i've gone through multiple methods but i keep missing some crucial fact here and there
#help-41
split sail
spark dragon
okay for the two planes take the constant to the other side
u get 2x -y + 3z -1 = 0
and x+y-z -2 = 0
we shall denote these as P1 and P2
now the general form for a plane passing through the line of intersection of these two is
P1 + AP2 = 0
where A is some arbitrary constant
u with me till here?
split sail
yeah
spark dragon
is there a reason this works?
its a general form with a derivation but i can send u the derivation later if u would like
split sail
but what makes P1+AP2=0 a family of planes sharing a line of intersection
spark dragon
writing it here will be confusing
split sail
i see
spark dragon
but what makes P1+AP2=0 a family of planes sharing a line of intersection
because we know a property that any plane can be expressed as a sum of two other planes multiplied with a constant
similar to vectors
split sail
right
spark dragon
because they re linearly dependant
split sail
in fact you kind of are working with vectors
spark dragon
if thats the right word
spark dragon
in fact you kind of are working with vectors
yep
split sail
the cross product of two orthogonal vectors is always 0, even if you scale one of them
spark dragon
correct
split sail
that makes sense
spark dragon
mhm so we cud just write any plane as AP1 + BP2 = 0
split sail
so really I could say AP1+BP2=0 as well for some arbitrary A and B ≠ 0
spark dragon
but since we dont want to have
split sail
lol yeah exactly
spark dragon
two variables
spark dragon
so really I could say AP1+BP2=0 as well for some arbitrary A and B ≠ 0
correct
so for simpler calculation just divide by A
split sail
yeah it doesn't really matter at the end of the day
spark dragon
u get B/A which u can take as some arbitrary constant
split sail
it's all arbitrary anyway
split sail
right
split sail
i'll do that now
spark dragon
mhm
what u can do is
after expanding it
u can take the x term common, y term common , z term common
spark dragon
u can take the x term common, y term common , z term common
this will convince u that is in fact, another plane equation
split sail
sorry i don't have access to writing the computation rn but i trust the concept
split sail
so when i get the means i'll do the computation
spark dragon
no need to
if u want ill write this one second
(2x-y+3z-1) + A(x+y-z-2) = 0
2x -y + 3z -1 +Ax + Ay -Az -2A = 0
x(2+A) + y(-1+A) + z(3-A) -1 -2A = 0
notice this is just another plane equation
but with arbitrary direction ratios ( because of A)
clear till here?
split sail
which is the point given
split sail
(-1,2,1), substitute
spark dragon
yes very quick
split sail
better than my cross products lol
spark dragon
u can also use it when they say "its perpendicular to one plane" too
because u know the normal vector of that plane in terms of A
just use the dot product condition
u can find A
spark dragon
sure
split sail
using that one cos thing
i'm not exactly sure what i would use but i have a vague idea
spark dragon
np
split sail
.close
solid mortar
amber waspBOT
solid mortar
,rotate
grizzled pagodaBOT
solid mortar
We have to solve for 1/d0
This what I got anyone wanna help check
There’s no answer key and I feel wrong
spiral zealot
can you show the full question and full work
jaunty shale
yes, show all
cuz what you found is apprently wrong
thats 1/f - 1/di, so its 1/d0
split sail
i think you did 1/d_i - 1/f instead of the other way around
split sail
i still dont understand but i get the hint of what you did
jaunty shale
no, just change that to (x-1)
and carry on the work
when you arrive to the final expression, multiply it by -
cuz what you did was 1/di - 1/f, which is -1/d0
split sail
i was just about to say this
jaunty shale
😛
split sail
if this was right, all you had to do was "take the negative out"
solid mortar
Ah thanks
This was a problem from last year I was helping a friend with took me too long
amber waspBOT
@solid mortar Has your question been resolved?
wraith shale
amber waspBOT
wraith shale
14b please
Here is the marking scheme but I don't understand how does this line come out
split sail
Here is the marking scheme but I don't understand how does this line come out
read the question again
wraith shale
only one x intercept?
split sail
Here is the marking scheme but I don't understand how does this line come out
if your question is this, the line comes out from the last line of the question
f(x)/(x+1) = 0
wraith shale
assume x-8 is one of the factors. f(x)/(x-8) will also be zero?
split sail
you too :)
wraith shale
.close
ionic zodiac
how can i do this?
amber waspBOT
how can i do this?
)
ionic zodiac
(I’m dying and about to sleep <a:bcaForgiveBeg3:592612557538328576>)
you have been summoned and cannot leave till you help me with this 
weak zinc
You’ll have to catch me first 
weak zinc
Anyways, a TL;dr is that you may wanna consider what you know about cdfs 
ionic zodiac
Anyways, a TL;dr is that you may wanna consider what you know about cdfs <a:Gent...
int from -inf to inf = 1
and the function must be positive over the interval?
weak zinc
int from -inf to inf = 1
Well, not of the CDF, the integral of the PDF is that
But related to that, that implies that as x goes to infinity, then F(x) should have a limit of 1, riiiiggghhtttt 
ionic zodiac
But related to that, that implies that as x goes to infinity, then F(x) should h...
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
weak zinc
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
What do you mean “uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh” 
ionic zodiac
y the limit equals 1?
weak zinc
Because $F(y) = \int_{-\infty}^y f(t) \dd t$, where $f$ is the pdf
grizzled pagodaBOT
@weak zinc
weak zinc
int from -inf to inf = 1
The statement here, that $\int_{-\infty}^{\infty} f(t) \dd t = 1$, is the equivalent statement that $\lim_{y\to\infty} F(y) = 1$
grizzled pagodaBOT
@weak zinc
ionic zodiac
<@788085606483361802>
ah okey
weak zinc
happy with that?
ionic zodiac
<a:GentleHug:585583462581403669> happy with that?
yeas
weak zinc
Cool, so bear in mind you wanna force the limit $\lim_{x\to\infty} e^{-kx}( e^{\alpha x} - 1)^2 = 1$
grizzled pagodaBOT
@weak zinc
weak zinc
How would you do it 
(Maybe think about expanding and rewriting that way 
remember that k and alpha are positive)
ionic zodiac
$lim_{x\to\infty}\left(e^{\left(-kx+\alpha x\right)}-e^{kx}\right)$
grizzled pagodaBOT
water beam
weak zinc
Forgot to expand first 
weak zinc
now you do
ionic zodiac
$e^{\left(-kx+\alpha^{2}x^{2}\right)}-2e^{\left(\alpha x-kx\right)}+e^{-kx}$
grizzled pagodaBOT
water beam
careful!
weak zinc
<:catangery:732013544186314834>
amber waspBOT
@ionic zodiac Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
stuck lily
hi can somebody help me with this logic problem? if i can just get the right propositional logic equation i can probably turn it into a circuit myself
stuck lily
for a it should be q or r and neg p and q for b
amber waspBOT
@stuck lily Has your question been resolved?
jaunty shale
for a it should be q or r and neg p and q for b
right
robust lagoon
jaunty shale
I'm struggling with c rn mainly
expression (a) evaluates to r when q is false
expression (b) evaluates to p* when q is true
thats all you need to work out (c)
amber waspBOT
@stuck lily Has your question been resolved?
jaunty shale
i gtg, i wont be here if/when you come back
so i'll share with you what you should find
compare
,, M(p,q,r) = \lnot(q \lor r) , \lor , (q \land \lnot p)
grizzled pagodaBOT
Emily
cerulean hazel
amber waspBOT
cerulean hazel
Totally forgot the process for part a)
IIRC do I need to integrate it within the domain?
that being 1 -> e^3?
amber waspBOT
@cerulean hazel Has your question been resolved?
cerulean hazel
so 1/k ln(e^3) = 1
oh so im not required to integrate anything?
ive done so in the past iirc
plain hare
u wud integrate the probability density function to find the cumulative distribution
shadow stump
you need to integrate the PDF to get the CDF. but in this case you are given the CDF to begin with
keen pawn
amber waspBOT
keen pawn
I can use any proof writing method for this
Direct proof?
I'm kind of lost
I know what I have to do
not too sure of how to do it
inland pulsar
I can use any proof writing method for this
Finally
pseudo crescent
do you recognize the relation of 120 to 5?
inland pulsar
5!? lmao
pseudo crescent
you could start with something simpler maybe, say I give you a product of 2 consective numbers, what number can you guarantee it will be divisible by?
inland pulsar
2!? 
pseudo crescent
you could start with something simpler maybe, say I give you a product of 2 cons...
@keen pawn , can you figure this out?
keen pawn
<@796939110815629322> , can you figure this out?
Just a minute
keen pawn
do you recognize the relation of 120 to 5?
5 is a factor of 120
like I know that $120 = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5$. And that I have to use that fact
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
pseudo crescent
like I know that $120 = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5$. And that I have to u...
indeed
keen pawn
but not sure of how to formalise it without modular arithmatic
pseudo crescent
you could prove that 2^3, 3 and 5 all divide the product
keen pawn
let $n\in \Z$. We now want to prove $120 \mid (n-2)(n-1)(n)(n+1)(n+2)$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
keen pawn
hmm, prime factorisation would probably help a bit
pseudo crescent
yes, indeed
have you already proven something like this?
If gcd(a, b) = 1, a | n and b | n, then ab | n
or at least if a and b are primes
keen pawn
yup
pseudo crescent
okay, thats cool
keen pawn
$120 = 2^3 \cdot 3 \cdot 5$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
pseudo crescent
if you can prove that 2^3 divides n, 5 divides n and 3 divides n, then you can conclude that 120 divides n
keen pawn
Yeah, pretty much
pseudo crescent
i actually just got a crazy idea
you already proved that binomial coefficients are integers, right?
or was it fungus
keen pawn
We wish to prove that $120|(n-2)(n-1)n(n+1)(n+2)$. To do this it's sufficent to prove that $2^3 \mid (n-2)(n-1)(n)(n+1)(n+2) \land 3|(n-2)(n-1)n(n+1)(n+2) \land 5 \mid (n-2)(n-1)(n)(n+1)(n+2)$. We asume two cases, first wherein the first number is even. so we have (2n-2)(2n-1)(2n)(2n+1)(2n+2). It's evident that $8|(2n-2)(2n-1)(2n)(2n+1)(2n+2)$.
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
pseudo crescent
okay, that's the first case
the second case is a bit harder
maybe avoid using the same variable twice tho
Some lemma like:
Among n consecutive integers, at least 1 is divisible by n
would be helpful
keen pawn
Yeah I know that lemma but I haven't proven it yet , so 
]
pseudo crescent
I think it's worth to prove it as a seperate lemma
otherwise you will have to do 3 proofs of the same lemma
one for 2 and 4, one for 5 and one for 3
pseudo crescent
Some lemma like:
Among n consecutive integers, at least 1 is divisible by n
wo...
if the integers are
k, k+1, ..., k + n - 1
I think it can be done by induction on k
keen pawn
I can't use induction
pseudo crescent
Why 
keen pawn
Haven't done it at uni yet
pseudo crescent
is this yorur homework or sth?
pseudo crescent
Formally proving this thing without induction will be tough
keen pawn
so I have to show $120|(n^5-5n^3+4n)$
grizzled pagodaBOT
Veni, vidi, perii is not f(wai)
keen pawn
yeah, I'll skip this for now then
pseudo crescent
you also covered no modular arithmetic?
keen pawn
Whatever hammack has done
pseudo crescent
you could go around it by using remainders after division by 5
there are 5 possible remainders
0, 1, 2, 3, 4
assume that there is no number divisible by 5
then that reduces to 4 possible remainders
1, 2, 3, 4
by pigeonhole, one of the remainders will be there twice
keen pawn
Hmm, yeah
pseudo crescent
by pigeonhole, one of the remainders will be there twice
and then you could probably conclude that the numbers with same remainder are at least 5 apart, which is a contradiction
amber waspBOT
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Available help channel!
vocal hearth
whats meant by a parametric plane curve?
amber waspBOT
whats meant by a parametric plane curve?
shadow stump
it's a curve which is given in the form (x,y) = (f(t), g(t))
vocal hearth
Normal Circular motion is given by the movement of an object in a circular orbit. More specifically, its speed remains constant, yet it is the angular velocity that makes the linear velocity change every time.
shadow stump
we can think of describing the position of an object moving in a circle by the angle it makes with a line (usually the positive x-axis). then the angular velocity is the rate of change of that angle
the linear velocity is the derivative of the position vector
slim pelican
angular velocity is the rate at which the object orbits around the centre (ω). linear velocity is a tangential velocity vector on the orbit (v)
slim pelican
yes
amber waspBOT
vocal hearth
Normal Circular motion is given by the movement of an object in a circular orbit...
wait sorry
with change every time
is every movement on the circle in the constant speed right
.reopen
amber waspBOT
✅
vocal hearth
"the curvature in circular motion is inversely proportional to the radius and directly related to the centripetal acceleration of the particle."
whats meant by inversely proportional
alpine flower
if the value of one quantity increases then the value of other quantity decreases
their product is constant
vocal hearth
huh
vocal hearth
is every movement on the circle in the constant speed right
also this
vocal hearth
their product is constant
so inversely doesnt really mean anything
alpine flower
say x is inversely proportional to y
if the value of x increases, the value of y decreases and vice versa
k is a constant
vocal hearth
oh i see
vocal hearth
is every movement on the circle in the constant speed right
??
split sail
if w is constant yes
amber waspBOT
amber waspBOT
Available help channel!
slow tapir
hey, i have such question: Find 2 orthonormal vectors x,y so that span{x,y} = span{(0,1,1), (1,2,3)}
I found the answer on stack exchange as in the picture, but i kinda dont understand, the intuitive meaning behind it. I know that it comes from gram-schmidt, but id like to understand it intuitevly
indigo cloud
iirc on the wikipedia article for gram schmidt there is the picture
which shows geometrically what the vectors v1,v2,u2 are
pseudo crescent
I'd also try searching on youtube, animated stuff can be easier to understand
and i'm pretty sure there is someone who tried to animate it
amber waspBOT
@slow tapir Has your question been resolved?
cursive knoll
can i use synth division on this?
amber waspBOT
can i use synth division on this?
inland pulsar
Yes you can
Tho I'm gonna recommend checking for some in your head and also use rational root theorem
cursive knoll
Tho I'm gonna recommend checking for some in your head and also use rational roo...
huh
grizzled pagodaBOT
elder harbor
looks good
cursive knoll
oh
grizzled pagodaBOT
grizzled pagodaBOT
k
cursive knoll
probably
cursive knoll
got it
split sail
Someone know why with scalar product in 2D u have (a,b).(c,d) = |(a,b)| *|(b,c)|*cos(g) with g the angle between the 2 vectors
split sail
the thing with | is the norm
mint nacelle
Someone know why with scalar product in 2D u have (a,b).(c,d) = |(a,b)| *|(b,c)|...
the scalar product is defined as $x \cdot y = |x| |y| \cos \theta$ for vectors $x, y$
that's the definition
grizzled pagodaBOT
higher's secret twin brother
split sail
yes but why is it also equal to ac+bd ?
mint nacelle
yes but why is it also equal to a*c+b*d ?
I mean it also comes from the law of cosines
using these axioms
yeah I think that's what you're looking for
it's more natural to conclude |v| |w| cos theta than to start from that and work your way backwards, you're right
split sail
ok i see thank you
amber waspBOT
@split sail Has your question been resolved?
vale garnet
I don't understand why the dimensions of acceleration should be LT^-2 instead of LT^-1
look at my steps
rancid raven
I don't understand why the dimensions of acceleration should be LT^-2 instead of...
What is the formula of acceleration?
vale garnet
What is the formula of acceleration?
I understand that it's a= v/t
which is LT^-2
but
there is an extra time in the equation here
a(t)
vale garnet
oh
rancid raven
🤔
rancid raven
well I didn't understand that
Oh you thought a(t) meanst a * t?
vale garnet
yeah a times t
vale garnet
hmm okay so if it's a function I don't count it
rancid raven
Like f(x) is function in terms of x not f multiply by x
amber waspBOT
amber waspBOT
Available help channel!
tawny harbor
amber waspBOT
tawny harbor
how are they able to apply limit comparison/comparison test here>
I thought it can only be used for sequences, and not seuqneces of functions?
i.e., must be discrete
so shouldn't something like the weierstrass m-test be used instead?
cunning birch
hearty inlet
this is not a series of functions
amber waspBOT
@tawny harbor Has your question been resolved?
primal holly
If $x, y \in \set R$ are chosen independently following a standard normal distribution, what is the expected distance of the point $(x, y)$ from $(0, 0)$?
grizzled pagodaBOT
krypton
grizzled pagodaBOT
krypton
amber waspBOT
edgy vector
correct @primal holly
amber waspBOT
Available help channel!
sudden arch
amber waspBOT
sudden arch
Is question 2 correct?
solemn escarp
yep
tulip tapir
no...
spiral zealot
no
sudden arch
Cause I asked someone else and they got - 5/2
tulip tapir
;-;
solemn escarp
oh y is incorrect
molten shale
nope
spiral zealot
your work is too cropped to see
sudden arch
1 + 4y = -9
4 y = -10
Y = -2.5
Or - 5/2
I messed up and put 4 y = -8
Ok thanks
.close
amber waspBOT
amber waspBOT
Available help channel!
slim epoch
[this is the Cauchy-Binet formula] i'm having trouble understanding over what the sum is taken, is it the same as summing over all subsets of {1, ..., n} that contain m elements? and then ordering them j1 as the smallest up to jm?
indigo cloud
yes
amber waspBOT
amber waspBOT
Available help channel!
hard frost
spiral zealot
how are you getting 1
spiral zealot
those are the values of time that they got
hard frost
oh
spiral zealot
you're not done yet
amber waspBOT
amber waspBOT
Available help channel!
hoary quail
I am not sure on how to do this
amber waspBOT
I am not sure on how to do this
hoary quail
And what laws to use
T = 2 h = 7,200 s
It's a circular orbit
So r is constant
But Idk what formulas to use to prove that mass is irrelevant
split sail
do u know the formula for a speed in polar coordinates ?
split sail
bc it is appropriate for this problem
naive pivot
Should be gravitational force formula and F=ma
hoary quail
Okay
maiden stratus
hoary quail
The formula I meant is
F=GmM/r^2
hoary quail
bc it is appropriate for this problem
Why's that?
naive pivot
The only force applying to the satellite is the gravitational force
So the net force=gravitational force
hoary quail
bc the sattelite is turning around
It doesn't spesify if the sattelite is turning around
split sail
it says a stable circular orbit
hoary quail
Yeah
split sail
i think it means that the sattellite is moving at constant speed and in circle
split sail
uh if it wasnt it would fall...
split sail
It doesn't mention if the sattelite is rotating
around earth u mean right ?
hoary quail
Wait we're talking about the same thing
My bad
I thought you meant the sattelite was rotating around its own axis
hoary quail
But yeah, it's orbiting around the earth in 2 hours
hoary quail
so what are u allowed to use ?
What do you mean?
split sail
about formulas
hoary quail
They didn't spesify
naive pivot
But yeah, it's orbiting around the earth in 2 hours
I don’t think T would matter in proving that velocity is independent of mass
hoary quail
I don’t think T would matter in proving that velocity is independent of mass
Maybe not
And radius
split sail
what about a=v^2/r
hoary quail
Is a area?
naive pivot
what about a=v^2/r
and
GmM/r^2
split sail
a is accelerzation
hoary quail
Oh obviously
hoary quail
I'll try the F=ma since I have an idea of what to do there
split sail
actually u cant use a = v^2/r
naive pivot
actually u cant use a = v^2/r
no you can
hoary quail
Can I cross out the small mass?
naive pivot
Can I cross out the small mass?
Going good
split sail
or i didnt well understand and u know that it is constant but u only want to prove that it is independant ?
split sail
v/t ?
naive pivot
should be v^2/r=a
split sail
t is time ?
hoary quail
should be v^2/r=a
Why v²?
hoary quail
t is time ?
Yeah
split sail
no
hoary quail
Wdym
split sail
a = dv/dt
hoary quail
Acceleration is the change in velocity over time
split sail
yes, still true tho
split sail
u want to prove it
hoary quail
Orbit is 7200s
so r is const
v is const
a can't change
And is always 0 m/s² in this scenario
hoary quail
should be v^2/r=a
Why is v²?
split sail
having an acceleration doesnt alway mean that ur speed change
naive pivot
Why is v²?
needs visual representation
hoary quail
needs visual representation
Do you know somewhere I can see that?
hoary quail
it is a formula when u have constant speed
For circular orbits?
split sail
yes
hoary quail
So
a = G • M/r²
Doesn't turn into
a = v²/r
?
split sail
wdym ?
hoary quail
Since that was a reply to this
split sail
idk what ur asking
split sail
So
a = G • M/r²
Doesn't turn into
a = v²/r
?
with these 2 equation u can plug the expression of a in the formula v=sqrt(a*r)
naive pivot
So
a = G • M/r²
Doesn't turn into
a = v²/r
?
unit wise yes you’ll get m/s
naive pivot
sorry meant m/s^2
(m/s)^2/m=m/s^2
naive pivot
Can I cross out the small mass?
+you already proved that the velocity and radius are independent of mass
but you should rewrite a as v^2/r and solve for v and you proved that velocity is independent from mass
split sail
+you already proved that the velocity and radius are independent of mass
when did he prove the radius is independenat ?
naive pivot
when did he prove the radius is independenat ?
They didn’t use the mass of satellite to rearrange for any of the variables
split sail
They didn’t use the mass of satellite to rearrange for any of the variables
i didnt understand
naive pivot
i didnt understand
so when using GmM/r^2
I refer to m as the mass of the the satellite
split sail
yes
hoary quail
when did he prove the radius is independenat ?
No idea
Or m is gone
So I guess that is when
naive pivot
Yep
split sail
hm but we still have no equation that give r as smthg independant of m
hoary quail
But m is gone
naive pivot
hm but we still have no equation that give r as smthg independant of m
we can just rearrange
split sail
for v its ok
naive pivot
v=sqrt(GM/r) just solve for r
hoary quail
Didn't need m
hoary quail
v=sqrt(GM/r) just solve for r
Yes
split sail
here it depond on v
hoary quail
here it depond on v
Yeah
naive pivot
here it depond on v
Yes but we still got r
hoary quail
But r and v don't need to be independent from each other
r and v need to be independant from m
split sail
by using the same equation to prove 2 different stuff, u assume that r is independant in first to show that v was independant, and then u did the opposite so it is wrong
hoary quail
naive pivot
by using the same equation to prove 2 different stuff, u assume that r is indepe...
We assume both are independent but not from each other but from the mass of the satellite
hoary quail
Since we were able to remove m
split sail
but u cant assume smthg u want to prove
split sail
with v= sqrt(GM/r) , u didnt prove that v is independant of m because r could depend on m still
split sail
cause it'll be smthg like v(m) = sqrt ( GM/ r(m) )
naive pivot
with v= sqrt(GM/r) , u didnt prove that v is independant of m because r could...
We literally did not use m to calculate v nor r
naive pivot
cause it'll be smthg like v(m) = sqrt ( GM/ r(m) )
It’s like 2x=2
we simplify the 2 by dividing it getting us
x=1
naive pivot
cause it'll be smthg like v(m) = sqrt ( GM/ r(m) )
+v is dependent on time
And r is just constant
split sail
no, it is like if u write a=x so a is independant of t
but u didnt veerified if x= x(t)
hoary quail
What
naive pivot
no, it is like if u write a=x so a is independant of t
yea but a originally didn’t depend on m in the first place
split sail
yea but a originally didn’t depend on m in the first place
u cant know while u didnt prove it
naive pivot
u cant know while u didnt prove it
The only thing that was dependent on m was the Force
split sail
and maybe v and r , u didnt know that before
naive pivot
and maybe v and r , u didnt know that before
v is always and always doesn’t depend on m no matter what case and same goes for r bcz it’s a constant value
split sail
but u cant tell that r is constant while u didnt prove it
naive pivot
but u cant tell that r is constant while u didnt prove it
r is a radius to a circle that won’t change
doesn’t even depend on any variable to begin with
split sail
idk how to tell
anyway that is probably enough, its just quibbling , but rigorusly u need an other equation
naive pivot
another equation is not needed
split sail
v depend on r and not on m ok
u get that with sqrt(GM/r)
but u need smthg else to tell that r is not r(m)
naive pivot
but u need smthg else to tell that r is not r(m)
r is just a simple length with meter units
naive pivot
a lengh can depend on a mass in other cases
no ?
split sail
in other cases yes
naive pivot
Like what ?
split sail
the lengh of a spring
naive pivot
the lengh of a spring
Doesn’t depend on mass
hoary quail
Why would r from Earth to sattelite depend on m to sattelite?
split sail
Why would r from Earth to sattelite depend on m to sattelite?
in this case no
split sail
Doesn’t depend on mass
so when u push on a spring it doesnt become less tall ??
naive pivot
so when u push on a spring it doesnt become less tall ??
Yes because you are applying a force to it
hoary quail
Why are we talking about springs?
split sail
Why are we talking about springs?
it is an example of a lengh that depend on mass
naive pivot
Why are we talking about springs?
idk wanted to hear his case
split sail
Yes because you are applying a force to it
so if the force is created by a mass, it will depend on the mass
naive pivot
so if the force is created by a mass, it will depend on the mass
yes but the mass is from another object and not the spring itself
hoary quail
Isn't that F = -kx?
split sail
yes
naive pivot
Isn't that F = -kx?
yep
split sail
yes but the mass is from another object and not the spring itself
and yes
hoary quail
So
split sail
but still depend on the mass
naive pivot
but still depend on the mass
Yes but mass from another object not the spring itself
(Same for the mass of the satellite)
split sail
so yes mass
hoary quail
And length stretched/compressed
naive pivot
Yes but mass from another object not the spring itself
(Same for the mass of th...
it depended on the mass of the earth
not the mass of the satellite
split sail
it isnt the same
hoary quail
Well thanks for the help anyways
I need to continue with the assesment
Y'all can continue in dm's so thia channel is open to someone that needs help
split sail
k
hoary quail
.close
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Available help channel!
sharp dock
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sharp dock
How would I do this?
inland pulsar
take log
sharp dock
Solve each exponential equation for x.
inland pulsar
log base 2
sharp dock
why base 2?
sharp dock
What r u talking about
inland pulsar
are you allowed calc?
sharp dock
Ok how would I use my fucking calculator
I'm about to break everything here
Fuck my teacher
SOMEONE HELP ME
HOLY
pallid canopy
Chill
shell barn
do you know how logarithms work?
inland pulsar
damn
sharp dock
And I got a quiz on this tmrw
My teacher can't teach for shit
Man teaches us the easiest questions then gives us the hard one
grizzled pagodaBOT
NatTaylorsV
sharp dock
Yes
alpine flower
write it as 2 * 4 * 4^(2x-3)
alpine flower
4*4^(2x-3) = 4^(2x-3+1) = 4^(2x-2)
sharp dock
When we used it for 4x4
sharp dock
4*4^(2x-3) = 4^(2x-3+1) = 4^(2x-2)
Write that now?
alpine flower
cuz we have to solve for x
sharp dock
The teacher said the final answer should be 2.30
sharp dock
But how tf do we get 2.30
sharp dock
yes you can solve it for it any easier manner
Please tell me
I'm erasing all of this
Im sorry
elder creek
ok start with this
sharp dock
But this takes too much time to do on a quiz
elder creek
how do we start by isolating x's
sharp dock
Alr
elder creek
alaska, your way works, but its hard for someone who is learning logs/exponetials to follow
elder creek
you can apply log 4 in the second step either way
@sharp dock
how do we start
what is the easiest step here
should be a 73 oops
sharp dock
Ok one sec
sharp dock
what is the easiest step here
Didn't u say to isolate the x?
sharp dock
I'm not sure
sharp dock
2
elder creek
this right
distrbute the 2
now
look at product
when we have two bases mutiplied, we add their exponets
how do we simply left side
elder creek
elder creek
did u simplify
sharp dock
This?
elder creek
yes
elder creek
yes
sharp dock
4^3^(4x-6)
sharp dock
Oh
sharp dock
Huh 😭
elder creek
2^2
sharp dock
If they were different numbers
elder creek
elder creek
mutiplying is just exponets
sharp dock
Or wtv the number is
elder creek
5^6=5x5x5x5x5x5
just write in exponet format
when solving these equations
remember
we made the oringal expression into this
elder creek
when turns into this
now just add the exponets
together
bc they have the same bases
sharp dock
It's 1
elder creek
3+(4x-6)=1?
elder creek
....
if you plug x into your calc
that doesnt mean anything
to it
it will spit out 1 just bc it doesnt know what to do
there is infintely many values x could be
you have to define x for it actually do something
but you are solving for x
sharp dock
elder creek
so you dont even know x
sharp dock
Or is it supposed to be -21?
sharp dock
Logbase2,73= 4x-3
sharp dock
How
sharp dock
Why
sharp dock
WTF
sharp dock
What's leui
sharp dock
I got 6.189
elder creek
sharp dock
1.547
elder creek
+3/4
sharp dock
0.75
elder creek
1.547+.75
sharp dock
Oh ok