But thanks for the help
#help-0
supple tundra
just use my fitness pal
supple tundra
it will do this sort of calcualtion for u
terse canyon
I have food scale
I put the food in scale to see how much grams
Its 105
Thanks nerds
🤓
@sterile idol
sterile idol
<@831504941083394059>
?
sterile idol
Yeah
sterile idol
Nice
empty terrace
lone heartBOT
tacit arch
that looks like the expansion of (a+b)^100
empty terrace
but 100C1 , 100C3 .. are not there
tacit arch
compare it to (a-b)^100
carmine heart
lone heartBOT
carmine heart
i am confused... what equation do you have to set up to find lengths
is this some sort of 45 45 90 triangle thing
placid zinc
No, it likely won't be a special triangle. The angles won't come into play here
carmine heart
then how would i set up the lengths? do i use a system of equations?
long iris
We have two legs right?
carmine heart
yes
long iris
Call one of the legs lenght x others y
carmine heart
alright guess im doing a system of equations
long iris
Will you try or should i go on
carmine heart
i kinda want you to explain
long iris
Okay it says hypotenuse is 1 more than twice as long as one of the legs
So it is 2x+1
Also it says it is 2 inches longer than the other
So it is y+2
long iris
We will do something like that but only one variables
It is early for that
It is the hypotenuse of same triangle so 2x+1 and y+2 must be same
Can you set a equation and write y with terms of x?
Like y=ax+b
carmine heart
im confused on what you are asking
long iris
Did you get that 2x+1=y+2
carmine heart
yes
long iris
Thats correct too but i want y=2x-1
carmine heart
okay
long iris
What is hypotenuse here
carmine heart
x^2 +(2x-1)^2= (2x+1)^2
long iris
You are welcome
carmine heart
.close
tacit epoch
This is what I got for #2
Not sure what to do next
lone heartBOT
This is what I got for #2
Not sure what to do next
@tacit epoch Has your question been resolved?
fiery flame
This is what I got for #2
Not sure what to do next
Have you tried solving by substitution?
Such as isolating A in your first equation and subbing it in your second
fiery flame
A and B are constants so you can do it with the x
hot bone
lone heartBOT
vale sluice
lone heartBOT
little drum
(ヘ･_･)ヘ┳━┳ I don't see any efforts with making a proper FBD
Also, sorry we're a math server. Check #old-network for a link to the physics server. Although I'd suggest making a proper FBD of the question before asking it there.
vale sluice
this was in a math textbook
glass lichen
all the forces cancel out
little drum
da heck
glass lichen
Vectors are apart of math
little drum
okie
wary stream
Draw FBD, Break T into x and y components, then equilibrium concept
little drum
including "Tension"? then what's the physics doing
wary stream
da heck
In my diff eq book, it had Hooke's law related stuff in there. It was a math class with physics problems
vale sluice
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lone heartBOT
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Available help channel!
flat gust
I’ve found the y-intercept and the x-intercepts already by factoring and making x = 0 to find the y-intercept. But, how do you find the turning points? Pre Calc 12
wary stream
I’ve found the y-intercept and the x-intercepts already by factoring and making ...
Calculate the values between the roots and use those
So like calculate a value in those ranges, like x < -2, -2 < x < 0, etc
restive palm
restive palm
I consider it quite helpful to understand what you are doing
restive palm
Once you build intuition for what you are looking for, you should be able to realize it will be the values between the roots as you mentioned.
"Values between the roots" isn't very helpful on it's own.
But ok
wary stream
The mathematical way, without a graph is my method
wary stream
"Values between the roots" isn't very helpful on it's own.
And I provide examples of the ranges to use
restive palm
I don't personally care what your way is, I care about ninki getting a intuition for the problem and learning.
wary stream
Well, if the problem says don't use a graphing tool, how would you do the problem then?
restive palm
Once you build intuition for what you are looking for, you should be able to rea...
^ : This is off-topic
wary stream
Or maybe you should present how to do it without a graphing tool, like me
wary stream
I didn't realize that was 1/2
flat gust
And get the yturningpoints
wary stream
x < -2, -2 < x < -1/2,
Like a value in those intervals
So something like f(-3), f(-1)
And then you can see approximately how the graph would look
flat gust
Wouldn’t that just give u like the left side of the graph? What about the right side?
wary stream
Same process, I just didn't provide the values for that side because I'm letting you do that part
flat gust
Ok so then for the right side. I choose x-values, x > 1, -1/2 > x > 1?
wary stream
Yep
lone heartBOT
lone heartBOT
Available help channel!
oblique stirrup
Can I get some help with this problem? I can’t even decipher the content, like what is the E symbol before the coordinates
tacit arch
$c \in (0, 1)$ means $0 < c < 1$
ocean sealBOT
riemann
oblique stirrup
so its saying g(t) x axis value is between 1 to 0 and
g(c) x axis value not between 1 to 0?
I dont get what its saying at
"but such that for no... does the equation g(c) = c hold"
tacit arch
$g(c) = c$ does NOT hold
ocean sealBOT
riemann
tacit arch
slowly read the problem again and ask questions if you don't understand
e.g. f(x) = x won't work because f(c) = c for all c, so DON"T pick g(t) = t
pick almost any other function
lone heartBOT
@oblique stirrup Has your question been resolved?
oblique stirrup
I dont get it..
oblique stirrup
.close
random mica
Hello, if 2 right triangles have angles of equals mesures, does this mean their hypotenuse is equal ?
random mica
if yes how do you prove it ?
(it seems to be true with geogebra, but i can't prove it )
wanton junco
you mean, if the triangles have the same angles ?
random mica
yea
random mica
i don't know, congruence is next chapter in my book, but i guess similar
random mica
like i have a RT of 60 deg + 30 deg + 90 deg and the other one too
wanton junco
if 2 right triangles
or rather
if ANY 2 triangles measure 2 equal angles
then they are similar
the hypotenuse wouldn't be equal in this case, it will be proportional
random mica
hmmm, how you solve this exercice, there is no solution for this one ( ex 14 ) in my book :/
i tried that because i thougth "equal" angles mean equal hypotenuse
wanton junco
notice that the chapter talks about the sides being equal
and not the angles
equal angles here are a consequence of the equal sides that are described but not vice versa
in this cause the hyp will be equal
given a triangle with angles a,b,c, there are infinite triangles that have the same exact angles, but are proportioned differently
lone heartBOT
@random mica Has your question been resolved?
random mica
notice that the chapter talks about the _sides_ being equal
if i suppose something, does my prove is valid ?
If i suppose d(P,S) = d(S,M)
it mean d(O,P) = d(O,M)
but it feels weird
opal dock
lone heartBOT
opal dock
can anyone tell me how to solve arcsine of .5 and get in this pi/3 form?
like is this jus tsomething you memorize or what
thorn kindle
Yeah pretty much
pale kestrel
Firstly, do you know what the domain and range of arccos is...
glass lichen
like is this jus tsomething you memorize or what
pretty much
thorn kindle
You should have the unit circle committed to memory
You only really have to memorize 1/4th of it even
opal dock
ok i was wondering if there is some method for solving that i missed out
thorn kindle
Its simple. Acos has to be the range of cos
opal dock
thanks guys
pale kestrel
You can work out the trig values
of 30, 60, 45 degrees
By drawing triangles
Here, you would have to recognise 1/2 ratio for cos corresponds to one of those. But you wouldn't be asked to remember anything outside of 0, 30, 45, 60, 90 (plus multiples of 90). ie. 0, pi/6, pi/4, pi/3, pi/2 + multiples of pi/2 in radians.
spark latch
lone heartBOT
spark latch
feeling really slow rn
this should be quick but what is the process that makes these equal
pale kestrel
distribute division over subtraction
spark latch
okay yup makes sense
just split it up like and its just -1/x + x/x which is -1/x + 1
ty
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lone heartBOT
spark latch
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jagged imp
if u=x^2+1, when x=0, u=? and when x=3, u=?
spark latch
ohh okay so its just that?
when x = 0 u = 1 and x = 3 u = 10
okay yeah I hadn't seen that throughout the lesson
when all does that rule apply?
just anytime I use u-sub?
jagged imp
whenever you apply a u sub to a definite integral you'll need to change the bounds accordingly
lone heartBOT
lone heartBOT
Available help channel!
serene heart
Hello! Im reviewing my mistakes on my test. Specifically Relations and Functions. Here are my questions.
Why is this not a function?
Here are my pre-thoughts.
The 1 in x is the same as the 1 in y (Im not sure what that symbol is, Perhaps +-?)
wary stream
It's because each x value has two y values
serene heart
It's because each x value has two y values
Is it 0 and the +- 1?
im not sure what that symbol is
wary stream
That's plus/minus
serene heart
So it can be either right?
wary stream
$$\pm 1$$ means +1 and -1
ocean sealBOT
dldh06
wary stream
Not either but both
serene heart
I see
serene heart
Is it 0 and the +- 1?
Though it is this right?
wary stream
It's mainly because the $\pm$ part
ocean sealBOT
dldh06
ocean sealBOT
dldh06
serene heart
oh that makes sense
wary stream
Because for that x =1, it's saying y = $\pm 1$ meaning that y is both 1 and -1
ocean sealBOT
dldh06
serene heart
Since its both that means if you plot it in, it is (1,1) and (1,-1)?
wary stream
So you have the coordinates of (1, 1) and (1, -1)
carmine badger
is there a method for finding the maximum value for a as x,y approach 10? $a = (tan(theta) * (x-5)) - (y-5)$
ocean sealBOT
Darcy
lone heartBOT
@carmine badger Has your question been resolved?
mossy lion
lone heartBOT
mossy lion
don't want a solution or examples, just want to know if my deduction for each is correct (so that i don't end up on a wild goose chase)
a. impossible.
b. impossible
c. possible
d. possible
blissful whale
Still reading
but I think a is possible
Something like
$$ A := { -2^{-2n} | n \in \mathbb{N} }, B := { -2^{-2n-1} | n \in \mathbb{N} }$$
mossy lion
would this work?
$A={\sin(n):n\in\bN}$
$A={\cos(n):n\in\bN}$
ocean sealBOT
nix
mossy lion
checking this out
blissful whale
I think it does but it is hard to proof that it does.
It has something to do with periods of sin and cos and pi being irrational I think.
ocean sealBOT
M8732
blissful whale
(just fixed my example, it was for inf not sup)
blissful whale
Okay let me see with b - d
mossy lion
okay so a is possible. ill try to come up with my own example.
blissful whale
I think b can be satisfied as well.
It would be non-possiböe if there was only finitely many intervals
but if there are infinitely many the intersection can be non-open and then it can contain a single element.
mossy lion
it says open intervals though so i don't think that would work. that was my first thought too
blissful whale
Should I give an example?
mossy lion
hmm. okay
mossy lion
darn. i was close but i didn't think of having the element be zero. i was thinking things like (1/(n+1),1/n). i need to start considering ways to use zero more.
blissful whale
The thing is that if the itnersection is open then it cannot work
open sets are either empty or uncountable.
But only fininitely many intersections of open sets stay open so I was thinking back to a counterexample why that was the case.
(c) exists but not sure about (d)
Did you find an example for (d)?
mossy lion
Did you find an example for (d)?
sorry. no i was thinking of one
blissful whale
sorry. no i was thinking of one
I think (d) might be impossible but I am only able to find a compelling reason no proof. xD
My compelling reason is that if the space was bounded (I mean the intervals are bounded at least), then there exists something called the finite intrsection property which is exactly what we want.
lone heartBOT
@mossy lion Has your question been resolved?
lone heartBOT
mossy lion
.reopen
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mossy lion
My compelling reason is that if the space was bounded (I mean the intervals are ...
i dont think we've learned about that but it's good to know that i should start looking for reasons it is impossible.
@blissful whale
sorry for the delay. was driving. thank you so much for the help btw
.close
frail shard
hello, can someone please help me with these types of problems? im confused on where to begin.
frail shard
the examples in the book are always y=e^something but there is no y here
im also able to find the derivative of natural log functions like e^1-x, but i cannot find how to apply it to these problems
harsh swallow
You can assign y = to them yourself if that helps
The point is that these expressions can be written in a way thats easier
For example the first one can be written as 15
harsh swallow
Yes
harsh swallow
Do you know inverse functions?
frail shard
im not sure
harsh swallow
Like x^2 and sqrt(x)
frail shard
yes
harsh swallow
e and ln are the inverse to eachother
Meaning if you apply both at the same time they cancel and you are left with whats inside
frail shard
ohhh that makes sense
im sorry if my mind is just foggy rn
but im trying to think of log properties, and i cant seem to apply it to 3a
harsh swallow
a ln b = ln b^a
harsh swallow
Ye
harsh swallow
Ye
harsh swallow
No because you have to apply the function
To apply ln you do ln()
Do apply e you do e^()
harsh swallow
Yes
frail shard
ok ik how to do 4b because its a function in the exponent, but im confused on 2b
would it just be -1?
because 1/e=e^-1
harsh swallow
Yes
frail shard
thank you so much!
harsh swallow
You got the hang of this
frail shard
😄
one last question on 3b, ik the answer is 10, but can i for all problems just cancel out ln with e? for example, if it was ln(ln(ln(e^e^e^10))) it would 10?
harsh swallow
There can be tricky cases but simple things like these can be just cancelled
tame sonnet
lone heartBOT
tame sonnet
Pls help
naive valley
Presumably you know about erf or erfc or some similar function for computing probabilities with normal distributions?
tame sonnet
Bro tell pls
lone heartBOT
@tame sonnet Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
royal meadow
brain is utterly utterly fried right now
lone heartBOT
brain is utterly utterly fried right now
royal meadow
what does part ii mean
what is ds
i can only think of dS??
and then what does it mean to integrate over that weeny little surface
tacit arch
what does part ii *mean*
That's the notation for boundary of a region
Eg the boundary for the disk is the circle
royal meadow
oh
then what's ds
oh i'm a fool it's just mag dr
i thought it was that but i also thought this sheet wouldn't go into straight line integrals yet
ok right
.close
cinder sundial
sin 90 degree will equals to 1
lone heartBOT
sin 90 degree will equals to 1
shell narwhal
True
quaint nebula
yeah
cinder sundial
i wonder what the triangle looks like
shell narwhal
its a vertical line
Since cos90=0
or see it as a triangle with an infinitely small width
That tends towards 0
cinder sundial
i can't imagine it
bright hedge
well if the angle is 90 degrees
cinder sundial
is it still a triangle
bright hedge
then the opposite side would be equal to the hypotenuse
cinder sundial
then the opposite side would be equal to the hypotenuse
then its still a triangle?
god i wanna see the shape
i wanna know what it looks like
its not a triangle right
little drum
A 2D shape where sine 90° = 1?
little drum
You want to use the Soh Cah Toa method to figure why sin 90° = 1?
cinder sundial
ohhh
little drum
:O
bright hedge
?
if 90 degrees is the angle in a right triangle, its opposite side would be the hypotenuse
so opposite/hypotenuse = 1
cinder sundial
if 90 degrees is the angle in a right triangle, its opposite side would be the h...
i don't get it, so its a triangle
i thought it was a line
cinder sundial
if 90 degrees is the angle in a right triangle, its opposite side would be the h...
then how the opposite side equals to hypotenuse
little drum
Yep it's a line
bright hedge
then it can't be a triangle?
because the hypotenuse needs to be less than the sum of the other two sides
oh wait...
😮
gray isle
a line would be a degenerate triangle
cinder sundial
its not line, its a triangle
cinder sundial
a line would be a degenerate triangle
ohh
can i call a line segment as triangle next time i see a straight line
is it legal
gray isle
you'd need to mention degenerate
cinder sundial
got it
i never heard about degenerate triangle before , i should take it to my note
i think the question is solved
thank you guys
gray isle
for angles outside of (0,90°) you should apply the unit circle definitions instead of sohcahtoa
stable zephyr
lone heartBOT
stable zephyr
hello can soneone help me with this?
vale wigeon
@stable zephyr what are you having trouble with?
stable zephyr
have you ever done anything with limits before?
not yet
vale wigeon
such as: $\lim (f(x) + g(x)) = \lim f(x) + \lim g(x)$ (assuming the limits of $f$ and $g$ exist and aren't, like, infinity or something)
ocean sealBOT
Ann
vale wigeon
or you could just have someone write it out explicitly for you.
vale wigeon
that's one way of saying it.
stable zephyr
okay okay thank you!
pine kettle
stable zephyr
.close
lone heartBOT
lone heartBOT
Available help channel!
odd rover
can someone help with b) ii and ii pleasee
lone heartBOT
can someone help with b) ii and ii pleasee
odd rover
<@&286206848099549185>
lone heartBOT
@odd rover Has your question been resolved?
odd rover
.close
alpine sable
wtf is b^2 - 4a? how does that indicate a double or single root
charred flint
the quadratic formula is basically [thing] +/- sqrt(b^2-4a)
if the inside of that square root is 0, the roots become [thing] +/- 0, so there's just a single one of them
alpine sable
but isnt it sqrt(b^2 - 4ac)
charred flint
right, but you can just check b^2-4ac instead
since when that's 0 the square root is 0
just a little simplification
bright hedge
i think his question
is that the picture says check b^2 - 4a
instead of b^2 - 4ac
charred flint
oh wow I missed that typo
bright hedge
what about x^2 - 2x + 3?
now its not a double root
it only worked b/c the constant was 1
so 4a = 4ac
alpine sable
ohhh good point
bright hedge
so ur teacher prob just forgot to write c
alpine sable
yea
bright hedge
cuz as we have just shown its not true for everything
lone heartBOT
@alpine sable Has your question been resolved?
covert agate
hi
bright hedge
bright hedge
its best to draw these things in 3d
cuz then you can see that the base (or some side length) of the figure would be a function of x
hence why you would be changing the value of x (that is, x would be your independent variable)
bright hedge
i mean if you try to visualize it
covert agate
i mean if you try to visualize it
can’t
bright hedge
if the cross-section would be perpendicular to the x-axis then you would slice it down the y-axis
covert agate
my brain is too weak
bright hedge
so the solid's base would be the y-coordinate
hence why you would be changing the value of x (b/c the y-coordinate would be dependent on the x placement)
in this case the cross sections are perpendicular to y
covert agate
oh
bright hedge
so you can see why you would wanna sum over y-values instead of x
covert agate
it’s not revolution
bright hedge
well its pretty much the same hting
covert agate
we’re given the base of the shape, and the cross sections perpendicular to x axis
bright hedge
it would just not have a nice looking shape
covert agate
well its pretty much the same hting
i dont see the relation
bright hedge
how?
you are slicing it down perpendicular to x-axis
and you are given an area function w.r.t. x
so wouldnt it logically make sense (even w/o visualizing it) that you would wanna sum over values of x
instead of y?
covert agate
(i still can’t visualise after watching khan’s vids that’s how suck i am)
bright hedge
you could also look into conic sections
(slicing the conic down certain directions, to make the four big shapes--hyperbola, ellipse, circle, and parabola)
bright hedge
and i told you to visualize it
in 3d coordinates
hence why i recommended that you go watch something about cross sections
covert agate
is there a proof of some sort?
hasty elk
well, each cross-sectional disk can be treated as an infinitesimal volume (i.e. A(x) dx is the infinitesimal volume)
so
little drum
The same riemann sum - integral method :o
little drum
Hmmmm. A physics lecture on finding the center of mass / moment of inertia would be pretty beneficial for your intuitive understanding tbh
Like, find the center of mass of a hemisphere or a part of sphere with solid angle theta.. and such :o
It would be a nice practice to not just see the $\lim_{n\to \infty} \sum_{k=1}^n f(x_k) \Delta x$ as just $\int_a^b f(x) \dd{x}$ but to be able to understand what the limit individually stands up for, and how it extends to more general cases.
ocean sealBOT
Ansh
covert agate
i literally fail to visualise ‘volume with cross sections’
i spent the afternoon trying to help me visualise
on geogebra etc
yet here i am lol
little drum
Check the link Chad sent
the "curve revolving" around x-axis, is literally, the curve y = f(x) revolving around the x-axis but since a 2D - cartesian plane fails to allow you the rotation of the curve tangential to the plane, you must turn to the 3D model.
bright hedge
what does tangential to a plane mean?
bright hedge
oh
little drum
i literally fail to visualise ‘volume with cross sections’
moreover, the "volume with cross-sections" thing you fail to understand, is just the same as how you did the area under curve by considering sums of smaller rectangles times delta x in the Riemann sum
covert agate
moreover, the "volume with cross-sections" thing you fail to understand, is just...
so smaller Δx is
the more it approaches a prism?
bright hedge
???
covert agate
base = cross section, height = Δx
covert agate
base = cross section, height = Δx
..?
bright hedge
add up all the tiny changes in volume and you get total volume
covert agate
screw naming
little drum
no he means, in a lateral sense
bright hedge
then yeah that is the same thing
little drum
Yep you're correct chromium
covert agate
big yey’s
little drum
base here, would be the y = f(x) cross-section, so uhh.. the area of cross-section would be: pi[f(x)]²
which is just pi(y²)
covert agate
bruh
little drum
and like you did, with the riemann sum
bright hedge
how r u guys typing delta \ square so quickly
covert agate
how r u guys typing delta \ square so quickly
text replacement on ios
bright hedge
i c
little drum
you consider the tiny change of volume to be: pi(y²) times Δx
bright hedge
on windows you can do alt + 0178 (numpad) for ²
little drum
lol I use alt + 253
bright hedge
WHAT
covert agate
(just type latex if on windows)
little drum
you consider the tiny change of volume to be: pi(y²) times Δx
Yeah and then similar to the idea of the riemann sum, your Volume = sum of such small cross-sections [ pi(y²) times Δx ]
which, can be made into an integral form 🤦♂️
check this out
little drum
check this out
what do you think this is lmao
bright hedge
why does it use the wrong delta
little drum
It's not the wrong delta lol.
bright hedge
wouldn't you normally use the triangle?
covert agate
δ = change
little drum
depends on the choice of delta hmpf
little drum
δ = change
little drum
oye oye oye.. where'd this pop up from
bright hedge
wouldn't delta in that case be a distance?
b/c |f(x) - L| is the distance between f(x) and L
oh that is a change
covert agate
best notation
covert agate
check this out
i understood this so quickly i don’t think i understood at all
bright hedge
i understood this so quickly i don’t think i understood at all
as they say, less = more
so you've actually understood more
little drum
Don't doubt yourself. It's the same idea as the Riemann sum to be honest.
little drum
It's understandable you'll get it
covert agate
It's understandable you'll get it
i’m like stuck in some void space
between understanding all and none
little drum
then just get the gist.. and try some problems
little drum
Hmm?
bright hedge
disc/washer and shell i think
little drum
ooo
covert agate
dish washer method
little drum
I haven't learnt of them tbh.. but I remember vaguely from my physics class in hs
I sucked at picking the right cross-section and variable 🤦♂️
bright hedge
I haven't learnt of them tbh.. but I remember vaguely from my physics class in h...
this the power of multiple variables!?
little drum
hmm?
bright hedge
like mv calc > solids of revolution
covert agate
wait
little drum
hey no! It was just basic.. find COM, M.I., etc. questions
covert agate
what about surface area
little drum
surface area of ... the solid of revolution?
bright hedge
that's a bit more complicated
little drum
Do you know how arc length of a curve is calculated?
covert agate
Do you know how arc length of a curve is calculated?
sqrt(1+(‘)²)
covert agate
i wanna eat some solids today
little drum
been on a diet lately?
hasty elk
you know i never learnt any sort of volume method by any sort of name
covert agate
i think they refer to different formulae that yield equivalent results?
so you pick the one best for you
i think?
hasty elk
meh, they're all integration
wraith solstice
Guys
autumn trench
lone heartBOT
@wraith solstice Has your question been resolved?
cobalt heath
Hi there, I'm wanting to work out the optimal length in time (days) to net the most return on an investment. This investment would be compounded by 1% daily up until a certain point, however this initial compounded investment cannot be withdrawn. Therefore, after a certain point, 1% interest daily; not compounded, would be withdrawn. What amount of time would result in the highest amount of 1% interest daily (not compounded) withdrawn?
cobalt heath
Over a time period of 365 days, I forgot to mention
edgy sparrow
need some help please
lone heartBOT
need some help please
jade sleet
vale wigeon
@edgy sparrow which part do you need help with
prime sail
What part a answer?
edgy sparrow
what's troubling you with part b?
commmon ratio finding
Its u2/u1 = u3/u2 right?
I dont get a cubi in thw end
hmm
ok, i got b finally
now for c...
polynomial division?
edgy sparrow
polynomial division
vale wigeon
Its u2/u1 = u3/u2 right?
you don't know anything about u3 here so using that as-is won't do
hazy knoll
I don't really know how to find an equation for PQ here
echo socket
You mean for the distance PQ?
hazy knoll
I guess
Slightly confused by this question
The coordinates of Q are always in the line L
But I don't get what it means by (PQ)^2
edgy sparrow
the use PQ^2
because they were hinting for u to use pythagoras theorem
to find the length of a line, you use the formula:
$PQ^2 = sqr root (delta y ^2 + delta x ^2)$
hazy knoll
Oh ok
ocean sealBOT
The Safe Sword
tardy robin
lone heartBOT
tardy robin
Can someone help me with quesiton 9
The 2nd parr
I already found the u value
Which is 50.5
lone heartBOT
@tardy robin Has your question been resolved?
pale kestrel
Little clue, but normal approximation?
I would perhaps sketch a graph of the original normal distribution
pale kestrel
Then you are adding a lot of them together
but you aren't taking the mean
you are taking the sum
pale kestrel
could you show me your sketch
tardy robin
i didnt sketch
i just imagined what the graph would look like and did part 1 from there
pale kestrel
we need one 🙂
pale kestrel
or i could describe
what im tryna say
is that the graph will kindof get slimmer and slimmer
tardy robin
pale kestrel
Oh what I said about the mean I take it back
tardy robin
here
pale kestrel
Its totally relevant
pale kestrel
Do you know what happens to the normal distribution as you add more of them
theres no math here.
tardy robin
it get smaller?
pale kestrel
kinda well
tardy robin
like the narrower
pale kestrel
what i should really say is as you take the mean
tardy robin
squeezed
pale kestrel
of more of them
tardy robin
okay
tardy robin
yea
pale kestrel
= P(S/n > 3.5)
You see how this division works fine there?
But then S/n is the mean of n observations, you could say
pale kestrel
I divided the inequality by n on both sides. So it is still the same one
pale kestrel
You get the steps so far?
tardy robin
yea i get the steps
pale kestrel
P(S > 3.5n) = P(S/n > 3.5)
Ok, but then we use our observation earlier
about the mean
tardy robin
okay
pale kestrel
as we take more and more samples
the distribution gets squashed towards the mean
Eventually the entire 'bulk' will be super close
So at that time whats the probability you'll be more than 3.5?
Like maybe draw on the same graph
the distribution super squashed
pale kestrel
Yes thats right
tardy robin
the probability approaches 0?
tardy robin
yup
pale kestrel
S/n
tardy robin
did i calculate it wrong?
pale kestrel
It feels like it to me, let me see
tardy robin
okay
pale kestrel
X ~ N(m, 2.5)
P(X > 3.5) = 0.97
tardy robin
yea
then i pressed inverse norm on my calculator
and i got that answer
well i got the z value
pale kestrel
I will try cus that answer seems off
tardy robin
variance
pale kestrel
X ~ N(m, 2.5)
(X - m) / sqrt(2.5) ~ Z(0, 1)
P(X > 3.5) = 0.97
tardy robin
oh i think i just realised a mistake
pale kestrel
,w z distribution probability 0.97
dumb bot
soooo
ok no i give up lol
,w P(Z > z) = 0.97
ocean sealBOT
pale kestrel
ahhhh finally
pale kestrel
X ~ N(m, 2.5)
(X - m) / sqrt(2.5) ~ Z(0, 1)
P(X > 3.5) = 0.97
,calc sqrt(2.5)*1.881
ocean sealBOT
Result:
2.9741221393884
Result:
0.52587786061164
i got my z= -1.881
pale kestrel
oh minus
pale kestrel
probably is, i aint done this for a long time
thinking
yes ok that makes sense
0.97
so we want the minus z
tardy robin
ya
pale kestrel
,calc 3.5 + sqrt(2.5)*1.881
ocean sealBOT
Result:
6.4741221393884
yep all good
tardy robin
okay back to the other question
pale kestrel
Ok so back to what we were discussing yh
tardy robin
yea
pale kestrel
uhhhh
tardy robin
okay
pale kestrel
mark the mean and 3.5 in the right place
tardy robin
is it not in the right place?
pale kestrel
nope mean is bigger than 3.5
tardy robin
ohh
pale kestrel
u marked your diagram as if mu is 0
pale kestrel
eh? the answer for the other part is a probability
tardy robin
yea
tardy robin
yup
pale kestrel
almost all of the distribution is near 6.5
tardy robin
yup
pale kestrel
and you are asking what the probability is that its greater than 3.5
tardy robin
cuz its for sure going to be more than 3.5 as it gets bigger
pale kestrel
P(S > 3.5n) = P(S/n > 3.5)
S/n ~(?, ?)
You should be able to work out this new distribution
(in terms of n)
pale kestrel
i can see
tardy robin
okay
little drum
~~meanwhile teach me stats too 
~~
pale kestrel
good timing, ansh will take over
little drum
i-
little drum
I never did any stat classes wdym
tardy robin
well ansh help me out xD
little drum
pale kestrel
I never did any stat classes wdym
didnt miss out on anything
tardy robin
okay soo
pale kestrel
so the 2nd part?