A polynomial of degree 2
#help-26
strange whale
sullen scarab
a,b,c?
strange whale
With 3 roots
strange whale
i am going to ask why?
Not sure what you're looking for
sullen scarab
no i mean
the ans is right
even satisfy the options of the ques
but now i want to know why the 2 degree quad have 3 solutions?
.close
topaz sinewBOT
strange whale
.reopen
topaz sinewBOT
✅
strange whale
I mean you checked yourself that the polynomial has 3 roots, what are you exactly asking ?
sullen scarab
I mean you checked yourself that the polynomial has 3 roots, what are you exactl...
no like my ques was how possible like mathmatically(even though that was mathmatically also) but the equation will be 2 degree and the 2 degree will almost posses 2 roots how three
like for me
it make sence
and not at the same time
strange whale
Well there's only one possibility
strange whale
Zero everywhere is that possibility
sullen scarab
when the equation is an identity
strange whale
So actually "exactly 3 roots" would also be incorrect
strange whale
Well it screwed up then
sullen scarab
and the funny thing is that
it is not a standard book
which solution
is easily aviable in
in internet
i have the pdf where there are solution for this book problem
but even in that the author has just put the option the solution
lmao
sullen scarab
sullen scarab
Maybe some random person who wrote the solutions
yeah mean that
strange whale
D is correct that's what i've been saying tho
strange whale
The zero polynomial has more than 3 roots
sullen scarab
see the wrong option
must kill myself
so its the idenitity right then?
so it must have infinte solutions
?
strange whale
When you say identity i think f(x)=x
strange whale
You're the one saying identity
sullen scarab
listen
strange whale
I mean f(x)=0
sullen scarab
listen
i know that when this type of thing happen when the degree is less but the roots are more than the degree it is usally an identity
that's why i conculed its an idenitity
strange whale
Well it's the additive identity of polynomials if you want
Just say zero polynomial there's less ways to be misunderstood
topaz sinewBOT
topaz sinewBOT
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potent crow
topaz sinewBOT
potent crow
How does one even start?
wispy pier
topaz sinewBOT
@potent crow Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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manic yew
$a^2 +4a + b^2 -6b +13 = 0$ find a,b where they both real number
manic yew
is this about 2 diffrent (a+b)^2
sinful flint
does it need to be equal to anything?
manic yew
sorry yes let me edit
thorny flameBOT
Simon James B
manic yew
Complete the square in both a and b
$a^2 + 4a + 4 -4 + b^2 -6b +9 -9 + 13 = 0$? is this right
thorny flameBOT
Simon James B
wispy gulch
It'll be an ellipse in a, b
point circle
sweet shard
Oh degenerate ellipse
manic yew
what is ellipse
sinful flint
stretched circle
manic yew
this is algebra tho 😦
manic yew
**Simon James B**
so is this right or not
wispy gulch
it is correct
manic yew
$(a+2)^2 + (b -3)^2 = -13$ now?
thorny flameBOT
Simon James B
wispy gulch
limber sphinx
it's 0 instead of -13
manic yew
$(a+2)^2 + (b-3)^2 = 0$
thorny flameBOT
Simon James B
wispy gulch
minimum value of a square is 0, so both terms must be 0
thorny flameBOT
ЯεтιяεĐ
manic yew
0?
wispy gulch
ye
manic yew
0^2 would be still 0
manic yew
they are both 0?
wispy gulch
yea
manic yew
right so now we divide it in 2 different equations?
wispy gulch
yeah
manic yew
$(a+2)^2 = 0$
thorny flameBOT
Simon James B
thorny flameBOT
Simon James B
wispy gulch
ye sqrt of 0 is 0
thorny flameBOT
Simon James B
manic yew
$(b-3)^2 = 0 => b-3 = 0 => b = 3$
thorny flameBOT
Simon James B
manic yew
Answer is (-2;3) for a,b
wispy gulch
yea
wispy gulch
so conclusion, if sum of squares =0, then all of terms must be equal to 0
manic yew
so conclusion, if sum of squares =0, then all of terms must be equal to 0
and if we have ab=0 and one of them is 0
right?
wispy gulch
one of them or both of them
topaz sinewBOT
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faint bay
I have shown by this condition is necessary but I am not sure how to show it is not sufficient. Currently, I am trying to show rxt1 = a1xt1 ==> t2.(rxt1) = t2.(a1xt1) but t2.(rxt1) = t2.(a1xt1) =/=> rxt1 = a1xt1 but am getting stuck with that.
topaz sinewBOT
I have shown by this condition is necessary but I am not sure how to show it is ...
gilded plume
let us think of this graphically
loud oasis
if it's not sufficient then it would suffice to give a counterexample
gilded plume
so let us think about what the dot product means
the dot product is 0 when the two vectors are perpendicular to each other right?
and, the cross product of two vectors represents a third vector which is perpendicular to the plane decided by the two vectors right?
gilded plume
so, this condition is equivalent to saying that the vector between the two points lies in the plane defined by both unit vectors
so a1-a2 lines in the plane defined by t1 or t2
it doesn't have to be "parallel" to one of them
essentially, it can be a linear combination of t1 and t2
faint bay
sorry could u explain that a bit more?
why would that disqualify it from being intersection
gilded plume
okay, so based on the dot product and cross product ideas, we have that this vector between the two points is perpendicular to this vector defined by the cross product right?
faint bay
ye
gilded plume
and that vector defined by the cross product
is the vector perpendicular to the original unit vectors right?
so if its any vertex "perpendicular" to those perpendicular vectors
then, it must lie in the plane defined by the original 2 unit vectors
faint bay
i understand that
so a1 - a2 must lie on plane defiend by pt1 + qt2 where p and q are scalar
gilded plume
yes
so they will always intersect with the exception of one case.
the thing is, this plane which i called the cross product isn't always well-defined
namely, suppose that $t_1$ and $t_2$ are equal to each other
thorny flameBOT
Arnavutköy
faint bay
ohhh ok
gilded plume
ok i gtg now, think you got it now
faint bay
thanks for helping
sinful flint
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
marble zealot
I'm a bit fuzzy with this question: personally I believe it's B but I'm not certain
topaz sinewBOT
I'm a bit fuzzy with this question: personally I believe it's B but I'm not cert...
marble zealot
I think it's B because of the fact that x + 1 and x - 1 are not divisible in the original polynomials, so the product must be something like x² - 1 and the -1 stays non divisible but not the x²
sinful flint
!show
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
marble zealot
and that the rest of the function stays divisble because they are just a product that keep their even coefficients
marble zealot
Show your work, and if possible, explain where you are stuck.
I don't really have a method
my reasoning process is above
I just don't really know a correct approach to this problem
golden blade
f mod x²+1 = x+1
g mod x²+1 = x-1
so
fg mod x²+1 = ?
marble zealot
dont know what 'mod' notation is
golden blade
modulo
but then you prob dont modular arithmetic
a mod m = b means a/m leaves remainder b
marble zealot
so x+1 times x-1 ?
golden blade
ya
marble zealot
x²-1
golden blade
fg mod x²+1 = x²-1
it means now, if you divided x²-1 by x²+1 what remainder would you get
marble zealot
1
golden blade
No
golden blade
Remainder not result
Yes 0 No, see: (x²-1)/(x²+1) = (x²-1+2-2)/(x²+1) = (x²+1-2)/(x²+1) = 1 + (-2)/(x²+1) so -2
marble zealot
okay
golden blade
meaning x²-1 = -2 mod x²+1
Basically whether you have (x²-1)/(x²+1) or -2/(x²+1) they both have the same remainder -2
golden blade
yes
marble zealot
okay
What do you mean?
yeah
or wouldnt it be like (x²+1)(...)+x+1 for f ?
and (x²+1)(...)+x-1 for g ?
marble zealot
Im not certain if there are more rules or not governing this modular arithmetic
opal vault
which means f(x)g(x) = ||(x^2+1)[(x^2+1)h(x)l(x) + (x+1)l(x) + (x-1)h(x)] + (x+1)(x-1)|| = ||(x^2+1)[(x^2+1)h(x)l(x) + (x+1)l(x) + (x-1)h(x)+1] -2||
spoilers, try it for yourself first
golden blade
What do you mean?
just forget it fucked up lol
but the other approach should work still
marble zealot
okay thank you for trying to help i appreciate it
opal vault
yeah the thing they were trying to do:
f mod x²+1 = x+1
g mod x²+1 = x-1
so
fg mod x²+1 = ||(x+1)(x-1) mod x^2+1 = x^2-1 mod x^2+1 = -2||
golden blade
yea... 
marble zealot
okay I'm just reading all the info
golden blade
marble zealot
<:boohoo:1008709758502568036>
it's fine, I immensely appreciate anyone who has the will to help a total stranger with their math problem lol
marble zealot
yeah the thing they were trying to do:
also thanks to you for the help, I'm still just doing the multiplication with the first answer
marble zealot
f(x)g(x) = ...
that this person did, also thanks for the help
potent crow
np
golden blade
it's fine, I immensely appreciate anyone who has the will to help a total strang...
what bothers me is that you trusted me blindly and i didn't notice we were calculating the right remainder for the wrong number lol
marble zealot
we're all living for the first time, no stress
golden blade
i edited it now above to make sense!
topaz sinewBOT
Available help channel!
wet sun
For part (d), I dont quite understand how there can be infinite functions g which satisfy it
topaz sinewBOT
For part (d), I dont quite understand how there can be infinite functions g whic...
mild hearth
For part (d), I dont quite understand how there can be infinite functions g whic...
intuitively, g(|x|) only cares about the values g takes for non-negative x
for x < 0, g could do absolutely anything
wet sun
ohhh i see
So can I think I prove by cases where f is either even or odd, and then define g piecewise in each case?
in a way which makes it equal to f(x)
grave pecan
i mean its more just that, since f(-x) = f(x), we can create a composite function where -x and x output the same inner function for g to compute
and thats |x|
vernal matrix
So can I think I prove by cases where f is either even or odd, and then define g...
(for part (d), you are to assume f is even)
wet sun
oh lol i didnt see the part where it said every even function
this makes more sense now
So define g(x) to be equal to f(x) if x>=0, and then g(x) for x<0 can be anything. Is it just sufficient to state that in the proof, and then say this means we can construct infinite functions g(x) which satisfy those constraints?
grave pecan
So define g(x) to be equal to f(x) if x>=0, and then g(x) for x<0 can be anythin...
yeah exactly
for some arbitrary even function f, let g = f for x >= 0
then, g(|x|) = f(x) since g(|-x|) = g(|x|) = g(x)
so g(|x|) is even
and describes f
and since we let f be arbitrary, theres infinite amount of g
topaz sinewBOT
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short trail
topaz sinewBOT
short trail
What's the best approach in solving this?
rotund valley
Graphing in my opinion
short trail
Last one you just split them into two intervals
rotund valley
It is a linear function with absolute value function
So the graph looks like a polygon
Especially the polygons is a union of some triangles
ivory sorrel
Try determining where the defn. of the function changes
short trail
Try determining where the defn. of the function changes
In theory there should be 8 definitions, some being invalid?
topaz sinewBOT
@short trail Has your question been resolved?
short trail
Try determining where the defn. of the function changes
Is this so far correct?
Usually you do something like this to determine what you do now
short trail
Oh now I understand, I can make them easily after having made the functions
topaz sinewBOT
topaz sinewBOT
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night abyss
What are the condition for a strictly convex function to have a minimum.
grave pecan
What are the condition for a strictly convex function to have a minimum.
Pretty sure it's just derivative is 0 and changes from decreasing to increasing
prisma mesa
is the func defined on all of R?
If it's defined on a compact set, then it surely does have a minimum
prisma mesa
Are we talking about R only or R^n?
night abyss
R^n
i know what a minimum implies, but i dont know the conditions for the minimum to actually exist on a convex set
grave pecan
Pretty sure the minimum part implies that the convex function is compact
Or rather that the convex set would need to be compact in order to have a minimum
prisma mesa
Or rather that the convex set would need to be compact in order to have a minimu...
idts
prisma mesa
consider x^2 on (-1, 1)
grave pecan
consider x^2 on (-1, 1)
Oh yeah I guess if it's just open bounds
So it might just be that the convex set must be bounded
prisma mesa
So it might just be that the convex set must be bounded
x^2 on (-inf, inf)
it doesnt have to be bounded
in R, the limits have to be -inf and +inf though (if unbounded)
at least that's what my intuitition suggests
grave pecan
Hm
Is it really just that there exists a point on the convex set where the derivative is 0?
prisma mesa
thats certainly a sufficient condition
grave pecan
Well only if the convex set is unbounded
If its bounded it could be at either the bounds or the 0 derivative point
prisma mesa
If its bounded it could be at either the bounds or the 0 derivative point
if its bounded, then it must be either the 0 derivative point or it must be compact
oh, it doesnt
well
it's probably quite difficult to characterize the exact conditions
prisma mesa
we can create many sufficient conditions (defined on compact set, 0 gradient somewhere...)
grave pecan
So like x^2 on [-1,1] is compact and still has its min at 0
prisma mesa
but creating a neccessary and sufficient condition is harder
prisma mesa
So like x^2 on [-1,1] is compact and still has its min at 0
yeah, sure
but it's still not necessary
x^2 on [1, 2) isnt defined on compact set, doesnt have 0 derivative but has a minimum
prisma mesa
we can create many sufficient conditions (defined on compact set, 0 gradient som...
specifically in case of R on (both side) unbounded domain, another sufficient condition is that the limits to -inf and +inf are +inf and +inf respectively
prisma mesa
specifically in case of R on (both side) unbounded domain, another sufficient co...
this is also necessary for functions R -> R
grave pecan
Wait no nvm
prisma mesa
is it not?
grave pecan
I mean for x^2, lim to -inf is inf
grave pecan
Nah ur good
prisma mesa
now its correct
grave pecan
Yeah there we go
prisma mesa
and that's sufiicient and necessary. Only for one tiny class of functions though...
grave pecan
I think the necessary conditions are situational
And depends on if the set in an interval is monotonic or not
prisma mesa
yeah, I dont think there is a nice way to characterize the conditions for all domains at once
grave pecan
yeah, I dont think there is a nice way to characterize the conditions for all do...
There's just too many ways things could happen
But we know that if the set is monotonic on an interval regardless of compactness, then the minimum will occur at a boundary
If it isn't monotonic then it occurs at the 0 derivative
grave pecan
do you mean function?
Yes sorry
I guess that's the functional case
Well for functions R->R only
Not sure how to consider it for other sets though
topaz sinewBOT
@night abyss Has your question been resolved?
midnight fractal
Need help
thorny flameBOT
hiidostuff
midnight fractal
yes
grave pecan
The only way that x1 and x2 can be opposite is if -b is 0
midnight fractal
the delta
grave pecan
Do u see why?
midnight fractal
thank you
midnight fractal
oh ok
grave pecan
So 2(m-1) = 0
midnight fractal
Do u see why b must be 0?
yes
grave pecan
Alr awesome
prime bane
i dont understand the part where he does substitution. can someone explain what he does?
topaz sinewBOT
i dont understand the part where he does substitution. can someone explain what ...
vernal shard
i dont understand the part where he does substitution. can someone explain what ...
Do you know what the substitutions are for spherical coordinates?
prime bane
no, you have a formula for that?
its the first problem im attempting fyi
is it this maybe?
vernal shard
With +Z up:
x = rho * sin(phi) * cos(theta)
y = rho * cos(phi) * cos(theta)
z = rho * cos(theta)
Where:
- phi is the azimuthal angle, angle on xy plane measured from +X axis (think unit circle)
- theta is the polar angle, angle measured from the +Z axis going down the sphere
You simply sub these into the integrand
prime bane
With +Z up:
x = rho * sin(phi) * cos(theta)
y = rho * cos(phi) * cos(theta)
z = ...
oh yeah this i know, its cofusing when he substitutes the values into the integral values on line 4
vernal shard
You mean the bounds?
prime bane
so he subs out u = cosφ i dont understand why and why (ρ^2 sin φ) dρ dφ dθ. p^2 * sinφ are included there
ill highlight it for you
vernal shard
rho^2 sin(phi) is the Jacobian of the transformation to spherical coordinates
vernal shard
is it this maybe?
Which is the furthest right term in this integrand
prime bane
ah okay.
i dont really understand how to set up the jacobian for tripple integrals. it differs from double integrals.
vernal shard
i dont really understand how to set up the jacobian for tripple integrals. it di...
It’s the same calculations
Just extended by one dimension
prime bane
so in double integrals they usually present values in such maners and you can easily just substitute them but in triple integrals i dont know what values im supposed to take.
topaz sinewBOT
@prime bane Has your question been resolved?
prime bane
<@&286206848099549185>
vernal shard
so in double integrals they usually present values in such maners and you can ea...
This may help
topaz sinewBOT
topaz sinewBOT
Available help channel!
wispy burrow
I don't remember how to use integrating factor
topaz sinewBOT
I don't remember how to use integrating factor
wispy burrow
timber crystal
dq/dt=-2q
Doesn't require integrating factor
wispy burrow
I don't understand what to do
timber crystal
I don't understand what to do
$dq/q=-2dt$
wraith patrol
whats the original ode
thorny flameBOT
AkitoLite
timber crystal
Too lazy to write fractions
wispy burrow
whats the original ode
On the top of the page
wraith patrol
dq/dt + 2q = 0?
wispy burrow
Yeah
wraith patrol
suspiciously simple
wispy burrow
I'm missing the t which confuses me
timber crystal
I.F is only used when the equation is in the form $\frac{dy}{dx}+P(y)=Q(x)$
thorny flameBOT
AkitoLite
timber crystal
There's no Q(x) ie no x
wraith patrol
I'm missing the t which confuses me
no t is fine
wispy burrow
There's no Q(x) ie no x
True
wraith patrol
you can just int a constant anyways
wispy burrow
What
thorny flameBOT
AkitoLite
timber crystal
I forgot to go next line mb
wispy burrow
Oh okay
timber crystal
I guess $\frac{1}{q}dq=-2dt$ would be more familiar notation if you're not used to it
thorny flameBOT
AkitoLite
wispy burrow
No no dw I get it
(Or I can't really say that, but I can read it)
Do I still need to add the ln(|q|)?
wraith patrol
always
neon iron
yes
wraith patrol
yo rhs should be in t not in q
wispy burrow
But there's a - there already
wraith patrol
its not conditoinal its literally a int rule
neon iron
that's beside the point
wraith patrol
to have ||
wraith patrol
rhs is in t
neon iron
also you have a mistake
wispy burrow
In previous questiond
wraith patrol
rhs please make it in terms of t
wispy burrow
Idk what rhs is
wraith patrol
right hand side
neon iron
It's -2t + C
neon iron
also drop that ± sign
wraith patrol
Vut why was it okay earlier?
what was ok
wispy burrow
It's -2t + C
±2t + c?
wispy burrow
what was ok
I never got complaints about not using || 1 or 2 days ago
wraith patrol
like what
wispy burrow
+- comes after you tackled that || away
Okay
timber crystal
I never got complaints about not using || 1 or 2 days ago
you'll learn it later
wispy burrow
In ODE
neon iron
I never got complaints about not using || 1 or 2 days ago
yeah, it's something people don't do it
timber crystal
I didn't learn it either in early hs
neon iron
but it is a rule
wispy burrow
I'm in uni 😭
neon iron
I'm in uni 😭
Europe right?
wispy burrow
Yeah
wraith patrol
if you dont do it youre neglecting the lnx where x<0
timber crystal
I'm in uni 😭
I mean I was talking about if you learnt it in hs😂
neon iron
Yeah, they learn stuff very early in the states
wraith patrol
thats half the number line youre messing up
timber crystal
you def wanna put the modulus
wispy burrow
I mean I was talking about if you learnt it in hs😂
I didn't
wraith patrol
wispy burrow
if you dont do it youre neglecting the lnx where x<0
But x can't be less than 0
wraith patrol
who said that
wispy burrow
ln
wispy burrow
Okay
wraith patrol
lnx failing doesnt stop x from reaching -
wraith patrol
replace Ae by B ig
wraith patrol
anyways my c is much cleaner
wispy burrow
I don't want my final answer to have B or c_2
When there's no A nor c_1
It doesn't look clean
Imo
wraith patrol
idrc
wispy burrow
But thanks again y'all
wraith patrol
::shrug
wispy burrow
idrc
That's how it should be
I'm just
Like
Idk
Weird
But thanks y'all
Again
I will be back 🥲
wraith patrol
fourth ika thread incoming
topaz sinewBOT
thorny flameBOT
brandon
opal vault
Yes
smoky sparrow
-1 congruent to 1 mod 2
opal vault
-x ≡ x (mod 2) as 2x ≡ 0 (mod 2)
smoky sparrow
so -1 * a congruent to 1 * a
thorny flameBOT
brandon
thorny flameBOT
brandon
opal vault
Sure you can do that
opal vault
But you can also stick to (0-x1) + (x1-x2) + ...
It can also be done like this
-x1 and x1 cancel, so do -x2+x2, etc...
thorny flameBOT
brandon
opal vault
0 = 2 • 0
It's also the mod class of even integers
You do you
But if I find something is ≡ 0 mod 2 then that's kinda the definition of even integers
Like, a ≡ b mod n iff n|(a-b)
serene dome
im strugglign to understand composite functiosn when theres a function and a set of coordinates
topaz sinewBOT
im strugglign to understand composite functiosn when theres a function and a set...
serene dome
i know how to do g rond f
but f rond g i am lost]
g rond f i do f(0) = 1
so g(1) = 2(1) + 1
but f rond g
clueless
serene dome
im confused
can yoiu give me a showcase with the first set of coordinates
and ill do the rest
restive inlet
what exactly are you being asked to evaluate
serene dome
f rond g
restive inlet
are you being asked to evaluate that at a specific value or something else
restive inlet
ok.
serene dome
and im assuming theres gonna be 4 since theres 4 coordinates
and f(x) is a infinite functinon
restive inlet
first you'd want to consider the domain
serene dome
the domaine is gonna be my result from f no?
i already have all my y values being the values from g(x) for my rangfe
restive inlet
you want the values of x where g(x) will be each input of f
serene dome
how do ig et those
restive inlet
solve g(x) = input of f
serene dome
what is input of f
restive inlet
the first value in each ordered pair
restive inlet
the first one, but that's not what i'd start with
serene dome
what would you start with
serene dome
yes
serene dome
so im just working backwords compared to g rond f?
restive inlet
yes
serene dome
so the summary of this is
i take my equation
and set it equal to all x values of my coordiantes?
restive inlet
yes
restive inlet
yes
restive inlet
f(g(x))
serene dome
wait can we go back a step
restive inlet
g(x) is the input of f here
serene dome
i just want to verify my logic
whenever i have something rond coordinates
lets say i wanna do my first one
i take my coordiante
g(f(x)
g(f(0)
f(0) = 1
so g(1)
i substitute my x value for my y value
whenever its a coordinate on the right side of the rond
and input is
g(input) = output?
restive inlet
yeh
serene dome
with input being x and output being y
thank you
alright back to the l;ogic
why am i setting it = to 0 and not 1?
if i typically take the output and not the input
(output being y input beign x)
restive inlet
f(g(x))
g(x) is the input of f here
you want that to be either 0,1,2,3
otherwise it'd be undefined
serene dome
wait
ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
f(g(x)
g(x) = 2x+1
so its really f(2x+1)
restive inlet
yes
serene dome
and as thats my input
i must set it equal to another input to find the corresponding output
restive inlet
yes
serene dome
because i cant set the input equal to an output
as it will not be equal
OHHHHHHHHHHHHHHHHHHHHH
thank you
tyvm @restive inlet
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
sudden marsh
Kind of last resort to ask for help here, but I have been stuck on this for a while since I don't even know where to start and my girl doesn't seem to want to help me on it..
"Arnaud throws a stone into a well. After 5 seconds, he hears the sound of the stone in the water. How deep is the well?"
I've asked ChatGPT but I don't want to just copy it without understanding what I'm writing..
topaz sinewBOT
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
vestal totem
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
!status ?
topaz sinewBOT
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
mystic jay
there are teo things to consider here
first its how much times it takes for the stone to hit the water
mystic jay
shreyan
mystic jay
thanks
mystic jay
first its how much times it takes for the stone to hit the water
second is how much time it takes for the the sound to travel up the well
sudden marsh
it's just an object falling under the influence of gravity.
Yes, I'm aware, I just have no clue on how to calculate this
mystic jay
do you know how to find average velocity? (given constant acceleration) ?
vestal totem
we have a nice equation of $S_y=u_yt+\frac12 a_yt^2\$ which you dont need to know the derivation for, just know that $S_y$ is distance along y axis, $u_y$ is initial velocity, along y axis, $a_y$ is acceleration along y axis, and $t$ is time
thorny flameBOT
Percy
vestal totem
i know shreyan
sudden marsh
do you know how to find average velocity? (given constant acceleration) ?
Nope, we didn't learn it, figured we'd have to look for it though
mystic jay
Nope, we didn't learn it, figured we'd have to look for it though
hm
ok
so basically
do you agree that if acceleration is contant
average velocity
will be (intial velocity + final velocity)/2 ?
sudden marsh
Yeah, makes sense so far
mystic jay
here intial velocity is 0
and final velocity is therefore just
accelration * time
right?
sudden marsh
And we have to find that time, right ?
mystic jay
yes
so
mean velocity = at/2 where a is accelration
and t is time
multipkying this by time
we get
distance = at^2/2 right?
sudden marsh
vestal totem
\begin{align*} u_{avg}&=\frac{u_1+u_0}{2} \ \implies u_{avg}&=\frac{u_0 + a \cdot t +u_0}{2} \end{align*} etc
thorny flameBOT
Percy
vestal totem
(i got tired of latexing and he got it anyway)
mystic jay
<a:nod:1167999126735167641>
so
we usually use the symbol s for displacement
S = 1/2 a t^2
now
in this case i think it is likely we will have to facrir in the speed of sound
sudden marsh
Which is 340m/s
mystic jay
yes
so
we have
root(2S/a) + S/340 = 5 secons
right?
now substitute
a= accleartion of gravity = 9.8 or 10
so substitue that
and you have an equation
that you can solve to find the value of S
sudden marsh
right?
Yeah, so far it makes sense, and I'm pretty sure it's what GPT explained poorly
mystic jay
now this part is calculation intensive
if you are allowed to use calulcator you should do this
but if you are not allowed
ig thwy would mean neglect the speed of sound
mystic jay
S = 1/2 a t^2
in which case you should directly use this
sudden marsh
if you are allowed to use calulcator you should do this
I'm allowed, just need to write the details of my calculation
sudden marsh
Uh ?
mystic jay
let us write
v = 340
so
root(2S/a)+S/v = 5
and
if we take
x = root(S)
we hget
root(2/a)x+x^2/v = 5
right?
sudden marsh
root(2/a)x+x^2/v = 5
Oh okay, yeah, I see
mystic jay
this is a quadratci that you will need a calculator (or amazing patience and calculative skill) to solve
vestal totem
holy shit this is still going?
sudden marsh
I'll be right back
mystic jay
you are finished tho?
sudden marsh
this is a quadratci that you will need a calculator (or amazing patience and cal...
I only have a calculator, I'm dogwater at maths xD
vestal totem
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
but lliterally just $s=ut+\frac12at^2 \ \implies s=\frac12 (10) (5^2) \ \implies s=5^3$, no?
sudden marsh
I'll be right back
(Imma eat)
mystic jay
no
thorny flameBOT
Percy
mystic jay
you forgot the speed of sounf
mystic jay
idt they give a damn about the speed of sound in intro kine
125m is a karge vakye
vestal totem
in formal terms, $\text{speed of sound} = \emph{really fucking big}$
thorny flameBOT
Percy
vestal totem
125m is a karge vakye
bro doesn't know the kinematic equations dude, he's not supposed to factor in the speed of sound
mystic jay
in formal terms, $\text{speed of sound} = \emph{really fucking big}$
125 is on the order of 340
around a 1/3
1/3rd of second is significant when thinking about 5 secs
vestal totem
,calc 1192/125
thorny flameBOT
Result:
9.536
if the wanted to neglect they would say "see the rock in water"
thorny flameBOT
Result:
0.37764350453172
significant
vestal totem
i still dont buy it
mystic jay
ehh
vestal totem
@sudden marsh do you even know what the speed of sound is
have you ever been told what the speed of sound is
mystic jay
Which is 340m/s
here
vestal totem
if he needs to factor it in then hoooboy is not knowing the kinematic equations not a good sign
i still feel like you're overcomplicating it for literally no reason
mystic jay
1/3 is important on the scale of 5 seconds
vestal totem
its important on the scale of like 2 seconds
1/3 in 5 seconds is like 1 seconds in 15
it's decent margin of error for a stone drop experiment
mystic jay
hm
topaz sinewBOT
@sudden marsh Has your question been resolved?
sudden marsh
I'm back @mystic jay
sudden marsh
So you know the value of x
I still don't get how I'm supposed to get x
mystic jay
You have a quadratic equation on x, right?
mystic jay
Yes
sudden marsh
root(2/a)x+x^2/v = 5
This ?
mystic jay
Yes
Now you can solve this
Right?
Also it is possible that they wanted you to neglect the speed if sound.
In which case it would be much easier
sudden marsh
Also it is possible that they wanted you to neglect the speed if sound.
Nope they mentioned it in the exercise
I just didn't want to type it all out
mystic jay
So you know how to solve a quadratic, right?
sudden marsh
So you know how to solve a quadratic, right?
No..
Wait lemme
We assume that a freely falling object travels (in meters) the distance 1/2gt² in t seconds, where g = 9.8 m/s², and that the speed of sound is approximately 340m/s
@mystic jay
That was the following
vestal totem
close your eyes and do $x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ lol
thorny flameBOT
Percy
sudden marsh
close your eyes and do $x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ lol
Wha
What you send me is always confusing mate 😭
mystic jay
Yes
vestal totem
he doesn't know basic algebra mate
mystic jay
He told that himself
vestal totem
(/nay snassy you're fine)
sudden marsh
he doesn't know basic algebra mate
I just suck
That's the thing
Like
I had 2 maths teachers which were horrible with me (and I used to love and be good at maths)
I'm supposed to know algebra but like :/
mystic jay
(a+b)^2=a^2+2ab+b^2, right?
sudden marsh
(a+b)^2=a^2+2ab+b^2, right?
Oh nvm I know what that is
I'm just like really shit at it
mystic jay
So you know completing the square?
mystic jay
Ok, so you get how to solve a quadratic?
sudden marsh
Learned it this year / last year iirc and it's the two years where I had issues
sudden marsh
Ok, so you get how to solve a quadratic?
I should've learned it I'm just bad at it :/
mystic jay
Dw, imo, just try to derive stuff
waxen flame
There's only a small set of rules to remember
And the idea that you do the same thing to both sides of the equation
leaden basalt
whats goin on
waxen flame
Then remembering how to complete the square is just remembering some insight into changing the form of something
mystic jay
Imo don't try to remember how to complete the square
Just derive it so many times
That is becomes common sense
waxen flame
In any case for the problem you don't need to solve a quadratic
Unless you're doing something where you want to take into account the sound's travel time
sudden marsh
We assume that a freely falling object travels (in meters) the distance 1/2gt² i...
I'm pretty sure it's asked here
waxen flame
And taking that into account here is actually pretty improper
Because I'm pretty sure the effects of air resistance are more than that
Possibly also the variation in the perceived gravitational acceleration if you're at the equator vs at the poles
timber tulip
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
Is there a diagram for it…?
And starting height
Or is that just it
sudden marsh
We assume that a freely falling object travels (in meters) the distance 1/2gt² i...
That's the second part
Which is just help ig
timber tulip
This just seems like a very annoying ap phys question
It would make sense if this is like a parabola
But like
sudden marsh
This just seems like a very annoying ap phys question
Nah it's just a maths question
waxen flame
We assume that a freely falling object travels (in meters) the distance 1/2gt² i...
Is this chatgpt or is this part of the question
waxen flame
What else does the question say
sudden marsh
That's it
waxen flame
Honestly it's a dumb question because it's introducing the effect of the speed of sound and yet not the effect of air resistance
Though I guess if you say the stone is small enough and made out of tungsten maybe
But to solve this, you can express distance fallen as a function of itself and then solve for it
You know the time spent falling is 5 minus the distance fallen divided by 343 m/s,
sudden marsh
You know the time spent falling is 5 minus the distance fallen divided by 343 m/...
Yeah but I don't get how to calc the distance fallen
waxen flame
But to solve this, you can express distance fallen as a function of itself and t...
Reread this
waxen flame
What don't you understand about it
You can't just say "I don't get it"; parse out the words and explain exactly what part doesn't make sense or you don't understand
sudden marsh
You can't just say "I don't get it"; parse out the words and explain exactly wha...
What do you mean, by making it a function of itself ?
waxen flame
You can write d = something involving d
And then solve for d by moving all of the d to one side
sudden marsh
You can write d = something involving d
Is d distance here ?
waxen flame
It's the distance fallen
sudden marsh
Yeah alright I see
topaz sinewBOT
@sudden marsh Has your question been resolved?
sudden marsh
Yeah alright I see
@waxen flame I can't do it 😭
waxen flame
What in particular can you not do
sudden marsh
What in particular can you not do
Put it in a function
waxen flame
I didn't say to do that
sudden marsh
But to solve this, you can express distance fallen as a function of itself and t...
^
That's the part I don't get, like how to do it 😭
mortal thunder
Kind of last resort to ask for help here, but I have been stuck on this for a wh...
Is it a "He throws" or a "He drops"? Or is initially assumed that v_0 of stone is 0 by default?
sudden marsh
Is it a "He throws" or a "He drops"? Or is initially assumed that v_0 of stone i...
He throws
But I think we should assume that initial speed is equal to 0
mortal thunder
Do you know second equation of motion?
sudden marsh
Nope
Parts of it are given in the second part of the paragraph
(just looked it up)
sudden marsh
We assume that a freely falling object travels (in meters) the distance 1/2gt² i...
^
mortal thunder
YES that'll be a big help
So now, assuming distance between origin of well and the surface of water to be d, time taken for stone to hit the water level is t. Then according to paragraph, d = ½gt² . Right?
Or t = √(2d/g)
Now after it hits the water level, the sound happens and starts crawling the same distance d with a uniform speed 340m/s ✓ got it?
So time taken for it to cover the distance is t' = d/v = d/340, right?
sudden marsh
Now after it hits the water level, the sound happens and starts crawling the sam...
Yes
Okay, I'm starting to get what you mean
mortal thunder
And what you're given is that the sum of the two times is 5 seconds
That is t + t' = 5s
=> √(2d/g) + d/340 = 5
Which is an equation in one variable so I'm hoping you can solve it
,w √(2x/9.8) + x/340 = 5
thorny flameBOT
waxen flame
you can also solve it as x = 9.8 * (5 - x/340)^2 / 2
,w solve x = 9.8 * (5 - x/340)^2 / 2
thorny flameBOT
waxen flame
this doesn't require you to explicitly solve for time anywhere
sudden marsh
Yep, found the same thing
Thanks, just gotta write it all down and I should be good ❤️
Thanks a lot, and sorry for taking literally ages to understand
flint glen
expand function into a maclaurin's series using the summation symbol: f(x) = (x-tan(x))cos(x)
topaz sinewBOT
expand function into a maclaurin's series using the summation symbol: f(x) = (x-...
thorny flameBOT
Arnavutköy
gilded plume
$=x\cos(x)-sin(x)$
thorny flameBOT
Arnavutköy
gilded plume
im assuming we are plugging in maclaurin series at $0$
thorny flameBOT
Arnavutköy
gilded plume
therefore, it is $\sum_{n=0}^{\infty}\frac{f^{(n)}(0)}{n!}x^n$
thorny flameBOT
Arnavutköy
gilded plume
let us calculate $f^{(n)}(0)$
thorny flameBOT
Arnavutköy
torpid shard
$=x\cos(x)-sin(x)$
problem i have been founding
gilded plume
$f'(x)=-x\sin(x)+\cos(x)-\cos(x)=-x\sin(x)$
thorny flameBOT
Arnavutköy
agile harness
just use the macularin series for cos and sin
don’t try differentiating infinitely
gilded plume
just use the macularin series for cos and sin
oh yes this also works
flint glen
just use the macularin series for cos and sin
that’s what i did just wanted to make sure i got it all right
torpid shard
multiply the cos one by x
ngl, didnt knew that was possible, lol
agile harness
ngl, didnt knew that was possible, lol
it’s quite obvious if you write out the terms
gilded plume
that’s what i did just wanted to make sure i got it all right
ok so $\cos(x)=\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{(2n)!}$
thorny flameBOT
Arnavutköy
gilded plume
this is what you have
flint glen
this is what you have
i mean ive expanded the func just need someone to check the solution
agile harness
i mean ive expanded the func just need someone to check the solution
if i’m being real no one is reading what you’ve written
flint glen
look at the photo ive attached
gilded plume
i read it up to the line f(x)=something
agile harness
and verify that you’ve done it correctly
gilded plume
and that line is right
agile harness
i saw crossed out things and said yea no
gilded plume
gilded plume
@flint glen can you explain this one
i believe your coefficient of $\frac{1}{(2n-1)!}$ is wrong
thorny flameBOT
Arnavutköy
flint glen
<@309344507068153873> can you explain this one
that’s some side calculations sry
i could try to latex it if my handwriting is a big problem
gilded plume
i believe the coefficient should be $(-1)^{n-1}\frac{1}{(2n-2)!}+(-1)^n\frac{1}{(2n-1)!}$
thorny flameBOT
Arnavutköy
gilded plume
okay im reading yours
gilded plume
that’s some side calculations sry
okay @flint glen this answer is correct
at least the bottom answer is right
topaz sinewBOT
topaz sinewBOT
Available help channel!