbers, I just wanna know...
You use the fact that $\lim_{x \to 0} \dfrac{\sin x}{x} = 1$, and so the reciprocal x/sin(x) also tends to 1 as x tends to 0. Then it's just substitutions y=2x and y=6x.
wraith daggerBOT
1345631
rustic siren
or you have problem with why (x/y) * (a/b) is (x * a) / (y*b)? @quiet shadow
quiet shadow
I suppose so yes
quiet shadow
I dont really get it, ive been away from math for a while so simple stuff like this confuse me now
:/
rustic siren
or you have problem with why (x/y) * (a/b) is (x * a) / (y*b)? <@254279757...
okay, then use this rule, and ur fine
cedar kilnBOT
@quiet shadow Has your question been resolved?
fair linden
This is gonna sound dumb but how did this happen?
K so differentiating with respect to x we have d(y^(1-n))/dx = dv/dx
now we can do d(y^(1-n))/dy * dy/dx = dv/dx
fair linden
what happened to the (1-n) that is to be multiplied on the left hand side
It seems like I am right
crystal raptor
What happens to the power when you differentiate, in general?
fair linden
What happens to the power when you differentiate, in general?
Well for example differentiating with respect to x and if we had the function x^n we would have n * x^(n-1)
crystal raptor
Oh I see what you're saying
fair linden
They missed the n part here
crystal raptor
Yes indeed
fair linden
which would happen to be (1-n) in this case
Oh alright that confused me and I panicked that I forgot how to differentiate basic stuff and had to ask here 
Thanks
.close
analog shell
I want to use sigma to make a function which basically adds multiples of six. So it would go 6, 18 (6+12), 36 (18 + 18), 60 (36 + 24) etc. How can i do this? I am new to Sigma (or advanced algebra in general), so i'm sorry if this is a stupid question
crimson sedge
I want to use sigma to make a function which basically adds multiples of six. So...
Hi, how would we write a multiple of 6 in general ?
analog shell
I've got to be honest: I do not understand the question. I am finishing 9th grade rn, so all this is very new to me. My best guess in n6
crimson sedge
I've got to be honest: I do not understand the question. I am finishing 9th grad...
Yes! this is correct, n is a multiple of 6 iff there exists k such as $n=6k$
wraith daggerBOT
AimaneSN
crimson sedge
So how would you write the function adding multiples of 6 with this in mind
or an easier question, how would you write two consecutive multiples of 6 (in general)
analog shell
i have no clue, sorry
crimson sedge
Okay no problem. We have 6=6x1, 12=6x2, 18=6x3, etc. each time we increment the factor in the right by 1, right ?
analog shell
yes, i think i understand that
crimson sedge
good! so for example the multiple of 6 that comes after 6x100 is what ?
analog shell
6*101?
crimson sedge
6*101?
Yep! exactly
So what comes after the multiple 6k ?
k is any number
(an integer of course)
analog shell
6(k+1)?
analog shell
6(k+2)
crimson sedge
exactly, you got it now
So the multiples of 6 are 6k, 6(k+1), 6(k+2), 6(k,3), etc.
with k taking what values ?
analog shell
integers
analog shell
all at once or individually?
crimson sedge
all at once or individually?
let's say we want their sum
the sum of the first 100 multiples of 6
what values would k take above
analog shell
?
analog shell
!!!!!!!
crimson sedge
what about the sum of the first n multiples of 6 ?
analog shell
Thank you so much! i'm so glad that you took time out of your day to teach me, and i wish all teachers (any teachers, really) were like you. Have a nice day, and again, tysm
.closed
crimson sedge
You're welcome buddy 
quartz ledge
hi
dire geode
quartz ledge
actually nvm ill go, its a series of questions…
dire geode
.close to free up the channel
quartz ledge
.close
stuck oyster
cedar kilnBOT
stuck oyster
How do I approach that
To find the f’(t) abs f(t) equations
Is it MVT?
Or something
strong lantern
f'(0) = 4 AND f'(0) = 8 ?
stuck oyster
Oh my mistake I think it’s supposed to be f(0) = 4 and f’(0) = 8
Ohh I got it!! It’s just anti derivatives
strong lantern
yes
cedar kilnBOT
@stuck oyster Has your question been resolved?
Available help channel!
@crimson sedge Has your question been resolved?
dire geode
you just need to use the definition of simple pole
versed pine
does anyone know, what is this step with div ((13(2+i)/(2i-3)) called ?
upper abyss
Take a look for "How to divide a complex number"
The step is specifically called "multipliyng by the conjugate"
versed pine
Just a sec, i will check
Soo whats below, we multply bouth, up and down but in conjugate version ?
I understand now
Almost the same as doing regular ones
but here you have a+bi
or a-bi
depends on problem
Cool
thanks for awnser 🙂
.close
cloud tusk
tight herald
Identify the scale factor
cloud tusk
whats a scale factor
tight herald
Why are you being asked this question if you don't know what that is?
Hmm
Well
Have you learned setting up proportions?
cloud tusk
i have not
tight herald
dire geode
Why are you being asked this question if you don't know what that is?
step 1 to being a helper: assume the person asking doesn't know anything about their problem
tight herald
step 1 to being a helper: assume the person asking doesn't know anything about t...
Lol
Do you know what similarity is @cloud tusk
cloud tusk
simplified is 5/2
cloud tusk
so what would i put in the angle box
tight herald
oh for angle?
cloud tusk
mhm
tight herald
Since the figures are similar, they share the same corresponding angles
Does that make sense?
cloud tusk
not to me now
tight herald
Hmm let me think of a way to explain
A bad drawing, but it gets to the point
A and b are corresponding angles, since the figure is similar we can say that a = b
Assuming it is similar
cloud tusk
mhm
tight herald
So, does that help?
cloud tusk
yessir
ok but in my picture
a-b is unknown
how do i figure out what the variable is?
then finding out what angle is
or is
that what im doing basically
tight herald
Angle D corresponds to angle N, in the two figures
Since they are corresponding angles in a similar figure, they are the same (Congruent)
You can notice this pattern for the other angles too
cloud tusk
so seeing that theyre the same
does that mean that
b = 98.87?
and then
n = 141.87
i also applied the scale factor for the sides making LM = 20, AB = 4
cloud tusk
<@&286206848099549185>
cedar kilnBOT
@cloud tusk Has your question been resolved?
cedar kilnBOT
@cloud tusk Has your question been resolved?
cedar kilnBOT
@cloud tusk Has your question been resolved?
cloud tusk
<@&286206848099549185>
crimson sedge
obsidian coral
Don't do people's work for them
crimson sedge
i also applied the scale factor for the sides making LM = 20, AB = 4
he already did it
obsidian coral
Yet you pretty much posted the answers
You can confirm their answers if needed but you don't need to post things like that
crimson sedge
oh ok wont happen again
cedar kilnBOT
@cloud tusk Has your question been resolved?
torn hare
u could just do the polynomial to 1/2 and then use u sub
yes
yes
u also need a dx on that too
but, now i realize there is issue.
-2xdx
the issue is that there is an x in the derivative
thus it is more difficult to then find your integral since now it has a u in terms of dx
correct, sorry i didn't spot it sooner
i have just googled
it appears it is a somewhat complex approach
it requires trig sub
according to the internet
all good
this is the sub
here is the first part of the answers
fallow locust
im having a tough time with this problem. I'll post the test associated with the picture in a moment.
Mainly, the issue is that when I try to solve for the CDF that I keep getting inconsistent constant values associated with the integral of the PDF. I think I should be able to solve using the monotonic theorm after I get the CDF -> use plug inverse g into F_{X}. However I wanted to double check this step
fallow locust
ok so first this is my range $y: [\frac{3}{26}, \frac{81}{26}]$
wraith daggerBOT
BeeGass
fallow locust
$$
\begin{align}
Y = X^{\frac{1}{2}} \
y = g(x) \ \
X = Y^{2} \
x = g^{-1}(y) \ \
y = g(x) = x^{\frac{1}{2}}\
x = g^{-1}(y) = y^{2}\ \
\bigg\rvert \frac{dx}{dy} \bigg\lvert = 2y \ \
f_{Y}(y) =
\begin{cases}
f_{X}(g^{-1}(y)) \bigg\rvert \frac{d}{dy}g^{-1}(y) \bigg\lvert & \text{if } y=g(x) \text{ for some } x \
0 \text{if } y \neq g(x) \text{ for all } x
\end{cases}\ \
F_{x}(x) = \int f(x) \ dx \
= \int \frac{3}{26}x^{3} \ dx \
= \frac{3}{26} \int x^{3} \ dx \
= \frac{3}{26} \cdot \frac{x^{4}}{4} + C \
= \frac{3x^{4}}{104} + C \\
0 = \frac{3}{104} + C \
C = -\frac{3}{104} \\
F(x) = (\frac{3x^{4}}{104} - \frac{3}{104}) \
= \frac{3}{104}(x^{4} - 1) \\
1 = \frac{3}{104}((3)^{4} - 1) \
1 = \frac{3}{104}(81 - 1) \
1 = \frac{3}{104}(80) \
1 = \frac{162}{104} \
\end{align}
$$
wraith daggerBOT
BeeGass
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fallow locust
**BeeGass**
Compile Error! Click the <:errors:504266556054962196> reaction for m...
ok I hope this is ok. That is my current (incorrect) work
cedar kilnBOT
@fallow locust Has your question been resolved?
fallow locust
<@&286206848099549185>
if you know probability and calculus I would be very appreciative if I could get a second pair of eyes
<@&286206848099549185>
dire geode
mistake here
You have exact limits for the integral. Why are you even solving for C?
fallow locust
You have exact limits for the integral. Why are you even solving for C?
im not exactly sure why but I thought it was because I need to find the constant associated with the integral of the PDF where the CDF "begins". My understanding is F(1) = 0
given that PDF is denoted as f(x) and CDF is denoted as F(x)
dire geode
im not exactly sure why but I thought it was because I need to find the constant...
$\lim_{x\ra 1-} F(x) = 0$ is true yes
wraith daggerBOT
riemann
dire geode
But
$\lim_{x\ra 1+} F(x) = \frac{3}{26}$
wraith daggerBOT
riemann
dire geode
draw this and you'll see
fallow locust
But
$\lim_{x\ra 1+} F(x) = \frac{3}{26}$
I dont fully understand this. How do you know?
wraith daggerBOT
fallow locust
also im not sure if it helps to justify what im doing what im doing but im referencing an old homework. I would be eternally grateful if you could help me make sense of it. Maybe this will also help with the fact the integral doesnt integrate to 1.
dire geode
just screenshot. don't make ppl dl files
fallow locust
fair
one sec
sorry in advance for the wall of screenshots
its not exactly the same question but its very similar
dire geode
yea at no point do they actually integrate the pdf of x
so i don't know why you're trying to
you sorta did some of this and just gave up
right track here
fallow locust
yea at no point do they actually integrate the pdf of x
I thought that was what was happening here
dire geode
oh right
fallow locust
you sorta did some of this and just gave up
yeah I gave up because I needed to know how to input into f_{x}. atleast i think
dire geode
idk pick one method and stick to it
fallow locust
oh am I trying to both do this algebraically and show using the monotonic theorem? my bad. I would like to try to use the monotonic theorem. I just didnt think I had all the pieces
fallow locust
this is what I hope to do
fallow locust
$$
\begin{align}
Y = X^{\frac{1}{2}} \
y = g(x) \ \
X = Y^{2} \
x = g^{-1}(y) \ \
y = g(x) = x^{\frac{1}{2}}\
x = g^{-1}(y) = y^{2}\ \
\bigg\rvert \frac{dx}{dy} \bigg\lvert &= 2y \ \
f_{Y}(y) =
\begin{cases}
f_{X}(g^{-1}(y)) \bigg\rvert \frac{d}{dy}g^{-1}(y) \bigg\lvert & \text{if } y=g(x) \text{ for some } x \
0 & \text{if } y \neq g(x) \text{ for all } x
\end{cases}\ \
f_{Y}(y) = (\frac{3}{26}(y^{2})^{3})(2y) \
f_{Y}(y) = (\frac{6}{26}y^{7})
\end{align}
$$
wraith daggerBOT
BeeGass
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
fallow locust
PDF = f_{Y}(y)
I think
oh and for the sake of simplifying
$f_{Y}(y) = (\frac{3}{13}y^{7})$
wraith daggerBOT
BeeGass
wraith daggerBOT
BeeGass
cedar kilnBOT
@fallow locust Has your question been resolved?
cedar kilnBOT
@fallow locust Has your question been resolved?
cedar kilnBOT
@fallow locust Has your question been resolved?
cedar kilnBOT
@fallow locust Has your question been resolved?
steep pelican
how do i do this?
cedar kilnBOT
how do i do this?
foggy merlin
look at the common factor of each term
steep pelican
bruh
sonic thistle
it really is
steep pelican
i dont care about the anwser
i want to learn how to switch from standored form to factored form
sonic thistle
just distribute
upper garnet
compact rain
looking for help on this stats review!
cedar kilnBOT
looking for help on this stats review!
@compact rain Has your question been resolved?
compact rain
<@&286206848099549185> 
cedar kilnBOT
@compact rain Has your question been resolved?
compact rain
brah
cedar kilnBOT
@compact rain Has your question been resolved?
pallid spire
cedar kilnBOT
upper abyss
AC is really code for C - A
upper abyss
I'd just do what they're doing
upper abyss
or as components of i j and k
That's the same. Choose your favorite.
pallid spire
I'd just do what they're doing
do i take the difference fo the two points?
upper abyss
Ye
cedar kilnBOT
@pallid spire Has your question been resolved?
cedar kilnBOT
pallid spire
.reopen
cedar kilnBOT
✅
pallid spire
cedar kilnBOT
@pallid spire Has your question been resolved?
cerulean star
Mathematics Discord is not a good place to seek definitions
you are better off finding a description you like from a search engine
Several benefits for this:
- it's fast
- you can curate the definition that makes sense to you
- pretty pictures (sometimes)
- videos
- we don't need to type rigorously accurate descriptions or discuss their context at length since that has already been done countless times elsewhere. We can focus on the application of the definition instead.
- ...and your math problem can get solved faster.
Dot Product: https://www.youtube.com/watch?v=LyGKycYT2v0
Cross Product: https://www.youtube.com/watch?v=eu6i7WJeinw
Enjoy.
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
I'm given the following question:
A 25-foot latter is leaning against a house. The foot of the latter is being puller away from the house at a constant rate of 1 meter/second. At what rate is the angle that the latter makes with the ground changing when the foot of the latter is 15 meters from the wall.
As I repeatedly err when attempting to solve it, might someone review my process for solving this?
crimson sedge
I see this as a triangle of base (x), height (y), and hypotenuse (25). time = t.
The angle between the base <-> hypotenuse = theta.
I want to solve (d theta) / (d t), for (x = 15).
At this point, it's intended that I use cos/sin/tan of the theta, then derive it, and algebraically solve for (d theta) / (d t).
(I'm not sure which one to chose, or whether it matters? Any should work?)
I arbitrarily chose cosine:
cos(theta) = x / 25
cos'(theta) × (d theta) / (d t) = x' / 25
(d theta) / (d t) = (x' / 25) / cos'(theta)
cos'(theta) = -sin(theta)
sin(theta) = y / 25
y = √(25² + x²)
upper abyss
Yeah all looks good
crimson sedge
y = √(25² + x²)
wait, this should be negative?
crimson sedge
y = √(25² - x²)
So, I'm left with
(d theta) / (d t) = (x' / 25) / [√(25² - x²) / 25]
After substitution for x' = 1, and x = 15, and running through a calculator, the online platform says that my solution is incorrect?
crimson sedge
So, I'm left with
(d theta) / (d t) = (x' / 25) / [√(25² - x²) / 25]
simplification: = (x') × [1 / √(25² - x²)]
Oh... wow, when substituting the sin & √ expression, I forgot the -sin(...)
negation..
Okay, that was all
.close
torn atlas
kind of confused about this, i thought cos(x) didn't have a limit at infinity?
crimson sedge
yeah but if you take the limit on the LHS of the inequality and RHS side of the inequality you get 0
so by squeeze theorem it's equal to 0
torn atlas
bc it was just oscillating ? or maybe it does have a limit because it is always some value away from zero ?
yeah okay, that makes sense i guess
crimson sedge
we're talking about a sequence here not a function
torn atlas
yeah i thought that might be where i was confused
so generally speaking does the sequence cos(n) converge?
tropic oxide
why does this say $\leqq$ and not $\leq$
wraith daggerBOT
Ann
tropic oxide
no, the sequence cos(n) does not converge
crimson sedge
as n goes to infinity? no
torn atlas
i'm not sure
crimson sedge
typo, probably
or maybe it's the same thing idk
i've personally never seen that notation before
tropic oxide
it's weird stylistically
torn atlas
okay so its literally just by virtue of the fact that we're using the squeeze theorem
tropic oxide
that's all
crimson sedge
okay so its literally just by virtue of the fact that we're using the squeeze th...
yessir
tropic oxide
yes we are using the squeeze theorem here.
torn atlas
yeah okay I'll take that. It feels a bit weird but I guess I'll get used to it
i guess the oscillation doesn't matter if you're just always dividing by infinity
i think that solves it, .close
.close
true nebula
Hey, I have this question; I know how to find the centre of mass of the two balls at launch, but how do I find how much they have moved?
true nebula
I found this relationship, but I dont know how to answer 1 or 2
i found this?
does that mean it moves
2 to the right?
Therefore the combined balls should land at x = 2
Therefore to answer b), the centre of mass moves 4 meters?
pls let me know if im right 😭
cedar kilnBOT
@true nebula Has your question been resolved?
reef venture
why did you substitute Vf = x/t? will the time it takes to fall down be the same as the time t given that the mass is 3m now?
true nebula
why did you substitute Vf = x/t? will the time it takes to fall down be the same...
im not sure 😭 what my process was. I got lost and desparate and chose that but yeah, iw oul dneed to find the time it takes for it to fall down if that was the case
reef venture
yeah I don't think you can substitute Vf as x/t
wait
nvm
It would be the same
cuz mass doesn't affect g
you're correct then
reef venture
no, if you drop m1 and m2 they will take the same to fall down
a feather and bowling ball will take the same time too (neglecting air resistance)
because
s = 0 + 1/2gt^2
true nebula
ah i get it
was my process correct then?
that it moves 2m to the right?
from the connection point*
reef venture
I think yes
true nebula
therefore the balls would land at x = 2
and since the centre of mass is at x = -2
that means the centre of mass travelled 4 m right?
reef venture
yes
soft sky
Teams are to be selected randomly from 12 people. If a team of 5 people is to be selected, what is the probability that it will contain the two oldest people?
I know the sample space would be 12C5, but I dunno what the numerator would be... I think it would be 12C2 * (something)
reef venture
Teams are to be selected randomly from 12 people. If a team of 5 people is to be...
so we can think of it like this
there is 1 oldest person, and a 2nd oldest person
and we need to select them
so
12C1 * 11C1 * 10C3 (any other 3)
it wouldn't be 12C2 because that is selecting any two people (not necessarily the oldest 2 people)
soft sky
Ah okay, that makes sense
reef venture
in general, if you have to select 'n' specific people there is only 1 way to select all n of them (nCn)
reef venture
sure
soft sky
Teams are to be selected randomly from 12 people. Two separate teams are to be selected: 1 is to have 3 people and the other is to have 4 people. How many different pairs of teams are possible?
Would it just be 12C3*9C4?
reef venture
I think yeah
quartz ice
I am currently working on a hill encryption and I’m currently trying to figure out how mod 26 works, all of the tutorials I have found have been unhelpful.
quartz ice
I am currently working on a hill encryption and I’m currently trying to figure o...
To clarify I am working on both encryption and decryption.
manic stratus
Are you asking about the mathematical function modulus?
manic stratus
Idk I think of them as the same
reef venture
they are not
obsidian coral
I am currently working on a hill encryption and I’m currently trying to figure o...
Do you understand what modulo is?
obsidian coral
But that is not the point <@556119013298667520>
Yes it is the point, because you should use the terms properly
manic stratus
@quartz ice 'modulo' is basically division but instead of returning a number, it returns a remainder. So 8 mod 3 is 2, and 7 mod 6 is 1. If we have x mod 26, then the function would return the remainder of x/26. It can also be thought of as b mod a = r, put more simply as ax+r=b
reef venture
@quartz ice let's say I had a letter c, and a key 10
if I convert c to 3, and multiply it by 10 i'd get 30, but we want this number to be mapped to another letter so we perform 30 mod 26, which in essence is the remainder of 30/26, or 4 or 'd'
this operation would convert any natural number to a number between 0-25, or 'a' to 'z'
quartz ice
Good god I’m an idiot
reef venture
what happened lol
reef venture
What if your mod is higher than your base?
What do you mean by that
manic stratus
something like 7 mod 8
reef venture
ah then it's just 20
manic stratus
20 = b, 26 = a
ax + r = b
26x+r=20
x=0, r=20
reef venture
if you divide 20 by 26 you'd get a number less than 1, which means the quotient is 0 and remainder is 20
quartz ice
Then subsequently how do I reverse that in decryption
reef venture
in decrypting you'd still do, mod 26 only
the operation doesn't change only the key matrix is inversed
quartz ice
Thank you, I have a presentation on Monday and this is a lifesaver
true dirge
Hello
still holly
cedar kilnBOT
still holly
how to do c??
tropic oxide
@still holly were you able to do part b?
still holly
yyes
tropic oxide
right
so if the equation read log(something with x) = <number> you would be able to solve it, yes?
still holly
yess
tropic oxide
right
so now take 4 + 8 log(4x) = 20
can you rewrite it so that log(4x) is isolated?
still holly
ohhh am i meant to do log(4x)^4+8
still holly
wym isolating it
tropic oxide
rewriting the equation so it reads log(4x) = ___
still holly
i minused 4
then divided by 8
is that right
and ended up with loge(4x) = 2
then i had 4x = e^2
but when i do e^2/ 4
the answer doesnt work as x
tropic oxide
it says log there
and from context it looks like decimal log and not natural log
natural log is written with ln in your problem
still holly
is it meant to be ln??
tropic oxide
no
still holly
I was tryna copy this method
tropic oxide
you were trying to copy...
but you ought to know how to solve linear equations, no?
tropic oxide
yeah so
what does it matter if the thing you're solving for is log(something) or ln(something) or something more scary
4 + 8 * [big mess] = 20
should not require you to "copy" anything to rewrite that into [big mess] = 2
still holly
cause that is the working for a similar question
tropic oxide
ok and?
for those two steps it literally does not matter whether you have log or ln or whatever
and you should realize that
still holly
im new to the log stuff
tropic oxide
so what
tropic oxide
for those two steps it literally does not matter whether you have log or ln or _...
.
just because you're learning about logs does not mean the laws of algebra you're already familiar with get thrown out the window
still holly
so where have i gone wrong in my working?
tropic oxide
i minused 4
then divided by 8
is that right
and ended up with loge(4x) = 2
then i had 4x = e^2
but when i do e^2/ 4
the answer doesnt work as x
is this your work?
still holly
yess
tropic oxide
you went wrong precisely when you read the log as log_e.
still holly
that is what my teacher did in her working
tropic oxide
which i said already, when you're only starting to learn about logarithms log without a base will refer to base 10, and logarithm to base e will be written as ln.
tropic oxide
that is what my teacher did in her working
for THIS problem or for the working in blue that you tried to copy?
still holly
the working in blue
tropic oxide
the working you tried to copy started out with ln.
she had a natural logarithm, while you have a decimal logarithm.
still holly
ohhh so i should have never went to ln
tropic oxide
you should have never misread the log as referring to log_e, yes.
still holly
okay ill try work through my question with no log_e
rugged palm
Hi! I have to start with an equation and end up with 2*tan(a)
rugged palm
I have to use basic identities only
Here's where I'm stuck
$\tan\left(a\right)+\dfrac{\sin^3\left(a\right)}{\cos\left(a\right)}+\cos\left(a\right)\sin\left(a\right)$
wraith daggerBOT
Nonna
dire geode
Hi! I have to start with an equation and end up with 2*tan(a)
are you starting with a specific equation?
rugged palm
Yes
dire geode
is it important to your question?
rugged palm
Wait, I'll type what I'm starting with
$2\tan\left(a\right)+\dfrac{\sin^2\left(a\right)}{\tan\left(a\right)}+\dfrac{\sin^3\left(a\right)-\sin\left(a\right)}{\cos\left(a\right)}$
wraith daggerBOT
Nonna
quartz vale
factor out sin(a) in the numerator of the third term
apply fundamental identity
and express the 2nd and 3rd terms in terms of sin and cos
rugged palm
factor out sin(a) in the numerator of the third term
From the beginning or from where I got stuck?
quartz vale
beginning
rugged palm
ok
unique meteor
livid hound
cedar kilnBOT
winged owl
oh im sorry
cedar kilnBOT
Available help channel!
hallow walrus
Idk how to do this
cedar kilnBOT
Idk how to do this
steady mason
cedar kilnBOT
steady mason
Can anyone teach me how to do part i? I stuck
cedar kilnBOT
@steady mason Has your question been resolved?
quiet lagoon
I'm trying to do part 2 of this question;
if I have understood what was written in part a correctly; we only have:
p(black car) = 0.8
-> p(not black car) = 0.2
p(Correctly Identified | Black Car) = 0.7
p(Correctly Identified | not black car) = 0.9
of which I think to answer part 2; to find P(Black|Correctly Identified); I need to find out what p(Correctly Identified) is; as the other values are already known, but I can't figure that out.
quiet lagoon
I get to here and then get stuck as I cant just substitute the P(Black car | correctly identified) into the p(correctly identified | black car) as then the p(identified) is just cancelled out
part of me thinks I've misunderstood how the conditional probabilities should be written out in what is written in part a; as its worded fairly confusingly to me.
cedar kilnBOT
@quiet lagoon Has your question been resolved?
cedar kilnBOT
@quiet lagoon Has your question been resolved?
quiet lagoon
.close
vast pike
which ring is R ?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
violet flume
is this abstract algebra?
what even is this
you might wanna ask in a dedicated channel @crimson sedge
people who like complicated math dont always putz around in these channels
cedar kilnBOT
@crimson sedge Has your question been resolved?
cerulean gale
Hello
lofty ridge
Disclaimer: This is not a very important question
So I saw this image in a discord server, it is very evidently a joke but I'm curious if its theoretically solvable
trim sentinel
You got 6 variables and 6 equations so ig yea
upper abyss
Basically a 2D heat transfer problem?
dire geode
Rewrite it in terms of real variables instead of stupid emojis
lofty ridge
I think that would take away from the stupidity of the problem
upper abyss
These are solved, but the solutions aren't satisfying
lofty ridge
Which is not ideal given the joke
crimson sedge
I have attempted to draw solution or illustration for two algebra expressions, one a3-b3, another (a-b)3. Are these solutions correct?
crimson sedge
I am fairly confident the illustration for a3-b3 is correct
modern compass
those look like correct expansions, yes
I don't know what you're trying to do with them though
crimson sedge
I don't know what you're trying to do with them though
In my math book I need to "verify" this apparently
modern compass
verify what?
that's the difference of cubes formula. That's what a^3 - b^3 equals
zenith sail
100%, my bad
crimson sedge
that's the difference of cubes formula. That's what a^3 - b^3 equals
is the (a-b)^3 true also
modern compass
yes
candid shoal
An analytical student is looking for a business over time. The X is given as an analytical result. The difference between the analysis and the analysis is normal with the stochastic variability of the inventory E (Y) = β0 + β1x and the standard deviation σ = 0.15. After observing the final analysis on:
b) Can it be shown that the annual turnover increase, β1, is greater than 0.5?
Formulate appropriate hypotheses and perform the hypothesis test at 0.1% significance level.
Critical value, k = ?
c) Find a 99% confidence interval for expected sales for x = 5.
d) Find a 90% prediction interval for turnover for x = 3.
candid shoal
Found out that
and that the formula for the confidence interval is
I got the standard deviation in the task, 0.15. the mean of x is 3,6 I guess I should use this one
that's how I tried to solve c, but I know that it's wrong
<@&286206848099549185>
cedar kilnBOT
@candid shoal Has your question been resolved?
cedar kilnBOT
@candid shoal Has your question been resolved?
candid shoal
.close
misty sail
https://cdn.discordapp.com/attachments/962367893352370267/972976521402781787/IMG_20220508_224026.jpg
I want to be able to know how to solve something like this as I have a math test tomorrow... it'd be great if someone could help
crimson sedge
which q in particular?
misty sail
10 in general
it's the first one I've seen of this kind and I want to make sure I can solve it
crimson sedge
do you know how to find BC?
olive stump
Can someone explain what to do in here?
cedar kilnBOT
Can someone explain what to do in here?
@olive stump Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
willow cove
Let $(X,d)$ be a metric space and let $S\subseteq X$ and define $d_S := d|{S\times S}$. Express the open ball $B^S{d_S}(a;r)$ in $(S,d_S)$in terms of the open ball $B^X_d(x;r)$ in $(X,d)$
wraith daggerBOT
ALBERTO BALSAM
willow cove
What i have so far is:
$B^S_{d_S}(a;r)={z \in S : d_S(z,a) < r}={z \in S: d(z,a) < r}={z \in X : d(z,a) <r} \cap S = B^X_d(a;r) \cap S$
wraith daggerBOT
ALBERTO BALSAM
willow cove
but i am not sure how to make it in terms of $B^X_d(x;r)$ for some arbitrary $x \in X$
wraith daggerBOT
ALBERTO BALSAM
willow cove
Any help would be appreciated, thanks!
versed glen
you should probably ask in advanced analysis
cedar kilnBOT
@willow cove Has your question been resolved?
cedar kilnBOT
@willow cove Has your question been resolved?
crimson sedge
cedar kilnBOT
violet flume
whats a pmf
crimson sedge
Probability Mass Function
violet flume
yea
does a pmf care if a heads happened first or last as long as only one heads showed up
crimson sedge
It said contract any possible outcomes
violet flume
yea
so how many of your outcomes have 1 heads?
0, 1 , 2 , 3, 4
these are the possible outcomes, right?L
crimson sedge
Yes they are
But my brain is like about to give up because of this stupid homework
<@&286206848099549185>
violet flume
But my brain is like about to give up because of this stupid homework
you need to count
count out how many outcomes land in each of those 5 possibilities
crimson sedge
So it's the exact same thing like count 40 times? Since it said on the activity tossing 4 coins 40 times
violet flume
are you sure you understand what a pmf is?
you need to count how many times you have one heads
if you divide this by 40, you have P(X=1)
crimson sedge
Ooooh I get now thx a bunch
dull stratus
hi everyone, bit of an analysis question but using change of variables how would I go about doing this
violet flume
hi everyone, bit of an analysis question but using change of variables how would...
try t=u/a
looks like it works nicely
dull stratus
so the integral becomes a/u?
sharp lotus
why do you need a change of variables?
violet flume
$t = \frac u a \to \dd t = \frac 1 a \dd u$
wraith daggerBOT
jan Niku (@pomodoro role)
violet flume
so $\int _{a} ^{ax} \frac 1 t \dd t \longrightarrow \int _{t=a} ^{t=ax} \frac 1 a \cdot \frac a u \dd u$
wraith daggerBOT
jan Niku (@pomodoro role)
dull stratus
oh that makes sense, thanks for the help, i dont have a lot of experience changing the bounds like that, i figured it was simple but havent done that before
thank you!
violet flume
dull stratus
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crude viper
cedar kilnBOT
crude viper
idek what that means
broken tartan
Can someone please help me?
When you have x - something inside then it’s shifted to the right and if you have x + something it’s shifted to the left
f(x-1) is the graph of a function f but shifted 1 to the right
And when you have a constant greater than 1 multiplying a function the graph becomes squeezed
crude viper
which one is it
broken tartan
Figure it out yourself lol
crude viper
??
broken tartan
Maybe rewatch the video
cedar kilnBOT
@crude viper Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
steady bough
Hey everyone, I'm stuck on a math problem and I was wondering if someone could help me out.
The problem is the following:
__Question: __
S= integers X natural numbers
R= {(a,b) ~ (c,d) <=> ad = bc}
Which of the following properties apply to this relation: reflexivity, symmetry, transitivity?
Answer:
I already know the following definitions:
Reflexivity: for every x out of S: xRx
Symmetry: for every x,y out of S: xRy = yRx
Transitivity: for every x,y,z out of S: (xRy and yRz) = xRz
The issue is I don't know how to examine that specific relation for those properties.
Help would be appreciated👍
tropic oxide
well the things related by R are pairs of (integer, natural)
but other than this you apply the definition all the same
verify whether for all a1, a2, a3 in Z and b1, b2, b3 in N the following holds:
- reflexivity: (a1, b1) R (a1, b1)
- symmetry: (a1, b1) R (a2, b2) implies (a2, b2) R (a1, b1)
- transitivity: (a1,b1)R(a2,b2) and (a2,b2)R(a3,b3) implies (a1,b1)R(a3,b3)
steady bough
Okay thank you
bleak jolt
can someone help me with this? a rough sketch maybe?
cedar kilnBOT
can someone help me with this? a rough sketch maybe?
@bleak jolt Has your question been resolved?
stiff ermine
okay
so i here you want to fix certain point to see what happens
so if you let
y,z = 0, what is x equal to?
that will give you a point
(x,0,0)
repeat this process for to get (0,y,0) and (0,0,z)
three points, you can define a plane
basically you want to find 3 points you know are on the plane so you can sketch
@bleak jolt
cedar kilnBOT
@bleak jolt Has your question been resolved?
unreal otter
hello, did I label this correctly? (trigonometry)
is 22.6 the opposite?
leaden snow
@unreal otter The hypothenuse is always opposite to the 90 deg angle
unreal otter
so 22.6 is the hypotenuse?
leaden snow
So you switched up hyp and adj
unreal otter
oh
leaden snow
so 22.6 is the hypotenuse?
No that is not opposite to the right angle
the right angle is where the square is drawn
bleak jolt
basically you want to find 3 points you know are on the plane so you can sketch
i already know this
unreal otter
ohh okay thanks
bleak jolt
how can i graph the 0,0,0
stiff ermine
just plot that point on the axes at the origin
bleak jolt
rustic ibex
cedar kilnBOT
rustic ibex
hi. can you explain what is the difference between divide difference method and newthon method?
cedar kilnBOT
@rustic ibex Has your question been resolved?
cedar kilnBOT
@rustic ibex Has your question been resolved?
cedar kilnBOT
@rustic ibex Has your question been resolved?
warm skiff
sin Q + sin P = 7/5
Q+P = 90
cedar kilnBOT
sin Q + sin P = 7/5
Q+P = 90
warm skiff
Find the value of sin2P without a calculator
warm skiff
sin Q + sin P = 7/5
Q+P = 90
so I've shaped it into cos P = 7/5 - sin P
and then sin 2P = 2sinP(7/5-sinP)
I have no idea how to go further though
cedar kilnBOT
@warm skiff Has your question been resolved?
past pond
can someone help me with my math notebook? its grade 8 math
cedar kilnBOT
can someone help me with my math notebook? its grade 8 math
past pond
please ping me if someone is welling to help
tepid trout
can someone help me with my math notebook? its grade 8 math
• Don’t ask permission to ask a question, or ask if anyone knows how to solve a type of problem. Just ask your question.
past pond
i did
tepid trout
It says just ask your question, you didn’t you asked if someone can help
Just ask the question mate
I’ll try to help you
past pond
its alot okay?
past pond
tepid trout
okay
