CDF $$F_X(x) = -\frac{\theta^2}{x^2} \le 0 ?$$
#help-0
proper tangle
ocean sealBOT
vin100
proper tangle
note that $F_X(x) = P(X \le x) \in [0,1]$, as the name "cumulative freq funct" suggests. you can't have negative freq.
ocean sealBOT
vin100
lone heartBOT
@frozen wren Has your question been resolved?
lone heartBOT
lost juniper
so if x = t, what does y = ? <@297567836254240768>
f(t)?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
ocean sealBOT
giannis_money
weary wyvern
maybe this is causing a problem... i'm not too sure
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
maybe this is causing a problem... i'm not too sure
I don't get it... I forgot to mention but y and z are independent of x
weary wyvern
yea i assumed they were all independent
weary wyvern
**giannis\_money**
then this would be true
basically in the "wrong" approach, you're missing constant functions so that might resolve the issue
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
basically in the "wrong" approach, you're missing constant functions so that mig...
Ohk, thanks a lot for your help :D
.close
white ledge
lone heartBOT
wary stream
Should be
vast marsh
lone heartBOT
vast marsh
Trying to graph trig functions and just wondering where does the 1/6 come from. Bc Ik how to find the amp, midline. Finding the period confuses me. And making the equation
alpine sable
Trying to graph trig functions and just wondering where does the 1/6 come from. ...
? 1/6 is in the definition of the function ig
vast marsh
how do I make the equations out of a graph
I’ll show you a problem and see if you can help
wary stream
? 1/6 is in the definition of the function ig
No, you have to find it
vast marsh
So basically I need to get that black line to match up with the dotted line
And write the right equation yk
alpine sable
Oh I see
vast marsh
Wait omg is this one of the ones where i use the unit circle
wary stream
General sine and cosine equations are in the form of y = Asin(Bx) + C and y = Acosine(Bx) + C
You already know how to find A and C, what's left is B
vast marsh
how do I find b
wary stream
Where the equation is Period = (2pi)/B
wary stream
The value you need
vast marsh
how do I find it?
vast marsh
oh so I plug everything in and find b
wary stream
You can find the period by look at the plot
wary stream
No
alpine sable
I don't think it is
vast marsh
shit
wary stream
Period is one complete cycle
vast marsh
How do u find it
wary stream
Because sine and cosine repeats
wary stream
You pick a point and go along the line until you go one cycle
The easiest method is going from peak to peak or trough to trough
alpine sable
And no that's not the two points
alpine sable
When is the first time the curve reaches 0
vast marsh
wary stream
wary stream
It's the same concept
Period is the same concept using pi or whole numbers
It's just one has a different scale
Pi is just a number
vast marsh
ok
lone heartBOT
@vast marsh Has your question been resolved?
lone heartBOT
@vast marsh Has your question been resolved?
dim sundial
Soo uhh lesson is solving oblique triangles and just wanted to check if my answers r right
dim sundial
c = 113.45m b=52.30m C=100 degrees
wary stream
Post your work
wary stream
,rotate
ocean sealBOT
wary stream
Looks right
wary stream
As I said, looks right
polar surge
elo
polar surge
i got a problem
and im confused
its
There are 200 light bulbs lined up in a row in a
long room. Each bulb has its own switch and is
currently switched off. Each bulb is numbered
consecutively from 1 to 200. You first flip every
switch. You then flip the switch on every second
bulb{turning off 2, 4,6..). You then flip the switch
on every third bulb (3, 6, 9). This continues until
you have gone through the process 200 times.
And how many of the light bulbs are illuminated
now?
i was thinking about 71
or 70
polar surge
its not about class
and
i arrived
by adding 3
starting from 3
and then counted the numbers
vale wigeon
@fallen parcel channel occupied, please take your own
fallen parcel
oh sorry
vale wigeon
and then counted the numbers
so you manually kept track of the status of all two hundred lightbulbs over all two hundred steps?
polar surge
so you manually kept track of the status of all two hundred lightbulbs over all ...
yes
vale wigeon
and you are sure that in all these two hundred steps you did not mess up anywhere?
polar surge
i dont know
vale wigeon
because i think you did.
and also because there is a better way to do this than that laborious bookkeeping.
merry coral
ye
polar surge
what way
merry coral
factors 😳
vale wigeon
we'll get to that soon, chunkin.
polar surge
bruuuuuuuuuuuuuuu
vale wigeon
don't spoil.
vale wigeon
if a lightbulb remains off at the end, what can you say about the number of times it was switched?
polar surge
1?
vale wigeon
so if a lightbulb is off at the end, it must necessarily have been switched exactly once?
vale wigeon
no, they started out off
vale wigeon
always exactly 2?
vale wigeon
what do we call those numbers
polar surge
even numebrs
vale wigeon
yes
so a lightbulb is off if it has been switched an even number of times
and if it is on at the end, then...?
vale wigeon
so you're now saying ALL lightbulbs have been switched an even number of times, so NONE of them are on?
is that what you're saying?
polar surge
no
but
read the question
every bulb is turned on
hen flip the switch on every second
bulb{turning off 2, 4,6..). You then flip the switch
on every third bulb (3, 6, 9). This continues until
you have gone through the process 200 times.
wait
lol
vale wigeon
i don't see your point
vale wigeon
we have established that if a lightbulb is off at the end, it must have been switched an even number of times.
now if a lightbulb is on at the end, what can you say about the number of times it's been switched?
polar surge
3?
vale wigeon
exactly thrice, no more and no less?
polar surge
yes
vale wigeon
then you're wrong again
there are ways to leave a lightbulb on by switching it some number of times other than 3
for example, switching it a grand total of 71 times will leave it on
vale wigeon
we haven't even GOTTEN to counting the lightbulbs that are left on
polar surge
e
vale wigeon
you really think i was looking at your BS answer?
i wasn't
i was just trying to get you to realize 3 isn't the only odd number in existence.
polar surge
vale wigeon
i mean
you said
you said that switching a lightbulb exactly once, or exactly 5 times, or exactly 7 times, etc. will NOT leave it on
polar surge
yes
vale wigeon
oh so you actually still stand by that?
polar surge
no
vale wigeon
then why say yes
polar surge
because i said that
vale wigeon
right
now can you go back to that question i asked you
and answer it correctly
if a lightbulb is on at the end, what can you say about the number of times it's been switched?
polar surge
odd numbers
vale wigeon
right
so, we are looking for those lightbulbs that have been switched an odd number of times during our procedure.
do you understand this or not
polar surge
yes
vale wigeon
okay
vale wigeon
i do not understand what you're saying
polar surge
i have to find the switches
that ended off with an odd
number
after 200 switches
vale wigeon
now you're just parroting what i have said already (albeit poorly)
polar surge
go on
vale wigeon
let's now look at a particular lightbulb
say #12 just to have an example
we'll generalize it soon enough
on what steps is lightbulb #12 switched?
polar surge
so
in the question it says
first y switch numbers 2 4 6 and on
and second i switch
3 6 9 and on
so
12 will always be switched evenly?
vale wigeon
sigh
vale wigeon
on step 1, you switch every bulb
on step 2, you switch every bulb whose number is divisible by 2
on step 3, you switch every bulb whose number is divisible by 3
on step 4, you switch every bulb whose number is divisible by 4
and so on, with 200 steps in all.
polar surge
ok
polar surge
divisible of 12?
vale wigeon
your answer should be "lightbulb #12 will be switched on steps _______" where the blank is a comma-separated list of numbers
vale wigeon
where the blank is a comma-separated list of numbers
if you want to get help then you will have to read my messages there's no way around it
polar surge
2 4 3 12 1
polar surge
6
vale wigeon
AND you're missing the commas that i asked you to put between those numbers
you're refusing to follow instructions
polar surge
wait a sec
polar surge
i dont see that
vale wigeon
but turns out you aren't
polar surge
message
vale wigeon
what do you mean, "don't see"?
vale wigeon
your answer should be "lightbulb #12 will be switched on steps \_\_\_\_\_\_\_" w...
.
the message i just replied to does not appear?
or are you shitting me again on purpose
vale wigeon
im not sure whether i want to go on after being shown such blatant disregard for the things i say tbh
polar surge
go on
vale wigeon
like, it would take going through hell and back at this point to get you to realize, understand and comprehend things such as ||a number has an odd number of factors if and only if it's a perfect square||
and i cannot do that with someone who refuses to read my messages
polar surge
i just read all u said
vale wigeon
too late
polar surge
so you not going to help?
oo
o
o
oo
o
o
o
o
oo
o
o
o
o
o
o
<@&286206848099549185>
@vale wigeon
polar surge
the only thing i didnt read fully
was the one from the answer your quetion here
bruh
you are being really anoying
im just trying to get help
dreamy cedar
muted
lone heartBOT
@polar surge Has your question been resolved?
alpine sable
lone heartBOT
wary stream
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
wary stream
Just wait patiently
wary stream
You already ping once, prematurely, so don't do it again
Do you know how to get 2 into y = mx + b form?
Or question 3 into Ax + By + C = 0 form?
alpine sable
Yes I know how to get them but those 3 questions dont make sense to me
The ones I stated
alpine sable
How the -7 became positive and how the -21 became +19
The questions in general dont make sense
I need help on them and then after I see how they’re solved I can apply my knowledge
wary stream
So then what do you have, after distribution?
alpine sable
After distribution it should normally be subtract y from both sides
But for those questions I have no clue
wary stream
I'm asking, what equation do you have after distributing
wary stream
After distribution it should normally be subtract y from both sides
It does not normally have to be like this
You can move everything else instead
alpine sable
I would have y-2=-7x+21
wary stream
Notice how the general form is Ax + By + C = 0
alpine sable
A must be positive
wary stream
Yes
So instead of subtracting y, because you'll still have -7x meaning A is still negative, did you trying moving the x term over instead?
alpine sable
You mean to add on both sides?
wary stream
Yes
alpine sable
I did that
wary stream
Then what did you get if you did that?
alpine sable
I did the same with 21
wary stream
What's 21 - 2?
wary stream
What happened to the x?
wary stream
So then what are you confused about?
wary stream
Do the same process
alpine sable
4y+20=-3x+12
4y+3x+20=12
-12 from both sides
4y+3x+8
Correct answer is 3x+4y+17=0
??
wary stream
Have you ever thought that typos could exist?
alpine sable
How could 8 become 17?
wary stream
Or that 17 is a typo
alpine sable
One is at the very left of the keyboard
alpine sable
Or that 17 is a typo
So I got it correct ? Or is there a way to get 17
wary stream
Did you try graphing the answers too?
alpine sable
No
wary stream
Because if your answer overlaps the key, then that means you're right. If not, either the key is wrong or you're wrong
Most likely the key, because you're doing the process right
Unless you make a small math mistake
alpine sable
I dont know how to put those into my calculator
wary stream
Use desmos, it's an online graphing tool
alpine sable
I can put the slope and y intercept but I dont know how to put these ones
wary stream
Where you can put in those equations
wary stream
Just type in -3/4
alpine sable
Hmmm, it seems like my teacher made a mistake
Okay now I understand these ones
But I dont understand how to turn y-2=4(x+5) into y=mx+b
<@&286206848099549185>
wary stream
But I dont understand how to turn y-2=4(x+5) into y=mx+b
Distribute
What do you get?
alpine sable
Yeah
Add 2 to both sides
Y=4x+22
It says that the correct answer is y=-7x-19
??
Makes no sense
How
wary stream
Have you ever thought that typos could exist?
alpine sable
I dont understand how hes making these typos
alpine sable
Yeah I did
It does
My teacher is very careful
I dont get how hes making these typos
And if hes prone to making these mistakes, who knows if hes ever made a mistake when grading someones examination
wary stream
I dont understand how hes making these typos
Probably just copy and pasting a previous year's assignment and changing up the numbers in the questions but forgot to change the answers
wary stream
Feel free to close the channel if you are done using .close
vocal fulcrum
lone heartBOT
vocal fulcrum
Can someone explain how that e stuff works
finite flax
Ooh! Me!
What are you wondering about
Like which part
The underlined part?
They took base e of both sides of the equation. You could have seen this operation before in Pre-Calculus or an Algebra II course.
vocal fulcrum
Assume I have no idea whats the relation of e and log
finite flax
That says "log" but it isn't really "log-base-10"; it's the natural log, "LN", aka "log-base-e".
vocal fulcrum
Taking base e both sides as in?
finite flax
$\log_b{x} \text{ and } b^x \text{are inverse functions}$
ocean sealBOT
Disorganized
vale wigeon
$\log_b(x)$ and $b^x$ are inverse functions, and you can end and start mathmode with dollars anywhere in your message
ocean sealBOT
Ann
vocal fulcrum
I see got it
Thnx 👍
finite flax
Yeah I've said it that way before
Shucks
Kids get that better but grammatically I think it makes sense to make "e" the subject, not the object. Ill switch back though because kids don't get it
My English is arite but my grammar is dogshit
vocal fulcrum
.close
lone heartBOT
lone heartBOT
Available help channel!
bitter violet
can somebody solve x^3+6x+9 without using the cubic formula
lone heartBOT
can somebody solve x^3+6x+9 without using the cubic formula
velvet condor
can somebody solve x^3+6x+9 without using the cubic formula
so basically you want to turn this into a quadratic equation
to apply the quadratic formula
agree?
let $x=y+\frac{\alpha}{y}$, where alpha is a constant to be determined later
ocean sealBOT
JavaTPx
velvet condor
so you sub that and multiply by y^3
and uhh im not gonna do the math
let wolfram do
wary stream
let wolfram do
Or let the user try it on their own
velvet condor
w/e lol
anyways
once you get the results
it should be in the form of $y^6+y^4(something)+6y^3+y^2(\alpha \times something)+\alpha^3=0$
ocean sealBOT
JavaTPx
velvet condor
you equate that something=0 to solve for alpha
and let z=y^3
you will have $z^2+6z+\alpha^3=0$
ocean sealBOT
JavaTPx
fallen venture
You can factor it I believe
floral pawn
You can factor it I believe
i checked on wolfram alpha, no rational roots
alpine sable
can somebody solve x^3+6x+9 without using the cubic formula
$x^3+6x+9=0$
velvet condor
idts
ocean sealBOT
Pi Creature
velvet condor
the method above is the general method
what is it called again
uhh
cardano i think
floral pawn
yea
alpine sable
cardano i think
ya
floral pawn
but i learned it a different way
wary stream
,w x^3+6x+9 solve for x
ocean sealBOT
wary stream
Ew
alpine sable
thats cubic formula ig
zenith carbon
Lol math innit
tight locust
let $x=y+\frac{\alpha}{y}$, where alpha is a constant to be determined later
What if x is zero tho
fallen venture
Just use newton’s method
alpine sable
newtons method is numerical
floral pawn
Just use newton’s method
but that's approximate
alpine sable
is it even allowed here?
velvet condor
What if x is zero tho
if you sub x=0 then x^3+9x+27=27 which is not 0
fallen venture
but that's approximate
Yeah but how tf you gonna find whatever shit wolfram alpha found lol
floral pawn
cardano's method
limpid spade
does synethic division work did u try
tight locust
if you sub x=0 then x^3+9x+27=27 which is not 0
I'm just talking about the general case. Is that substitution justified
Does it preserve domain
floral pawn
Does it preserve domain
if x can be 0, then you can factor out the x and be left with a quadratic
rare gale
well the person asked "without using the cubic formula"
velvet condor
well the person asked "without using the cubic formula"
so basically just derive it xd
floral pawn
lol yea
rare gale
: )
tight locust
if x can be 0, then you can factor out the x and be left with a quadratic
The cubic formula works for all cubics tho
floral pawn
im pretty sure x = 0 works fine
stone pilot
the way i learned is to substitute x=u+v
this is the method where youd get uv = -2 and u^3+v^3 = -9 right
floral pawn
yes
tight locust
Thank you Tchirnhaus
alpine sable
Or at least what you would go through to derive it
oh
stone pilot
then that should work fine
velvet condor
or you can try this
if they only asks for the real root
if x>that root then f(x)>0 and vice versa
xd
cuz for this case as x incrases/decreases, f(x) also increases/decreases
you just need to know what the exact real root is
lone heartBOT
@bitter violet Has your question been resolved?
brisk fossil
lone heartBOT
wary stream
Honestly, I would just use a graphing calculator
velvet condor
you can use desmos
rare gale
is this something you're supposed to do by hand?
velvet condor
i personally hate this graph transformation thing alot lol
rare gale
looks like a problem thats meant to demonstrate various transformations by graphing by hand
velvet condor
i can help you list the transformation steps from y=sinx
tight locust
What possible language could this be
velvet condor
but cannot help you with drawing
tight locust
Swedish?
velvet condor
looks like indonesian to me
tight locust
don't Indonesians have their own script though
velvet condor
no?
rare gale
basically if you start out with a basic y = sin(x) graph, -3 in front means flip it over vertically (mirror over x axis) and stretch by a factor of 3, +30 degrees means you will move the graph over to the left by 30 degrees, and +1 at the end means you will translate (move) the graph up by 1
velvet condor
basically if you start out with a basic y = sin(x) graph, -3 in front means flip...
you forgot 3 in x+30 deg
rare gale
you can kind of follow how each successive transformation changes the graph
dunno if that helps
brisk fossil
oh well i already got help thank you all for trying to help me appreciate it
.close
lone heartBOT
faint shuttle
lone heartBOT
tight locust
how old are you?
3
lone heartBOT
Available help channel!
lone heartBOT
<:AAAface:464054379541168130>
vocal fulcrum
Removed the log using the inverse function
But now how does t/20+C become the power
<@&286206848099549185>
worn fox
$\log(P) \cdot e^P \neq P$
ocean sealBOT
iCaird
lone heartBOT
@vocal fulcrum Has your question been resolved?
ocean sealBOT
Fire Dragon
$\log_b{x} \text{ = } y \text$
```Compilation error:```! Extra }, or forgotten $.
<recently read> }
l.57 $\log_b{x} \text{ = } y \text$
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.```
vocal fulcrum
$\log_b{x} \text{ = } y$
ocean sealBOT
Fire Dragon
worn fox
It means putting the things on both sides in the exponent of e
ocean sealBOT
Fire Dragon
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vocal fulcrum
Then you do e^(stuff 1) = e^(stuff 2)
Then it will be e^lnp
So e^lnp is = P??
worn fox
Indeed
Thats what it means that they are inverse of eachother
not that timesing them gives P
lone heartBOT
@vocal fulcrum Has your question been resolved?
vocal fulcrum
Ah thnxxx
sly comet
lone heartBOT
sly comet
how would u do B?
lone heartBOT
@sly comet Has your question been resolved?
elder grail
ok what does 'annual rate of decay' mean
lone heartBOT
@sly comet Has your question been resolved?
sly comet
ok what does 'annual rate of decay' mean
amount of decrease per year
wet minnow
how to solve this
lone heartBOT
how to solve this
wet minnow
<@&286206848099549185>
median gorge
Think about the area of the rectangle containing the entire cross section
Perhaps start with drawing this rectangle
And you'll find that this rectangle can be broken down into 3 smaller areas
kindred anchor
lone heartBOT
flat ore
what have you tried
lone heartBOT
@kindred anchor Has your question been resolved?
kindred anchor
<@&286206848099549185>
alpine sable
When you see word problems, try to convert them to equations, it's easier that way :D
lone heartBOT
@rose schooner Has your question been resolved?
placid zinc
Do which?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
re
alpine sable
I need help
So
I need to prove
the products of two consecutive multiplies of 5 = even
So I did it
(5n)(5n+5)
25n^2+25n
25n(n+1)
How can I prove it's even?
????
Even=2n
odd=2n+1
gray isle
n(n+1) is the product of two consecutive integers
which you can pretty much assert will be even
gray isle
given two consecutive integers,
one of those integers will be even and the other odd
the product of an odd an even integer will be even
alpine sable
ohhhhhhh
so
n(n+1)
is like even times odd=even?
because one of them must be even and the other odd
flat ore
you could think of it like that too
alpine sable
oh
flat ore
you could let n = 2m (even),
then n(n+1) = 2m(2m+1) = 4m^2 + 2m = 2(2m^2 + m) = 2z meaning its even
same would happen if you took n = 2m+1 (odd)
stone pilot
what it basically boils down to is for 2 consecutive integers, if the first is odd, the second would be even, and if the first is even the second would be odd; thus the parity of the product of these 2 integers would be even * odd = even
flat ore
just a variable
flat ore
I mean you can just conclude directly that 2m(2m+1) is divisible by 2
flat ore
so we will always get even times odd= even
yes
alpine sable
even if n is =2m or 2m+1
flat ore
yees
stone pilot
you can apply the same logical reasoning to prove that say for 3 consecutive integers, the product of these 3 integers would be divisible by 3
and so on
tall hearth
even if n is =2m or 2m+1
if n = 2m + 1 then n + 1 = 2m + 2
n(n + 1) = (2m + 1)(2)(m + 1) which is obviously divisible by 2
lone heartBOT
@alpine sable Has your question been resolved?
median mason
dark sage
(U ∧ V ) ∨ (U ∧ ¬V ) ⇐⇒ U
lone heartBOT
(U ∧ V ) ∨ (U ∧ ¬V ) ⇐⇒ U
dark sage
how would u prove this through natural deduction
lone heartBOT
@dark sage Has your question been resolved?
dark sage
<@&286206848099549185>
swift shore
@dark sage does natural deduction have different rules than normal deduction
dark sage
umm
swift shore
Sorry i know I’m not familiar with it but nobody seems to be helping u lol
dark sage
yeah yeah
swift shore
Is it very different
dark sage
i think i have to prove that
U => to that
and that entire thing => U
with premises etc
(U ∧ V ) ∨ (U ∧ ¬V ) ⇐⇒ U
i have to prove this
lone heartBOT
@dark sage Has your question been resolved?
lone heartBOT
@dark sage Has your question been resolved?
pulsar willow
Can anyone help explain why these are/are not subspaces?
lone heartBOT
Can anyone help explain why these are/are not subspaces?
pulsar willow
This is the answer
Just don't understand it fully and think in part d is a mistake
alpine sable
Just don't understand it fully and think in part d is a mistake
there is a typo in d I think, but U is still not a subspace
alpine sable
5A rather than 5A^2
Yep. exactly
pulsar willow
Do you know why part c is not a subspace?
pulsar willow
My bad. I don't understand the explanation or what they are trying to achieve. I know you have to prove closure properties remain
Not sure what a fixed matrix is to begin with and also how they say OB=O=BO
Question only tells us AB=BA, not AB=A=BA
alpine sable
Not sure what a fixed matrix is to begin with and also how they say OB=**O**=BO
That's because they trying to prove that $0 \in U$ so the zero matrix has to verify the property $0B=B0$ for any matrix B (A=0)
ocean sealBOT
AimaneSN
alpine sable
Not sure what a fixed matrix is to begin with and also how they say OB=**O**=BO
they wrote 0 in the middle to prove RHS and LHS are equal
pulsar willow
Ahh okay that explains a lot
Then they just sub in values for proving addition and multiplication closure?
And when they say fixed matrix does it simply mean we assume it is a predefined matrix called B and is not a placeholder
alpine sable
Then they just sub in values for proving addition and multiplication closure?
i don't understand wdym by sub in
alpine sable
And when they say fixed matrix does it simply mean we assume it is a predefined ...
they're trying to prove the property for any matrix B, so they fix a matrix B and do the proof
no B is a placeholder
it's arbitrary
pulsar willow
I actually read it wrong my bad, I don't get why they have A1+A2 considering A is a single matrix but they replace with the sum of 2 matrices
Perfect thank you
alpine sable
I actually read it wrong my bad, I don't get why they have A1+A2 considering A i...
you need two matrices to prove additivity, that's what they did here I guess
pulsar willow
Oh I guess given A1(B) + A2(B) = (A1+A2)(B)
Different way of writing out proofs then used to, forgot that lol
I understand it much better now I appreciate it!
alpine sable
haha
pulsar willow
.close
lone heartBOT
pulsar willow
.reopen
lone heartBOT
✅
pulsar willow
Saw you still typing my bad
alpine sable
wanted to write you're welcome xd
pulsar willow
Ohhh lol, well thank you!
alpine sable
np bro
pulsar willow
.close
ornate timber
hi
i have to rearrange it to y = mx + b form and i have the y = down, but the mx and b are switched up. how do i move the mx to be in front of the b ?
real escarp
(10/2)-(5/2)x = -(5/2)x + (10/2)
btw 10/2 = 5
so you have y = -(5/2)x + 5 to the form y = mx + b with
m = -(5/2)
and b = 5
ornate timber
i see
how does 10/2 - 5/2x turn into -5/2x + 10/2 though?
real escarp
because 10/2 - 5/2x = 10/2 + (-5/2)x
and you can switch terms when you have an addition
real escarp
no it's not +-5, it's just +5
for example you have 7 - 3, it's equal 4. If u want to switch terms and keep the equality right, just let the minus sign with his term, so : 7 - 3 = -3 + 7 = 4.
and 3 - 7 is not equal to 4, but to -4
ornate timber
why is it + 5 though, wouldnt it be -5?
because 10/2 - 5/2x is equal to 5/2x + -10/2 ?
real escarp
no, 10/2 - 5/2x = -5/2x + 10/2
the minus sign stay with 5/2x, and the plus sign stay with 10/2
ornate timber
ohh i see
real escarp
in a more general way, a+b=b+a and a-b=-b+a
ornate timber
yea i see now that the negative must stay with the 5/2x
thank you for your help!
lone heartBOT
@ornate timber Has your question been resolved?
prisma prawn
The product of the first three terms of the geometric sequence is 8, and the sum is 7. Write the first 5
terms, calculate the twelfth term and the sum of the first six terms.
prisma prawn
anyone help witht hat?
The product of the first three terms of the geometric sequence is 8, and the sum is 7. Write the first 5
terms, calculate the twelfth term and the sum of the first six terms.
.close
quaint pine
If 0.35 of men are smokers, and three men are selected at random, find the probability that at least one of them is a smoker.
tacit arch
use the binomial distribution
quaint pine
use the binomial distribution
this formula isn't included in the module i'm studying. I believe my professor used the "complement of the probability" concept or w/e it's called
do you know what it is or do you know any other way to solve it?
tacit arch
P(at least 1 smoker) = 1 - P(no smokers)
quaint pine
P(at least 1 smoker) = 1 - P(no smokers)
so 1-0.65 is the answer?
quaint pine
P(at least 1 smoker) = 1 - P(no smokers)
so we already did 1-0.35 to get non smokers right? why did you do 1-non smokers?
again
tacit arch
P(at least 1 smoker) = 1 - P(no smokers)
rephrase this with 3 men specifically
tacit arch
idk why we would subtract by 1
It's the complement event
Write it in words instead of equations
quaint pine
Write it in words instead of equations
you already did
quaint pine
P(at least 1 smoker) = 1 - P(no smokers)
this
tacit arch
rephrase this with 3 men specifically
.
tacit arch
so 1-0.65 is the answer?
this was your answer to my equation for 1 man. you need to tweak what i said to get the right answer for 3 men
quaint pine
so 1-0.65*3?
I wrote this but idk if it's true
tacit arch
It's the complement event
right. so you answered your own question
quaint pine
right. so you answered your own question
so is my answer true or false? you're speaking in puzzles😭
tacit arch
idk why we would subtract by 1
my bad, i meant to reference this
for 1 man, do you understand 1 - P(non smoker) = P(is smoker) ?
quaint pine
yeah
tacit arch
For 2 or more men, write out in words what it means for there to be no smokers
quaint pine
for 1 man, do you understand `1 - P(non smoker) = P(is smoker)` ?
I understand this because the sum of every probability = 1
tacit arch
yea that logic doesn't apply to 2 or more
quaint pine
For 2 or more men, write out in words what it means for there to be no smokers
you do that😭
idk
would it be easier to solve with binomial distribution? I haven't studied it and it isn't included in my module but if it makes life easier:(
tacit arch
if you want to understand why 1 - P(no smokers) = P(at least 1 smoker), the easiest way is for you to write it out in words
you should understand the basics before moving onto something more advanced
quaint pine
if you want to understand why 1 - P(no smokers) = P(at least 1 smoker), the easi...
well you're doing it idk what I would add to that 1-P(no smokers)=P(at least 1 smoker)
at least means 1 or 2 or 3 and if it's or we multiply right?
tacit arch
well you're doing it idk what I would add to that 1-P(no smokers)=P(at least 1 s...
write this specifically for 3 men
quaint pine
write this specifically for 3 men
1-P(no smokers)=P(at least 1 smoker*3)?
quaint pine
write this specifically for 3 men
so the probability that at least one smokes is 0.65^3
or it's 1-0.65^3
it's one of the two not sure
tacit arch
expand "no smokers" to include 3 men
quaint pine
expand "no smokers" to include 3 men
well depends, we want at least 1 so we're okay with 1 smoking and 2 don't. OR 2 smoking and 1 doesn't. OR all 3 smoke
tacit arch
and what's the complement event to all of those?
quaint pine
and what's the complement event to all of those?
1-.35x.65x.65+.35x.35x.65+.35x.35x.35
there should be a multiplication sign between every probability but discord modifies text with those signs so
is that right
I put x instead of *
tacit arch
,calc 1-.35x.65x.65+.35x.35x.65+.35x.35x.35
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol x
tacit arch
try for yourself using ,calc command
quaint pine
.calc 1-.35x.65x.65+.35x.35x.65+.35x.35x.35
quaint pine
,calc 1-.35x.65x.65+.35x.35x.65+.35x.35x.35
you put , instead of .
,calc 1-.35x.65x.65+.35x.35x.65+.35x.35x.35
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol x
tacit arch
need to use * for multiplication
quaint pine
,calc -.35*.65*.65+.35*.35*.65*.35*.35*.35
ocean sealBOT
Result:
-0.144461078125
,calc 1-.35x.65x.65+.35x.35x.65+.35x.35x.35
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol x
quaint pine
,calc 1-.35.65.65+.35.35.65.35.35*.35
ocean sealBOT
The following error occured while calculating:
Error: Unexpected part ".65" (char 6)
quaint pine
,calc 1-0.350.650.65+0.350.350.65+0.350.350.35
ocean sealBOT
Result:
0.974625
@tacit arch there you go
tacit arch
,calc 1 - 0.65^3
ocean sealBOT
Result:
0.725375
oh this is missing some combinations
there are 3 ways 1 man among 3 men could be a smoker
etc. for 2 men
quaint pine
etc. for 2 men
yeah I feel like I understand this a little better, thanks a lot
.close
wise elbow
Stuck*
dusty flare
so do you know exponent rules?
wise elbow
Yes
dusty flare
actually i’d start with simplifying the (2k)^3
placid zinc
Division really means "flip, then multiply"
keen mason
^^
placid zinc
After that, this is all just exponent properties
dusty flare
yeah
wise elbow
So (2K)^3 changes to 8k^3 ?
keen mason
so in reality its just $\frac{-5k^2}{2k^5} \times \frac{10k^5}{8k^3}$
ocean sealBOT
Mortta
ocean sealBOT
sdash
unkempt dove
'
tacit arch
i closed your other channel
open folio
Oh
tacit arch
since it was getting hairy and this seems like a new problem
open folio
Opposite is the side that the angle isn't touching
So for example, angle B is touching 9 and 41
It's opposite is the other one
open folio
Yes
That one
The adjacent is the side the angle is touching (THAT ISNT THE HYPOTENUSE)
For angle B that would be 9
gloomy pewter
lone heartBOT
gloomy pewter
Have to find the unique solution using laplace transformation
Currently stuck on finding the inverse
ivory ivy
gloomy pewter
@ivory ivy check #❓how-to-get-help
tacit arch
Currently stuck on finding the inverse
gotta get the partial fraction decomposition
https://www.youtube.com/watch?v=7OzVkmO9AKw
gloomy pewter
.close
silk magnet
lone heartBOT
silk magnet
Currently confused on how to approach questions containing Sigma
dawn birch
sum{k=1 to 3} f(k/4) = f(1/4) + f(2/4) + f(3/4) by definition @silk magnet
so plug those values in for x and sum them
frosty blaze
hi!
frosty blaze
i'm currently struggling on this problem
i was trying to tackle it a couple days ago but ended up getting really bogged down and did not end up solving it
tacit arch
i'm currently struggling on this problem
isn't this a solution?
frosty blaze
no no the bullet point is just how far i got
tacit arch
this one's the closest to yours i think
https://math.stackexchange.com/a/2771579/142904
this one uses complex numbers if you've learned that already
https://math.stackexchange.com/a/165613/142904
frosty blaze
this one uses complex numbers if you've learned that already
https://math.stacke...
our class has not gotten into complex numbers at all
placid zinc
That one with the pictures is exactly the intended proof, I think
frosty blaze
That one with the pictures is exactly the intended proof, I think
are you referring to this, specifically?
placid zinc
Ye
frosty blaze
ok thank you i think i comprehend that one in entirety.
placid zinc
It'd be nice if it were written more "mathematically" but the idea is there
frosty blaze
It'd be nice if it were written more "mathematically" but the idea is there
i am perfectly happy with writing using an intuitive geometric proof
explaining it in english rather than the crazy looking math shorthand
so the second issue i was having revolved around this problem
there's no reason to take the coefficients out, right?