which in this case, it's ×(-1) on both sides
#help-38
wise dagger
cosmic plinth
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ripe plank
May someone help me with probability? It’s outing something that’s in a superposition through a measure gate. I’m just a bit lost because I don’t know where to go
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May someone help me with probability? It’s outing something that’s in a superpos...
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red tundra
if a1>0 prove find monotone of an (by induction probably), how??
lone saffron
you need to prove this right?
naive otter
Any value given ?
red tundra
no, only that a1>0
red tundra
we consider a1 as the first term btw
naive otter
a1 > 0
So a2 = a1/(1+a1)
Numerator is greater than denominator
Therefore the statement holds true for the a2
let be true for a_m , therefore a_m <a_(m-1)
red tundra
cook
naive otter
Thefore a_m+1 = (a_m)/(1+a_m)
now since a_m < a_(m-1) evidently , a_m+1 < a_(m-1)
ai think this doesn't requires this sort of induction based proof
You can generally write the logic and proof it
red tundra
I don't understand how this proves that a_n is decreasing
can anybody help?????????????
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fringe cedar
Hello, quick question, why is the conditional probability P(A given B) = P(A by applying B), I'm referring to this
by doing $\operatorname{nCr}\left(3,1\right)\cdot\left(0.6\right)\cdot\left(0.4\right)^{2}$ one can get the same probability but i dont know why
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Edsel Di Meo
fringe cedar
I followed my intuition but i dont know why it holds true
I ask this because I know P(A given B) = P(A and B) / P(B)
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rotund moth
hello
rotund moth
I need someone to explain me what differentiation is
rotund moth
Okay. Is differentitation related to limits/continuity?
zinc ginkgo
read the article
rotund moth
Thanks
woven nova
it is
rotund moth
Okay
woven nova
https://tutorial.math.lamar.edu/classes/calci/DefnOfDerivative.aspx
that is a pretty nice article, well written
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pale valve
Hellooo, i'm not sure how to solve this, the person that gave me his problem, told me that its supose to get a number whit out calculator or aproximation
zinc ginkgo
!15m
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pale valve
No😓
I still waiting for help
Sorry for taggim You but i been waiting for 35 minuts😓
<@&286206848099549185>
marble spruce
Hellooo, i'm not sure how to solve this, the person that gave me his problem, to...
Do u want to solve for x?
pale valve
Yep😓
marble spruce
does your teacher teach you by doing graphing
marble spruce
oh
pale valve
😓
marble spruce
Don’t you just bring it to the other side to make it x=-2^x+5?
Or is there more to it?
Isn’t it straightfoward?
pale valve
The person that gave me this problem, asked for an entire number
Because if you try whit log
You get this
And its kind the same situation
marble spruce
Yeah, thats literally the answer
What’s the person learning for them to get a whole number out of it?
pale valve
The teacher came to the class and just said "resolve it" without context, he just said that there is a way to get an entire number without calculator
😓😓
Can i tagg helpers again?
<@&268886789983436800> can i tagg helpers again?
knotty oriole
I think the rules are kinda vague as far as whether you can ping only once after the first 15 mins from posting your q or once every 15 mins. I think once every 15 min might annoy ppl though.
Might as well just ping now and give it like 30 min to an hr before pinging again.
But for your actual question, I don't see an easy way to solve this
There is a function called the W-lambert function that is supposed to be usable to solve this kind of equation I think.
But that seems unreasonable here to expect you to know.
Sometimes you can check this kind of thing via inspection, brute force, looking closely at the graph
For finding particular nice values.
I don't think that kind of thing works in general though.
pale valve
I whant to know, been honest, i been 5 days tring to resolve it
knotty oriole
,w solve 2^x = 5 - x
solid kilnBOT
knotty oriole
Wolfram alpha thinks this also requires the lambert w function
I don't think there is going to be an easy solution that doesn't use that.
Sometimes you get lucky.
For ex, try and solve 3^x=1-x
Do you see the solution?
Try x=0
Do you see it now?
pale valve
Yes i get it
knotty oriole
But this only works because we got lucky and I happened to pick a nice set of values for our equation.
Same idea applies for something like solving 2^x=3
You might say, aha! Just take the log!
But we had to invent a function, the logarithm, for this to be solvable in the first place.
pale valve
Thats crazy, i mean at the begining the problem didnt look that hard
knotty oriole
Yah sometimes things look a lot easier than they are lol.
pale valve
😓 its crazy
knotty oriole
It happens
Fwiw you can't just define a function that gives you a solution to every equation.
The function has to actually exist.
For ex x^2 + 1 = 0 doesn't have a real valued solution
Because squares of real numbers are always positive or zero.
knotty oriole
It's hard to tell what the person asking you this question had in mind.
pale valve
Dont know lmao
knotty oriole
Your best bet is probably to ask them directly.
Maybe they know some trick neither of us know.
knotty oriole
You too
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rustic kiln
is this the correct answer?
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is this the correct answer?
wraith hinge
This strikes me as a power rule derivative problem, but are you there yet in your course?
rustic kiln
yes
rustic kiln
This strikes me as a power rule derivative problem, but are you there yet in you...
is 15 the correct answer?
dry copper
it is
austere pebble
SU TAOOOOOOOO
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swift forge
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swift forge
i’m confused
zinc ginkgo
i’m confused
Which part of that is confusing you first
swift forge
how is it R?
zinc ginkgo
They explain it
swift forge
still confused
zinc ginkgo
Which part of their explanation is confusing
brazen zephyr
Absolute function always give you positive result that means whatever the value of x, the expression will always be greater than -11. So x belongs to all real numbers
swift forge
what’s an absolute value @obsidian valley
obsidian valley
absolute value is a fuction notated by the big bars | | where no matter what is inside it, it will return the positive version of it
swift forge
so why is it R if it’s -11
obsidian valley
so like |-7| = 7
swift forge
that’s a negative
obsidian valley
yeah this is saying all real numbers inside an abs value will be bigger than -11
swift forge
ah
obsidian valley
since an abs value will only return a positive number
and positive is always bigger than a negative
swift forge
oh so it abs can only return positive number
swift forge
so it’s automatically positive?
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earnest crater
is a loop in basic circuit analysis
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is a loop in basic circuit analysis
earnest crater
just basically any closed contour that you can draw from a node
is that a complete way to put it or is there an exception
austere cedar
That's it!
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versed lark
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versed lark
no additional context
i'm a bit stumped on whether it would be a trick question or not
zinc ginkgo
Why is it not just 1/7
versed lark
Why is it not just 1/7
that's what i was thinking but it just seemed like a trick question to me
lusty delta
if you want to take the question seriously, answer 1/7
but keep in mind this is very poorly designed
versed lark
got it, i was overthinking this question a lot lol
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upbeat yarrow
what if someone not responding to my thing
empty wyvern
We come to 2(n+k), but wouldn't that be 2n + 2k, not 2n + k?
upbeat yarrow
huh
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weak kiln
how does the bottom give -inf? if I plug in 0 in lnx, why does it give -inf?
celest fractal
note that if y = ln(x), then e^y = x. what happens when x is a really small positive real number? -- ||y (or lnx) must be a large negative number||
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tepid junco
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tepid junco
not relaly sure why this is true?
as sqrt(i) is not a cycle of 4 for a complete i cycle
vagrant marsh
how would you define i?
tepid junco
e^(i*pi/4)^2 = e^(ipi/2)
vagrant marsh
whats the barebones definition of i that you might have learned early high school
vagrant marsh
yeah, i was looking for "i^2 = -1"
thus we define sqrt(-1) = i despite it not really making sense
we can apply a similar idea that since (e^(i pi/4))^2 = i, then it would follow that e^(i pi/4) = sqrt(i)
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radiant zealot
I konw its a physics question but Can somebody help me w this
prime crystal
The graph is here
draw free body diagram first
then write the relations for each mass
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supple bridge
Need help with simplifying square roots
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Need help with simplifying square roots
supple bridge
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Alberto Z.
dusty sleet
No 😅
supple bridge
oooh
wait
so you get 10√2
then multiply the 5 on the outside to get 50√2
how did you get to 10√2?
is there an easy method that isnt done using a calculator
like not using the √ function
we could only divide the numbers to simplify until we got decimals which is where it would end
but i was wrong with my initial method
can 200 be simplified down to 2?
oh because it comes down to 10√2
and 200 was the radicand so it would be where the 2 is
and i only could get down to 10√25 before it couldnt be simplified anymore
since 25 cannot be divided by 2 since it becomes a decimal number
prime crystal
supple bridge
i apologize for my negative braincells 😭😭
prime crystal
$\sqrt{200}$ -> $\sqrt{2\times100}$ -> $\sqrt{2\times(10\times10)}$ -> $\sqrt{2\times10^2}$ -> $10\sqrt{2}$
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Astar777
prime crystal
you basically split 200 in such a way that you make a perfect square inside the sqrt (for example here u got 10^2), then u can take it out
wind cloak
$\sqrt{200}$ -> $\sqrt{2\times100}$ -> $\sqrt{2\times(10\times10)}$ -> $\sqrt{2\...
\implies is a thing too
supple bridge
you basically split 200 in such a way that you make a perfect square inside the ...
yeahhh
because it turns into 2 x 100
and 100 is 10 x 10
which is perfect square so it escapes the radical
so its on the outside
leaving 2 on the inside
prime crystal
\implies is a thing too
uhh yeahh
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prime crystal
(just an advice no offense)
yeah i keep using -> for some reason
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fair meteor
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wraith hinge
what is commute
fair meteor
transferable
flint mauve
consider $(A+B)(A^{-1}+B^{-1})$ (assuming they exist). is it $=I$?
solid kilnBOT
eigentaylor
flint mauve
you can distribute
flint mauve
no i meant distribute on the other thing
flint mauve
**eigentaylor**
unless this is true for all invertible A and B, you cannot say that in general
PEMDAS sorta thing. if you have (stuff)inverse, then you generally don't wanna mess with the stuff in parentheses.
matrix inverses are not that nice
half goblet
can someone give me full answer and explanation? It is pretty important 🙂
half goblet
u can explain only one of them
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sour crescent
can someone explain why the outer function from the perspective of the axis of rotation is first in h for shell in this example
sour crescent
and is inner in this one for shell
i cant find a pattern with which equation goes first with regards to h
<@&286206848099549185>
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limpid dawn
Here 4x is vertically greater than x³
limpid dawn
can someone explain why the outer function from the perspective of the axis of r...
Here x³ is horizontally greater than 4x
limpid dawn
limpid dawn
can someone explain why the outer function from the perspective of the axis of r...
blue denotes the greater distance, green smaller
sour crescent
Here 4x is vertically greater than x³
then why is it y^1/3 before y/4
limpid dawn
Because in terms of x it's greater
limpid dawn
You can see horizontally that y = x³ aka x = y^(1/3) is greater
Otherwise draw it into the yx plane
sour crescent
so what should always go first in h
limpid dawn
Vertically it's here 4x
limpid dawn
Horzizontally it's y^(1/3)
sour crescent
from the axis of rotatin
limpid dawn
perpendicular?
sour crescent
here x^3 is outer on the x axis, but 4x is outer on the yaxis
limpid dawn
Thats what I am basically saying
sour crescent
the only thing i can justify it by
from what you are saying
is to look at the graph from the perpindicularly from the axis of rotation
so if we are rotating around yaxis
limpid dawn
In the end it's all about finding h which should be a positive difference. So drawing what you need to subtract should clear your doubt.
In worst case the difference is negative, but good news is you will still get in terms of absolute value the same result, just in negative, so you can put a minus infront
sour crescent
find the outer function on the xaxis
limpid dawn
Yea so here in terms of horizontal height (x-axis) y^(1/3) is outer and y/4 inner
Nothing more or less
limpid dawn
What system
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potent edge
what do they mean when they say in the w space?
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what do they mean when they say in the w space?
dry copper
what do they mean when they say in the w space?
plot the function you got versus the angular frequency w
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dry copper
its going to look like a cosine that decays in amplitude
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potent edge
can someone please explain how they went from the first line to last line?
potent edge
the question is to find fourier transformation of cos(t)
potent edge
this right
dry copper
their version is quite hard, ours is simpler
$\mathbb{F}[1] = \delta(\omega) \ \ \int_{- \infty}^{\infty} e^{-i \omega t} , dt = \delta(\omega)$
wait, no
their s is frequency
our w is angular frequency
the formula is
$\mathbb{F}[1] = 2\pi \delta(\omega)$
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Emily
dry copper
yeah, this is it
potent edge
oh that makes sense
but
now i have trouble understanding why fourier of 1 is that
i will watch a video
dry copper
ill tell you
$\mathbb{F}[1] = 2 \pi , \delta(\omega) \ \ \int_{- \infty}^{\infty} e^{-i \omega t} , dt = 2 \pi , \delta(\omega)$
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Emily
potent edge
yup
dry copper
shall we move to why the first line is correct?
potent edge
yeaaa
dry copper
okay, so, when you try to go from time domain to frequency domain
you find trouble computing the integral and extracting delta
even i dont know how to do it
buuut, the good thing is
take in frequency domain delta(w)
and compute its inverse fourier transform
you will find 1/(2 pi)
dry copper
yeaaa
what i want to say is... if you go forward from time to frequency, you cant show it
but backward, from frequency to time, you can easily show it
using inverse fourier transform
potent edge
ohhhh so we try to find the inverse
dry copper
yeah, go find inverse of delta(w)
potent edge
yeah, go find inverse of delta(w)
okay one thing, here delta is the krnocker delta right?
potent edge
dirac delta
dry copper
$\int_{- \infty}^{\infty} \delta(t) , dt = 1$
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Emily
potent edge
okay so
dry copper
yeaaa so delta(t) = integral of e^iwt
delta(w)
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wind cloak
how does this work, this promotion thing? lol
nah you just became a member of some cult thing
secret clubs
lol
wind cloak
how much helping you do?
no one actually knows besides mods
I think there's specific number of help one do
then they'll get this role
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wraith hinge
New to maclaurins series and wanted to see if my approach to this question was right
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zinc ginkgo
,w maclaurin log(1+x)
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zinc ginkgo
New to maclaurins series and wanted to see if my approach to this question was r...
Yup you're right
mossy dagger
This is the question I need help in:
Find the set of values for 'k' for which the equation 3x^4 + 4x^3 - 2x^2 + k = 0 has four real roots.
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This is the question I need help in:
Find the set of values for 'k' for which t...
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stone kiln
This is the question I need help in:
Find the set of values for 'k' for which t...
What you have done?
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wraith hinge
Yup you're right
Thanks so much
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wraith hinge
It is known that pressure is IP to the volume that contains a certain amount of gas. To what pressure is a gas subjected, if by increasing this pressure by 10 atmospheres the volume varies 2/7 of its value?
A) 25 atmospheres B) 18 atmospheres
C) 14 atmospheres D) 32 atmospheres E) 35 atmospheres
wraith hinge
.close
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ionic relic
If I have 3 planes and i want to know if they intersect or not ,
Can i put z=0 and then check if the three lines intersect or not?
median torrent
If I have 3 planes and i want to know if they intersect or not ,
Can i put z=0 ...
Do you have the equation for the 3 planes?
To answer your question, no because they may intersect somewhere where Z =/= 0
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mossy dagger
What you have done?
literally nothing yet I dont know WHERE TO START
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literally nothing yet I dont know WHERE TO START
mossy dagger
it's like
i feel like if i can find a quartic equation
i can just find the discriminant of it
and solve the inequality discriminant>0
but quartic equation ain't a part of my syllabus
stone kiln
You know what is derivative?
mossy dagger
uh yes! d/dx?
stone kiln
You can solve it by it graphics
mossy dagger
graphics?
main sigil
by sketching the graph, if you know where the derivative is positive, negative and 0, you can create a quite good sketch of the function
stone kiln
You only need to sketch
main sigil
is that the only way?
Not the only way, but quite certainly the best way. You don't have to draw it if you can at least imagine it
mossy dagger
okay if i sketch then what's next?
stone kiln
3x^4 + 4x^3 - 2x^2 = -k and then right and left side of equation are function and you can sketch it
f(x) = 3x^4 + 4x^3 - 2x^2
g(x) = -k
And intersection of graphs are solution
Lets first do g(x) what is it?
For example if k=1 what is grapth of g(x)
somber ginkgo
bruh i gotta draw now?
you don't have to
i'd probably do this question by first finding the maxima and minima of 3x^4 + 4x^3 - 2x^2
once you have hose you know k has to lie between the minima and maxima for 4 solutions
stone kiln
once you have hose you know k has to lie between the minima and maxima for 4 sol...
Yeah
mossy dagger
i understand
stone kiln
Graph allow you to see how many solution it has for specific k
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limpid sleet
How would you graph f'(1) does not exist ?
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How would you graph ``f'(1) does not exist`` ?
zinc ginkgo
,w plot abs(x)
solid kilnBOT
zinc ginkgo
|x| is famously not differentiable at 0
limpid sleet
|x| is famously not differentiable at 0
So do I just draw |x| on the graph?
zinc ginkgo
no idea what you're trying to do
limpid sleet
How would you graph ``f'(1) does not exist`` ?
I just need to graph all the points in the first photo and I am stuck on f'(1) does not exist
zinc ginkgo
I just need to graph all the points in the first photo and I am stuck on ``f'(1)...
the derivative isn't defined for a single point
limpid sleet
the derivative isn't defined for a single point
How would I graph that though? I could have a hole at x=1 but one of the points I am supposed to graph is f(1) = -2
dull temple
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sinful brook
help me solve for x
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help me solve for x
bright quarry
just subtract 1 and flip
river willow
that is the easiest way yea
solid kilnBOT
knief
sinful brook
then i multiply both sides by x-7?
bright quarry
you could
solid kilnBOT
knief
sinful brook
i’m so confused 😭
bright quarry
is this supposed to be finding the inverse function or something?
sinful brook
no im just solving for x
bright quarry
why
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hexed shard
I tried to prove that an image of a sphere from far enough away results in essentially parallel rays at the image plane. However, I need help rewriting it for clarity.
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waxen patio
How do I use the (f(x) - f(a))/f(a) formula to solve this problem?
bright quarry
How do I use the (f(x) - f(a))/f(a) formula to solve this problem?
what formula?
bright quarry
you mean $\lim_{x \to a} \frac{f(x) - f(a)}{x-a}$
solid kilnBOT
knief
frail heron
Top formula
did you copy it correctly?
bright quarry
apparently not
waxen patio
nope
frail heron
nope for?
a. knief wasn't mentioning the formula that I'm looking for
b. My copy is flawless
waxen patio
no, I did not copy it correctly
frail heron
alr, it is normally used for looking derivate of a function
which can also be used for finding tangent
waxen patio
Ye that's what I'm doing
would you be able to walk me through solving it? I keep getting stuck
waxen patio
ok can you ping someone else to
frail heron
the helper up there may be able to resolve your problem
waxen patio
@bright quarry
simple haven
As a hint, let a = x - h, and let h -> 0 instead.
These are equivalent, and this form is significantly more convenient to work with.
waxen patio
ok. what's the use for the other formula then?
simple haven
It's equivalent
Might be useful in some situations
Depends on the function in question
waxen patio
As a hint, let a = x - h, and let h -> 0 instead.
Also, what's the difference between this one and then one that is f(x+h)?
The bottom two in my picture
waxen patio
Ok
solid kilnBOT
tank_driver011
ember hull
plug in x+h or the others, which depends on the definition of a derivative that is being used.
e.g.,
ember hull
**tank\_driver011**
i made a mistake of not putting limit h app 0 next to the 1/sqrt(x)..
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zinc ginkgo
yes it does
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wanton minnow
can someone explin
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can someone explin
wanton minnow
i don't understand solution/or example to show it is false
if not explanation at least step/nudge to understand it
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somber ginkgo
can someone explin
the idea is if we set z=0 we can simplify slightly
so if z=0 it suffices to find vectors x,y such that
$x \cross y = 0$
solid kilnBOT
LY
wanton minnow
now any 2 parallel vectors will cross to the 0 vector
last part i don't understand
somber ginkgo
that just comes from the cross product
what do u know about the cross product so far?
wanton minnow
well x X x = 0
cuz there's not really a unique solution to finding something orthogonal to X and itself
and the direction matters
x X y = - y X x
btw i kinda got this question, and i have another about the scalar equation of a plane
in the form n1x1 + n2x2 + n3x3 = d
where n = [n1, n2, n3] normal vector and x1, x2, x3 variable for any point in the plane
what does D represent?
it feels like a y-intercept when you're solving sometimes because once you find the normal vector you have to sub in a point and solve for D then you're done
somber ginkgo
cuz there's not really a unique solution to finding something orthogonal to X an...
yeah so it's basically that same idea
if instead we had 2 vectors that are parallel
then there's not really a unique vector that's perpendicular to x and say kx
hope that made sense
somber ginkgo
in the form n1x1 + n2x2 + n3x3 = d
where n = [n1, n2, n3] normal vector and x1,...
d = (shortest) distance from origin
wanton minnow
no but how is that derived
cuz in the original definition, the scalar equation of a line is derived from the dot product of the normal against any line PQ where P is some point and Q is x1, x2, x3
which equals 0
so if P = (1,1,1)
so n*PQ = n1(x1-1) + n2(x2-1) + n3(x3-1)
= 0
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civic dune
Solve w Limit Comparison Test
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Solve w Limit Comparison Test
civic dune
It is obviously done with Direct Comparison
But we are asked to do it with LCT
Is it possible?
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cedar nacelle
could u compare it with 1/n^3/2
then it would be lim cos^2(n)
then you only need to know the convergence of 1/(n^3/2) and whatever cos is
I think
its been a while since I touched anything comparison test @civic dune
cedar nacelle
yea
civic dune
so i cannotu se it
for the LCT I need some real number A
as the result of the limit
civic dune
unlike the nth term test which allows for DNE 🙄
cedar nacelle
then isnt the answer unsolvable with lim comparison test
I know some textbooks use that card
mine does
civic dune
My teacher is trying to get us to focus on one test
So yeah its not likely to be possible
Just wondering though
.close
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unborn palm
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zinc ginkgo
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!15m
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fair meteor
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fair meteor
is this true?
lusty delta
(to be honest when i first reacted to that, i had not read the statement 
i just saw the three yes reactions and based on that assumed it must have been true)
trail ingot
(to be honest when i first reacted to that, i had not read the statement <:hmmca...
LOL i just did that
i still have not read the question
and i refuse to
whole coral
Proof by popular vote 
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pseudo fossil
How do I start this? Usually a question like this gives only one equation but now there are two so I'm confused...
leaden atlas
First what do you expect the dimension of the set to be?
pseudo fossil
Not sure, one?
leaden atlas
It is reasonable to assume that indeed you are looking for one vector.
Then by substracting the second equation to the first you get y = 2z and the first to twice the second gives you 3x = 4z. This suggests you fix z to a random value (say 1)
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pseudo fossil
Do I set up both equations as a matrix first and solve?
leaden atlas
You can
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shrewd nacelle
I'm working on part (a). The parameterization of z=2x^2+y^2 is (1,t,2+t^2) because its in the x=1 plane, so we know that x is 1. For y it would be t. And for z we just plug in t and 1 right? am i missing something or is it just this simple?
lament reef
I'm working on part (a). The parameterization of z=2x^2+y^2 is (1,t,2+t^2) becau...
it is just that simple yes
shrewd nacelle
huh, ok. Normally when i think something is really simple its because im doing it wrong. So i just wanted clarification
thank you
and in part b, what does it mean by analogous?
or is it just asking me to find another parametrization where instead of it being x=1 its y=3?
lament reef
or is it just asking me to find another parametrization where instead of it bein...
this yeah, idk why it says analogous
just trying to say it's similar to how it's done in (a)
shrewd nacelle
ok, so i should just be able to plug in 3 for y then
wait no
would i plug in sqrt(3) instead?
no its 3
ok, so i did b. now im working on c. how would i determine the equation of the tangent plane here?
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shrewd nacelle
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rare sapphire
Hey guys, I need assistance.
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Hey guys, I need assistance.
rare sapphire
Some directions more specifically.
charred trail
sure, just ask
rare sapphire
It's an statistics problem and I don't know where to start.
Basically is this:
The average value of land and buildings per acre of a sample of farms is R$ 2,500.00, with a standard deviation of R$ 350.00. The dataset has a bell-shaped distribution. Furthermore, it is known that the region considered for the study has 768 farms. Thus, the number of farms that have the value of land and buildings per acre in the interval between R$ 1800.00 and R$ 3200.00 is approximately:
730
760
Impossible to estimate the result
522
499
384
752
I've also included the answers for reference.
*Possible answers.
It is very tempting to pick the third option because I don't if you can estimate the result using any of the formulas.
Like standard deviation, mean, median, mode, etc.
charred trail
so you have a random variable, say X, which is distributed normally, N(2500, 350^2), and you need to find P(1800<=X<=3200), and then multiply this by 768
have i understood the question correctly just to confirm?
rare sapphire
You have the average value of real estate property among a sample of data, which is R$ (which is my local currency)2500.
Which I guess that's the mean, represented by x with a macron.
charred trail
okay yes, so first, recall how we denote normal distributions, by N(mean, standard deviation^2)
here, X~N(2500, 350^2)
rare sapphire
Ok, that tilde is supposed to be on of the X right?
charred trail
the tilde reads as "X is distributed normally/X follows a normal distribution" with parameters (mean = 2500, sd^2 = 350^2)
rare sapphire
Ok, sorry I've encountered this format before, lol. My professor never taught this.
charred trail
no need to apologise haha
rare sapphire
He just showed us the bell curve graph and how to find quartiles.
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rare sapphire
No
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unborn creek
can someone pls help
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can someone pls help
unborn creek
I'm trying to find the distance between A to B
i found the slope, it gave me 1,43x
because i did 0 = 1,75x + 2,5
-2,5 = 1,75x
-2,5/1,75 = 1,75/1,75
x = 1,43 am i wrong
potent bone
...well that seems to be a correct calculation of where that line intersects the x axis, but i have no idea what you'd be planning on using that number for
unborn creek
...well that seems to be a correct calculation of where that line intersects the...
because im trying to find the point B
B (?,?)
marsh wigeon
maybe you could try splitting into x and y components somehow
potent bone
well B isn't at y = 0
it's the point where the two lines (y = 1.75x + 2.5 and y = -1.5x + 9) intersect
unborn creek
maybe you could try splitting into x and y components somehow
wdym
marsh wigeon
wdym
like in physics with vectors you split into components
turn each side into a right angle triangle sorta thing
unborn creek
it's the point where the two lines (y = 1.75x + 2.5 and y = -1.5x + 9) intersect
yeah the 1,75x + 2,5 is the formula of the line
unborn creek
like in physics with vectors you split into components
..
potent bone
yeah the 1,75x + 2,5 is the formula of the line
well it's the formula of one of the lines, there's also another line
unborn creek
well it's the formula of one of the lines, there's also another line
yes but what would i be doing with that line cause im not sure
potent bone
well with both lines you can find the coordinates of B
unborn creek
oh so wait how would the calculations look like
potent bone
well, how do you find the point where two lines intersect?
unborn creek
i think i would like have to find both of their slopes
marsh wigeon
just equate them right
potent bone
the equation of the line is satisfied by every point on the line, and B is a point on both lines, so it's the point that satisfies both equations
unborn creek
just equate them right
im sorry cause i dont speak english that good since the maths im in are french
potent bone
the equation of the line is satisfied by every point on the line, and B is a poi...
y = 1.75x + 2.5 and y = -1.5x + 9, so 1.75x + 2.5 = -1.5x + 9
then solve that
unborn creek
ohhhh so like y1 = y2
marsh wigeon
exactly
unborn creek
thanks guys
marsh wigeon
find x then plug it in
marsh wigeon
by pluggint it in to any one of the equations
potent bone
yeah once you have the x you can just put it into the equation of one of the lines
unborn creek
alright so like by doing it with the (-2,1)?
potent bone
...no, you'd take the x value of B and put it into one of the equations to get the y value of B
potent bone
y = 1.75x + 2.5 and y = -1.5x + 9, so 1.75x + 2.5 = -1.5x + 9
and you'd find the x value of B by solving this
unborn creek
alright im solving it right now ill keep u guys updated
alright so i got x = 2 and y = 3,5
im assuming those are the points for B?
marsh wigeon
yep
potent bone
wait how did you get 3.5
unborn creek
wait how did you get 3.5
alright let me begin
1,75x + 2,5 = -1.5x + 9
+1,5x
both sides
3,25x + 2,5 = 9
-2.5 both sides
3.25x = 6.5
divide it
i got 2
so x = 2 now
y = 1,75x +2,5
wait ur right
i didnt so + 2,5
do
i just did 1,75(2)
whoops
my mistake
marsh wigeon
👍
potent bone
alright so yeah B is (2,6)
unborn creek
alright alright
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unborn creek
i have 1 more question
astral merlin
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astral merlin
For A) I got $100
But I can't find out how to solve B)
The topic is derivatives
<@&286206848099549185>
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shut spade
Really struggling with these two problems down here:
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Really struggling with these two problems down here:
shut spade
The lecturer mentioned to use double set inclusion for both, but I don't exactly see how in this case
trail ingot
have you made venn diagrams yet?
shut spade
Since the definition of what we're given (A delta B) doesn't give us enough to work with for the double set inclusion (at least, that's what I think)
trail ingot
what do they look like?
trail ingot
it might also help to think of what this means in english. x is in A \Delta B means x is in exactly one of A or B (not both, not neither)
yea those look fine
shut spade
Right right
trail ingot
errr
trail ingot
yea, like this
shut spade
God bless
shut spade
The lecturer mentioned to use double set inclusion for both, but I don't exactly...
Moving on to the latter part of the question, how would we use double set inclusion?
Like I'd get it if we had basic operators like AND and OR to manipulate around
trail ingot
proving something is the empty set by double inclusion seems weird 
i wouldn't do that for A \Delta A
shut spade
But since this is a completely new operator (from what they've introduced) I wouldn't exactly know how to manipulate the left side to match the right side
Do you get what I mean
trail ingot
yea. but it is just AND and OR
shut spade
But on the left side right
How would you prove the left side if a subset of the right
trail ingot
wait are you talking about b
shut spade
Yeah
trail ingot
what does it mean for $x$ to be in $(A\setminus B) \cup (B\setminus A)$?
solid kilnBOT
:bending_skull:
shut spade
x exists in A without B and B without A
shut spade
Right, sorry
shut spade
and what's A without B?
A without B is
The set A disregarding all elements that exist in B
(right?)
shut spade
Yes
trail ingot
looks a lot like this
shut spade
See that's what I was thinking
But how would you write that
Also (and I don't mean to be difficult, appreciate all the help I can get) but the Piazza (our student help centre) mentioned 1b should prob use double set inclusion
trail ingot
there are different ways you can do it, but sure, you can use double inclusion
trail ingot
so x is in A\B means x is in A and x is not in B
this is really all there is to it though
shut spade
I totally get that but I don't exactly know how to write that in a way that's rigorous enough to hand in
Does that make sense
trail ingot
yes that makes sense. you are trying to prove 2 sets are equal. let x be an element of one of them, then show x is in the other one
so....
trail ingot
it should go like: let $x \in A \Delta B$. then... thus $x\in (A\setminus B) \cup (B\setminus A)$
shut spade
Yep
solid kilnBOT
:bending_skull:
shut spade
Like use that definition above
To get to A \ B U whatever whatever
Ofc
Isn't that kinda weird shifting from words to math symbols
I'll try the proof out on my own but
trail ingot
Isn't that kinda weird shifting from words to math symbols
not at all
shut spade
Is there anything I should look out for/
Got it
So like
Let x be an element of A delta B
It follows that x is an element of A and x is not an element of B OR x is an element of B and x is not an element of A
trail ingot
the key to the proof is that $$x \in A \Delta B$$ is equivalent (by definition) to $$(x\in A \text{ and } x\not\in B) \text{ or } (x\in B \text{ and } x\not\in A)$$ and that's equivalent (by set minus definition) to $$x\in (A\setminus B) \cup (B\setminus A)$$
solid kilnBOT
:bending_skull:
shut spade
I'm not exactly sure what other steps to take bc after this is basically just the end stmtt
shut spade
**:bending\_skull:**
Yep
This is what I'm talking about right
Is that not too simple
trail ingot
no, the question is pretty simple really
shut spade
God bless
trail ingot
like piazza says, you just need to use the definition of set minus
trail ingot
or set difference whatever you wanna call it
shut spade
Holy shit you're cracked
Yeah
Got it Got it Got it
Ok I get the first part
I get the second part
Would the first part (a) be (b)?
Same thing we did?
But this time without the A \ B U whatever
We're just using the same first definition
trail ingot
for A \Delta A = \emptyset, i would just write there are no elements x with the property x is in A and x is not in A
so it is empty
trail ingot
yea that would be weird for showing something is the empty set
shut spade
I guess like
You know the empty set is the subset for anything
So that's easy to prove
And then the other side
shut spade
for A \Delta A = \emptyset, i would just write there are no elements x with the ...
Is just this
trail ingot
for A \Delta A = \emptyset, i would just write there are no elements x with the ...
i suppose. i would say this is enough but whatever you wanna say
shut spade
I'm just gonna follow whatever the instructor wants rs
And then the one where its A delta empty
shut spade
for A \Delta A = \emptyset, i would just write there are no elements x with the ...
I suppose I could borrow what you said here for it
Thank you so much! That really helps
trail ingot
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hard sundial
an urn contains r red balls and g green balls. a ball is drawn at random and then it is returned to the urn with k additional balls of the same color. prove by mathematical induction that if n=2,3,… such experiments are made, the probability of a red ball at each draw will always be r/(r+g) and the probability of a green ball will always be g/(r+g)
i’m struggling with the induction step of the proof
indigo latch
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hard sundial
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shrewd nacelle
this isnt their channel mate