i dont think my steps are right
#help-19
old agate
odd edgeBOT
odd edgeBOT
Available help channel!
hardy meadow
Hello, I have this problem, would someone be able to help me with the problem?
pliant nexus
you probably can ask this in the specalized channels
hardy meadow
you probably can ask this in the specalized channels
Oh okay, I am sorry. I just assumed to ask in here because I have asked measure theory problems before in these channels. I am not sure which of the specalized channels that would be appropriate for this problem?
sand horizon
Oh okay, I am sorry. I just assumed to ask in here because I have asked measure ...
You can but you will wait probably a bit longer unfortunately
hardy meadow
okay thank you very much
hardy meadow
is this functional analysis
would it be the advanced analysis since I do not see anything called functional analysis?
pliant nexus
would it be the advanced analysis since I do not see anything called functional ...
probably
odd edgeBOT
odd edgeBOT
Available help channel!
fresh hornet
Hey, diff eq question here, I understand how to do part a for this question but for part b i’m having trouble figuring out how -kxy = x’ translates to X’ and same for y’ and Y’. Is this the right approach?
odd edgeBOT
Hey, diff eq question here, I understand how to do part a for this question but ...
@fresh hornet Has your question been resolved?
odd edgeBOT
@fresh hornet Has your question been resolved?
distant marlin
Is the "?" 110° ?
odd edgeBOT
Is the "?" 110° ?
vale vortex
a triangle has to add up to 180
so we know the angle PDA is 75
and using gemoetry
the ? mark is 105
verbal nebula
the ? mark is 105
I don't believe it's a straight line i.e DB
verbal nebula
By inspection doesn't look like it, first thought was cyclic quadrilaterals but it's probably just more angle chasing
robust wyvern
Is the "?" 110° ?
is ABCD a rectangle given?
vale vortex
I think its 125
degrees
360 - (50+60+55+60)
turn it into a circle
and that should be ur angle
distant marlin
we have just the information you see in the picture
robust wyvern
so no rectangle
pliant nexus
I think its 125
no its 110
distant marlin
110 seems like very basic answer
distant marlin
given that it is from a difficult test :Dd
robust wyvern
its correct then
pliant nexus
by subtracting 90 from the corresponding angles
and thus, since the sum of the angles in triangle PAB must be 180, this implies APB is 110
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
There are two magnitudes A and B such that they satisfy the following relations:
A DP B when B ≥ 20
A^2 IP B when B ≥ 20
If when A=9, B=10, find the value of A when B=45.
mystic saffron
A√B/B = k, B ≥ 20
DP = directly proportional
IP = inversely proportional
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
odd edgeBOT
mystic saffron
!status
odd edgeBOT
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
keen stream
Its correct
mystic saffron
Its correct
What number??
keen stream
1
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
<@&286206848099549185>
mental lotus
<@&286206848099549185>
3 and 4 are correct
You have Q5 written down wrong
so the answer you got is incorrect
odd edgeBOT
@mystic saffron Has your question been resolved?
torpid flicker
Hello i need help with this partial fraction decomposition problem for pre calc its just that coeffecient is confusing me
torpid flicker
Hello i need help with this partial fraction decomposition problem for pre calc ...
Leading coeffecient on the bottom i mean
velvet heart
factor it out
steel spire
since they're all even you could factor it out entirely
vocal karma
1st factor out the bottom using complex trinomial or decomposition whatever you call it
torpid flicker
Holding
vocal karma
mb i’m studying for my own test
ur just trynna find the zeros right
@torpid flicker
vocal karma
values for a and b for that? hm idk i’ve never had to do that
velvet heart
why do you have a C
vocal karma
This is pre calculus
yeah we have similar but different curriculum
im from canada grade 12 our equivalent to what u call precalc is advanced functions
torpid flicker
why do you have a C
Because our teacher tells us to
The real reason is uh
I guess because theres 3 values so 3 letters
X squared, x, and the number
velvet heart
you don't need it for a constant
torpid flicker
yeah we have similar but different curriculum
I see
torpid flicker
you don't need it for a constant
Thats probably true since this guy using it for all xs
odd edgeBOT
@torpid flicker Has your question been resolved?
torpid flicker
Not yet
warped glacier
Mario my man
warped glacier
you shouldn't have A/2 in there
torpid flicker
Ok
warped glacier
so you should have (5x + 14)/2 = B + C(x + 3)
basically divide the numerator by 2, then on the bottom you are left with (x + 3)^2 after completing the square
there are a few ways to continue but you could compare coefficients
5x/2 + 7 = (B + 3C) + Cx
so C = 5/2 and B + 3 * 5/2 = 7 or B = -1/2
torpid flicker
there are a few ways to continue but you could compare coefficients
Alriiight
warped glacier
one sec something is wrong with this answer
warped glacier
But its not a pretty answer
yes that's correct
my algebra must really not be working today
oh yeah I was doing the wrong equation
,w simplify (-1/2)/(x + 3)^2 + (5/2)/(x + 3) - (5x+14)/(2x^2+12x+18)
clever fjordBOT
warped glacier
5x/2 + 7 = (B + 3C) + Cx
so C = 5/2 and B + 3 * 5/2 = 7 or B = -1/2
corrected
tidal storm
determine a formula for cos3x in terms of cosx
odd edgeBOT
determine a formula for cos3x in terms of cosx
tidal storm
how do i do this
i got it down to cosx cos2x - sinx sin2x but idk what to do from there
west hull
determine a formula for cos3x in terms of cosx
In terms of just cosine?
west hull
Do you know what sin^2x + cos^2x equals?
tidal storm
1
west hull
And do you know what 2cos^2x -1 equals?
tidal storm
sin^2x
west hull
It equals cos2x
west hull
What does 2sinxcosx equal
tidal storm
sin2x
west hull
Yes, those are all you need
inland rover
determine a formula for cos3x in terms of cosx
one way of doing this is by the help of complex numbers
tidal storm
what
inland rover
do you know complex numbers if not you can do what mari said
tidal storm
no
west hull
I looked it up and an identity for cos3x exists already in case you knew it offhand or this is just a step in a larger problem
west hull
Alright, you have everything you need to find it by hand
tidal storm
idk wht to do from here
west hull
It wouldn’t be sin^3
warped glacier
jeez you have sin^2 not sin^3
I told you before
and we're at square 1 again I believe
tidal storm
so is it this
warped glacier
wait where did the -cos x go
tidal storm
oh yea
warped glacier
that still gets distributed, cause it's a(b - c)
west hull
Do you know what sin^2x + cos^2x equals?
^
inland rover
convert sin^2 x in terms of cos
tidal storm
so this
west hull
Yes
warped glacier
?
you shouldn't get that
you should have $2 \cos^3 x - \cos x - 2 \cos x + 2 \cos^3 x$
clever fjordBOT
southlander!
warped glacier
try multiplying (2 cos x)(1 - cos^2 x) to see how
oh then you multiply that by -1
tidal storm
why would i multiply 2cosx by the brackets
its just 2
do i just combine it with the cosx at the end
warped glacier
do i just combine it with the cosx at the end
you need to multiply by -2 and by cos x
both of those
warped glacier
yes, finally!
warped glacier
determine a formula for cos3x in terms of cosx
that's it, you've done what the question asks you
tidal storm
.close
odd edgeBOT
odd edgeBOT
Available help channel!
unkempt plaza
odd edgeBOT
unkempt plaza
i dont get why the testcase gives a matrix of [[1] , [0],[0],[0],]
fair prism
Thats what u got
velvet heart
i don't see the complete code nor what you're trying to code
fair prism
Send the entire code lol
Prob has smth to do with u using r and c as a variable twice though
U said for r in range(r):
unkempt plaza
class Solution(object):
def matrixReshape(self, mat, r, c):
"""
:type mat: List[List[int]]
:type r: int
:type c: int
:rtype: List[List[int]]
"""
m = len(mat)
n = len(mat[0])
old = []
for i in mat:
for term in i:
old.append(term)
newmat = [[0 for _ in range(c)] for _ in range(r)]
k = 0
if m * n == r * c:
for r in range(r):
for c in range(c):
newmat[r][c] = old[k]
k += 1
return newmat
else:
return mat
If you are done with this channel, please mark your problem as solved by typing .close
@unkempt plaza Has your question been resolved?
Available help channel!
zenith shell
where do i start with b and c
odd edgeBOT
where do i start with b and c
thick hill
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@zenith shell Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
mellow rose
odd edgeBOT
mellow rose
can someone help me out please
hasty dome
Is this beginning calculus?
mellow rose
yeah
hasty dome
OK, do you know how to do derivatives of x to a power?
hasty dome
OK, so the derivative will give you the slope at a point on the graph.
So fill in x with x_0 to get the slope when x is 1.
What do you get for the slope?
mellow rose
1/2
hasty dome
OK, on the graph of f, what is the point on the graph at x = x_0?
mellow rose
sqrt 1?
hasty dome
OK, that's the y value, right?
mellow rose
yesw
hasty dome
So, the point on the graph is (1, 1).
So, now we have the slope and a point, so we can use point-slope form.
What is the point-slope form for (1, 1) and 1/2?
mellow rose
y = mx + c?
mellow rose
just move sqrt 1 over?
hasty dome
Right.
Then, you can fill in x with the sqrt(1.2).
And then you can simplify the right side.
mellow rose
what does sqrt 1.2 means?
hasty dome
That's the input given in your problem.
mellow rose
why is there x = 1 and x = sqrt1.2
hasty dome
Well, they want us to make a linear approximation when x = 1.
Then, they want us to use that for when x = sqrt(1.2).
Basically, change the curve to a straight line.
mellow rose
ok my ans is 1 though
hasty dome
How did you get 1?
hasty dome
y = 0.5(x - 1) + 1
y = 0.5(sqrt(1.2) - 1) + 1
y = 0.5 sqrt(1.2) - 0.5 + 1
y = sqrt(1.2 * 0.25) + 0.5
y = sqrt(0.3) + 0.5
Which is 1.047..., so it should be rounded to 1.05 if you're getting an approximate answer.
hasty dome
,w linear approximation of sqrt(x) at x = 1
clever fjordBOT
hasty dome
,w (x + 1)/2 where x = sqrt(1.2)
clever fjordBOT
hasty dome
1.0477 is close to 1.05, which rounds to 1.1, so perhaps there's a rounding error in the answer in the key.
hasty dome
Oh, I see what happened.
I misread the question.
They don't want you to do it for x = sqrt(1.2). They want you to do it for x = 1.2.
You get an approximation for sqrt(x) at x_0 = 1, which we did. Then, you use the approximation for sqrt(x) to get sqrt(1.2).
,w (x + 1)/2 where x = 1.2
clever fjordBOT
mellow rose
but ours do
hasty dome
Well, yours has y - sqrt(1) and his has y - 1.
sqrt(1) is 1, you just didn't simplify it to 1.
hasty dome
No problem.
mellow rose
ill leave it open abit if i have qn xd
hasty dome
OK.
mellow rose
You can check by checking the endpoints.
to get the games, sub in x = 24 and 36?
hasty dome
18 = -0.4(20 - 30) + 14
18 = -0.4(-10) + 14
18 = 4 + 14
18 = 18
14 = -0.4(30 - 30) + 14
14 = -0.4(0) + 14
14 = 14
We know for sure what y values we have at x = 20 and 30, so we use those to check that everything works.
mellow rose
We know for sure what y values we have at x = 20 and 30, so we use those to chec...
i subbed in x=36
but cant get the ans of 12.8
mellow rose
yes
hasty dome
But 36 is in the middle of 30 and 40 on that table.
hasty dome
Exactly.
hasty dome
You're welcome.
odd edgeBOT
odd edgeBOT
Available help channel!
late willow
odd edgeBOT
late willow
hi im trying to use the cylindricial method but I do not see how they got 6pi/7 my work is circled in blue
odd edgeBOT
@late willow Has your question been resolved?
odd edgeBOT
@late willow Has your question been resolved?
wide drift
odd edgeBOT
wide drift
Why is 0 also a solution??
south plume
what does (x-1)^0 equal to
wide drift
1
wide drift
-1/3
wide drift
To what tho?
Does that mean 3x + 1 is an oblique asymptote?
Any straight line is some kind of asymptote?
tacit wasp
An asymptote is a straight line that the function approaches when x → ∞
Or, if you prefer, line y=mx+b is a horizontal asymptote for f(x) iff
lim as x → ∞ of | f(x) - (mx + b) | = 0
odd edgeBOT
@wide drift Has your question been resolved?
wide drift
odd edgeBOT
wide drift
Im not really sure how to do this one
The VA occurs where the denominator is equal to 0
x^2 - 2x - 8 factorizes to (x+2)(x-4)
But the +2 outside of the fraction is complicating things for me a bit...
steel spire
I'll help a little, when a=4, then the denom becomes 2x-4 = 2(x-2)
x-2 doesn't cancel with anything in the numerator you factored, so nothing interesting happens in this case
wide drift
Where did you get a=4 sry?
steel spire
I just picked it at random
main thing is that it's even so I could factor the 2 out of it
I'm just looking to see if it cancels out with something in the denominator
does that make sense? basically try the same thing with the rest of the a values to see
wide drift
Hmmm yeah I see what you mean
Is there a way that I could figure it out what values they are without trial and error? Like lets say they didnt give me the list of options of what the answer could be...
steel spire
yeah, really just a matter of picking a to force one of the two terms in the numerator to cancel with it
my idea for you was to just start trying them by trial and error to get a feel for it, then you'd hopefully figure out that trick while doing it on your own
but I'm telling you this cause I gotta go to bed so hopefully someone else can step in, or you can work it from here, good luck!
wide drift
but I'm telling you this cause I gotta go to bed so hopefully someone else can s...
I will try on my own haha
Thank you so much for your help!!
Sleep well and sweet dreams!!
steel spire
yup!
odd edgeBOT
steel spire
haha thanks
odd edgeBOT
Available help channel!
sharp thunder
is this integration correct?
odd edgeBOT
is this integration correct?
mystic saffron
Try u = sin x instead of u = sin^2 x
sharp thunder
Try u = sin x instead of u = sin^2 x
can you look into this
mystic saffron
Remember when you do the Integration Power Rule, you divide by the new exponent. 2 dividied by 1/3 = 6
feral halo
A square pyramid is inscribed in a sphere.
What is the maximum ratio of the volumes of the pyramid and the sphere, and what are the corresponding proportions of the pyramid
feral halo
Need to find h as a function of r
then i got the rest covered
but not sure how to do that
<@&286206848099549185>
odd edgeBOT
@feral halo Has your question been resolved?
odd edgeBOT
warped glacier
A square pyramid is inscribed in a sphere.
What is the maximum ratio of the volu...
unfortunately you need to take d/dh of $\frac{1}{3} (r^2 - (h - r)^2) h$, if $h = TM$
clever fjordBOT
southlander!
odd edgeBOT
✅
warped glacier
if it helps you, since it just asks you for the ratio
warped glacier
i don't get it
which part don't you get?
warped glacier
why take d/dh
cause the height of the pyramid can vary
but if you change the radius, now you're also changing the radius of the sphere
warped glacier
right but
don't u find r as a function of h
no
feral halo
and then d/dh
warped glacier
not for this question at least
so yeah you are taking a partial derivative, where you are letting h vary and assuming r stays constant
that's what we want for this question
warped glacier
if it helps you, since it just asks you for the ratio
I was about to say, by volume similarity, the ratio is unaffected if you multiply r and h by the same amount
so without loss of generality, you can sub in r = 1
or r = 2 or whatever
odd edgeBOT
odd edgeBOT
Available help channel!
autumn heron
odd edgeBOT
autumn heron
what did i do wrong
nimble blaze
try redoing the expansion for the right side
you messed up signs again
same issue as last time
nimble blaze
pay attention to which things you're multiplying to get each term
autumn heron
so im gussing what im doing wrong is this
right?
idk what i did wrong tbh
is it cuz i change it from * to + in the middle
or something else
nimble blaze
wdym * to +
distant relic
perhaps when ur expanding (15x-2y)² u only applied the -1 to the coefficient of (15x)² instead of the whole expansion
autumn heron
one sec
autumn heron
wdym * to +
i mean this in the middle it goes from * to +
autumn heron
perhaps when ur expanding (15x-2y)² u only applied the -1 to the coefficient of ...
and i dont understand 😭
whats the coefficient
nimble blaze
lets go to the basics of multiplying two binomials
autumn heron
😭
nimble blaze
with the simpler case with two plus signs
(p+q)(r+s)
would you be able to expand that?
autumn heron
give me a sec ima try
distant relic
and i dont understand 😭
js use the identity
(a-b)² = a²-2ab+b²
(15x)² -2(15x)(-2y) + (-2y)²
but be careful with negative signs
nimble blaze
you yourself were not careful with said signs
nimble blaze
yes
autumn heron
js use the identity
(a-b)² = a²-2ab+b²
(15x)² -2(15x)(-2y) + (-2y)²
thats what chatgpt wold me but i didnt get it
nimble blaze
that works
distant relic
(a-b)² = a²-2ab+b²
(15x)² -2(15x)(2y) + (2y)²
thanks for spotting the error @nimble blaze
nimble blaze
(15x - 2y) can be viewed as (15x + (-2y))
autumn heron
im not sure but does it become to this
nimble blaze
no
autumn heron
isnt this done then?
nimble blaze
yes
autumn heron
ima try to do it again
the other one i mean
better?
wait thats wrong
there
nimble blaze
last term is still wrong
(15x + (-2y))(15x + (-2y))
note that for the last term, you should be multiplying
(-2y) with (-2y)
autumn heron
ohhhh
i see it now 😭
is that the only thing or was there more that was wrong?
no wait nvm i dont see what ii did wrong
i mean im saying 15x*(15x-2y) then im saying 2y*(15x-2y)
is that wrong?
im a dumb ass
i see why there should be a *
mb
ima keep going now
if this is wrong ima give up
i forgot a x^2
autumn heron
(15x + **(-2y)**)(15x + **(-2y)**)
note that for the last term, you should be mu...
you there?
autumn heron
bruh
nimble blaze
lets go back to what you did for
(p+q)(r+s)
autumn heron
mhm
nimble blaze
distribute each term in the first bracket to each term in the second
your four terms will be
pr
ps
qr
qs
autumn heron
wait ima show you what we learnt but idk how to use it
nimble blaze
here you have
(15x + (-2y))(15x + (-2y))
and apply the same thing
nimble blaze
ok, lets use what we had before, but make the second part the same
(p+q)(p+q)
expand that
just write out the four terms (don't combine and simplify het)
autumn heron
i mean i get how to do that i just dont know how to do it when theres a ^2
ima try rq tho
nimble blaze
^2 is just denoting squaring, multiplication by itself
autumn heron
wdym
nimble blaze
pq and qp can be combined into a single term
nimble blaze
yes
autumn heron
now i get it
let me try 1 last time if its wrong just tell me what i did wrong
give me a second
odd edgeBOT
@autumn heron Has your question been resolved?
autumn heron
oh yes my teacher helped me
odd edgeBOT
odd edgeBOT
Available help channel!
spring bluff
can someone help me understand how we can apply axioms on the given statements?
Let V be the set of all ordered pairs of real numbers, and
consider the following addition and scalar multiplication op-
erations on u = (u1, u2) and v = (v1, v2):
u + v = (u1 + v1, u2 + v2), ku = (0, ku2)
(a) Compute u + v and ku for u = (−1, 2), v = (3, 4), and
k = 3.
(b) In words, explain why V is closed under addition and
scalar multiplication.
(c) Since addition on V is the standard addition operation on
R2, certain vector space axioms hold for V because they
are known to hold for R2. Which axioms are they?
(d) Show that Axioms 7, 8, and 9 hold.
(e) Show that Axiom 10 fails and hence that V is not a vector
space under the given operations.
clear current
Which axiom specifically are you working on
spring bluff
all statements require different axioms
clear current
I know but which part are you working on now
spring bluff
part c
clear current
Do you know the vector addition axioms?
spring bluff
yes i do
clear current
So vector addition is defined the same way for this as R^2 so all the same addition axioms would hold
So just state the axioms
spring bluff
my question is, how do i understand what axioms im supposed to state
clear current
All of the ones for vector addition
spring bluff
like in part a
clear current
Cause they all hold
spring bluff
what about part a?
clear current
What do you mean
You aren’t applying any axioms in part a
It’s just definition of vec addition
spring bluff
computing u+v and ku
oh can i show you another question?
im sorry if this is long
Let V be the set of all ordered pairs of real numbers, and
consider the following addition and scalar multiplication op-
erations on u = (u1, u2) and v = (v1, v2):
u + v = (u1 + v1 + 1, u2 + v2 + 1), ku = (ku1, ku2)
(a) Compute u + v and ku for u = (0, 4), v = (1, −3), and
k = 2.
(b) Show that (0, 0) = 0.
(c) Show that (−1, −1) = 0.
(d) Show that Axiom 5 holds by producing an ordered pair
−u such that u + (−u) = 0 for u = (u1, u2).
(e) Find two vector space axioms that fail to hold.
what am i supposed to do here?
spring bluff
its from elementary linear algebra applications by howard anton
clear current
What do you think the answer is for a
Unless I’m missing something or you left something out b is just wrong
spring bluff
What do you think the answer is for a
i add the values of u1 and u2 to find u and then the same with v, and then add u and v ?
clear current
You’re not adding anything within u
spring bluff
Unless I’m missing something or you left something out b is just wrong
lets leave that part then
clear current
You add the first element of u, u_1 to the first element of v, v_1 and then do the same thing for the second element
spring bluff
You add the first element of u, u_1 to the first element of v, v_1 and then do t...
that gives u+v?
clear current
Yes because that’s how they defined vector addition
spring bluff
okay i see
The set of all triples of real numbers with the standard vector
addition but with scalar multiplication defined by
k(x, y, z) = (k2x,k2y,k2z)
clear current
Slow down finish the other questions
spring bluff
my question is still the same, how am i supposed to understand what axioms apply on this one?
spring bluff
Slow down finish the other questions
oh hehe okay
spring bluff
Let V be the set of all ordered pairs of real numbers, and
consider the followin...
so b is wrong, what about c?
spring bluff
but what axioms should be applied to prove it
spring bluff
But solve the questions
I don't have time for this i have an exam in an hour
ill just go through all this thats why im rushed
clear current
There aren’t any axioms being applied except the field axioms
And I dont think you’re gonna be asked to specify field axioms you could just leave it
spring bluff
yeah okay
spring bluff
The set of all triples of real numbers with the standard vector
addition but wit...
can u explain this to me?
spring bluff
how am i supposed to understand what axioms apply on this one?
to prove the statement
clear current
It has nothing to do with axioms it’s just defining scalar multiplication
What statement is it asking to prove
spring bluff
and to solve it i have to?
clear current
I don’t understand what you are solving there is no question
It’s just a definition not a question
spring bluff
us bro
thats the question just that
idk what they want me to solve
i have some solutions should i show u
clear current
Just take a picture of the question because there is no question with what you sent
spring bluff
clear current
Which one you want me to look at
spring bluff
7
clear current
So you have to go through all the scalar multiplication axioms and show that they’re true
clear current
Actually it doesn’t ask you in this case it only asks you to show if an axiom fails and point it out
spring bluff
omg thanks bro i hope you have a cozy night
thank u so so much ure a life saver
i gtg byeee
clear current
Bye good luck
odd edgeBOT
verbal nebula
I don't have time for this i have an exam in an hour
good luck
odd edgeBOT
Available help channel!
odd edgeBOT
odd edgeBOT
@cloud pollen Has your question been resolved?
odd edgeBOT
@cloud pollen Has your question been resolved?
haughty scaffold
(3+y+xy)dx + (3+x+xy)dy = 0
ive been trying to get into my ODE's and i just cannot solve this one. looks deceivingly simple too. any ideas?
quasi sparrow
Is it exact?
haughty scaffold
Ny is 1+x and Mx is 1+y
so unless im doing something very wrong it doesnt seem like it
quasi sparrow
Is the goal to find y = f(x)?
haughty scaffold
well if thats not doable then id settle for just a general relationship between y and x
but yes the best case scenario would be y=f(x)
quasi sparrow
What is the question asking for
haughty scaffold
solve the ODEs:
this one would be c
its all in greek but this is the original question
odd edgeBOT
@haughty scaffold Has your question been resolved?
odd edgeBOT
@haughty scaffold Has your question been resolved?
odd edgeBOT
@haughty scaffold Has your question been resolved?
quasi sparrow
since it's been a few hours, maybe try asking in #odes-and-pdes .
wolfie doesn't really give anything useful
,w solve dy/dx = -(3+y+xy)/(3+x+xy)
clever fjordBOT
haughty scaffold
yeah i guess ill try that tomorrow, kinda late now
thanks anyway riemann you the goat
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mighty rampart
odd edgeBOT
mighty rampart
how to start to go about integrating this?
i know 1/cosx = secx and sinx/cosx=tanx
ember oak
how to start to go about integrating this?
trig integrals are always nasty and unintuitive
I don't often think there are ways to easily see how to find some of their antiderivatives
for $\int \tan x \dd x$, you could try $u=\cos x$ maybe?
clever fjordBOT
SWR
ember oak
$\int \sec x$, I have no idea
clever fjordBOT
SWR
mighty rampart
I don't often think there are ways to easily see how to find some of their antid...
haha okay thank you!
mystic saffron
The integral of sec x involves multiplying and dividing by (sec x + tan x) so just look that one up
You can do a simple u-substitution for the sin x / cos x part though
odd edgeBOT
@mighty rampart Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
nimble sail
odd edgeBOT
nimble sail
I need your help here.
I'm stuck.
So, I'm asked to find maximun and minimun of this.
The thing is that in order to do that, I gotta differentiate it, great.
crude skiff
which part are you stuck on
nimble sail
Well, I gotta find the Xs that make it zero, right?
Now, that's where I'm stuck on.
Lemme send you a screenshot.
nimble sail
find where h'(x) = 0 and use first or second derivative test
but how xD
Look at that crap.
That's the derivative of the function.
But look at that. How am I supposed to get h'(x) = 0
I do not know how to work with that.
How to find Xs= 0 in that expression.
crude skiff
$12x^2*(x-1)^2 + 8x^3(x-1)$
clever fjordBOT
Smiley ッ
crude skiff
factor
crude skiff
what common factors do the two terms share
nimble sail
4x^2(x-1)?
crude skiff
yes
nimble sail
so, 4x^2 (3(x-1) + 2x)?
crude skiff
simplify and set to 0
nimble sail
But how???
crude skiff
its just algebra
nimble sail
its just algebra
could you please help me to do so?
crude skiff
its straight up just distribution and combining terms
not as complicated as it might seem
nimble sail
not as complicated as it might seem
Okay
so 3(x+1) + 2x
3 (x+1) becomes 3x+3, right?
now, what's next?
crude skiff
so, 4x^2 (3(x-1) + 2x)?
btw its $4x^2*(x-1)*(3(x-1)+2x)$
clever fjordBOT
Smiley ッ
crude skiff
zero product property?
crude skiff
have you taken algebra yet
nimble sail
set each factor to 0 and solve
so, if 0, everything becomes zero because of 4x
if 1, everything becomes zero because 1-1 = 0
and finally, if 3/5, everything becomes 0 because 5*3/5-3 = 0
is that correct? @crude skiff
crude skiff
great
now you have to check with first and second derivative tests if they're min/max
im assuming you're searching for local min/max not absolute
nimble sail
yeah
@crude skiff
do you have any algebra video I can watch
I mean
I didn't know about this whole zero product thingy
crude skiff
I didn't know about this whole zero product thingy
are you taking calc in school or just learning it for fun
might be a dumb question on my part rip
nimble sail
are you taking calc in school or just learning it for fun
I'm at college xD
but like
I didn't really pay attention in classes
nor in highschool
so I do not not know some stuff
crude skiff
ouch
well I'm going to be honest
you need to be strong in algebra and algebraic manipulation for calculus
so I strongly suggest making sure you have that down first
nimble sail
Yeah
gonna watch some videos
and then be ready
I did this with chemistry
whole highschool chemistry in one week
and then, passed my test.
edgy warren
how do i establish the relationship between x and why
warped glacier
how do i establish the relationship between x and why
calculate 2/1, 4/2, 8/4, 16/8, 32/16
do you notice a pattern?
edgy warren
calculate 2/1, 4/2, 8/4, 16/8, 32/16
oh i get it now lol the 0 confused me
i kept calculating it as odd numbers
warped glacier
i kept calculating it as odd numbers
ah cool well with enough practice you'll be able to go that's just y = 2^x
if the common ratio is still 2 but you have say x = 0 and y = 5 for example
then you need to do y = 5 * 2^x
edgy warren
ah cool well with enough practice you'll be able to go that's just y = 2^x
k ic thanks
grave owl
Hi there. I'm trying to solve the following conformal mapping problem and I'm not sure if I am over-thinking it or not
grave owl
By inspection it looks lik this conformal map is f(z) = z
As in, it doesn't look like there's any change at all.
So would I be correct to assume that the correct answer is simply.... 0.35?
It can't be that easy, right?
I have no idea how to graph conformal maps in desmos, so I'm only really able to go about it by inspection...
But looking at it, the left-most plot and the middle plot are the same, so it must mean there is a one-to-one mapping.
I was over-thinking it
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
odd edgeBOT
halcyon stump
derivative w.r.t t
mystic saffron
can u explain
mystic saffron
i ask about the value of t when the answer of dw/dt = cos(2t)+1
halcyon stump
when you do the product rule
for dw/dt
you get
$ \frac{dw}{dt} = cos^2(t)-sin^2(t) + z'(t)$
and the identity for cos^2(x)-sin^2(x) is cos(2x)
So in this case when you compare the result with the answer we can see that z'(t) = 1 implies z(t) = integral of 1 dt which is just t.
odd edgeBOT
@mystic saffron Has your question been resolved?
steady tide
odd edgeBOT
steady tide
beginning with 1 has 2^6 strings
ending with 1 has 2^6 strings
having exactly 4 1s has 2^4 strings
but im not sure how to count number of strings beginning with 1 and has exactly 4 1s
my approach is to use inclusion-exclusion
oh wait, maybe fix 1 on one side and its just 2^3?
summer cradle
you could do that but you could also avoid inclusion exclusion
steady tide
but that would also double count those that has 1 on both ends
steady tide
you could do that but you could also avoid inclusion exclusion
how?
summer cradle
count how many there are for each of these forms
0 _ _ _ _ _ 0
0 _ _ _ _ _ 1
1 _ _ _ _ _ 0
1 _ _ _ _ _ 1
steady tide
each are just 2^5 isnt it
steady tide
ohhh
summer cradle
the rest are 2^5 each though, yes
steady tide
so the first one is choosing 4 slots out of 5 to put in a 1
so 5c4?
oh wait the rest are the same
summer cradle
yep
summer cradle
no?
steady tide
oh what
summer cradle
the rest have 2^5 each
they satisfy the begins or ends in 1 condition no matter what the empty spaces are
summer cradle
no
summer cradle
yea
clever fjordBOT
summer cradle
,w (5 choose 4) + 3*2^5
leaden karma
where are generating function
clever fjordBOT
summer cradle
where are generating function
this is combinatorics 101
no generating functions yet
odd edgeBOT
leaden karma
no generating functions yet
this is so sad
summer cradle
it's more sad nobody laughed at my pun
steady tide
wheres mqnic laugh emote when you need it
zinc glacier
brilliant
leaden karma
hahahahahahahahaha
summer cradle
@fluid tundra
fluid tundra
odd edgeBOT
Available help channel!
hollow jacinth
Find the maximum value of n where 15ⁿ divides 2023!
odd edgeBOT
Find the maximum value of n where 15ⁿ divides 2023!
spice ridge
Find the maximum value of n where 15ⁿ divides 2023!
Have you tried anything so far?
hollow jacinth
15^n \mid 2023!
spice ridge
I can think of one possible approach
clever fjordBOT
daring_maypole_43356
spice ridge
So I would split it up in the statement that both $3^n$ and $5^n$ divide 2023!.
clever fjordBOT
Casper
hollow jacinth
Oh yeah I've tried that
spice ridge
Than the question reduces to counting the 3's and 5's in 2023!
hollow jacinth
**Casper**
But not further than that
hollow jacinth
Than the question reduces to counting the 3's and 5's in 2023!
And how do I do that
spice ridge
And how do I do that
Its a bit tricky, but the factorial gives the numbers a nice structure right?
What would you do if you had to count the prime factors 3 and 5 in 20!?
hollow jacinth
I havent worked with factorials yet since im still in secondary school so this is my first time encountering them
spice ridge
That's alright, do you know the definition?
spice ridge
That is correct, though we are more intested in what it looks like computationally. That is n! = 1 * 2 * ... * n, does that make sense?
hollow jacinth
Yes
spice ridge
What would you do if you had to count the prime factors 3 and 5 in 20!?
Okay, than we can now get back to this question, can you solve this simpler problem?
hollow jacinth
Wait, i think ive got it
I divide 20 by powers of 3
Im lost
I wanted to do 2023/5 initially but i tried to do it on your problem and realised i wasnt solving for anything
spice ridge
I see, but dividing by 5 is indeed the right idea.
spice ridge
I divide 20 by powers of 3
This is also exactly what I would do
So where did you get confused in this approach?
Or maybe you can explain why you want to do this.
hollow jacinth
Because i tried it on your problem and i wasnt actually solving for anything..
On my problem im solving for 15ⁿ
hollow jacinth
Or maybe you can explain why you want to do this.
Honestly i don't know
spice ridge
Oooh, I see.
What if I tell you you dont need to solve for 15^n in the ordinary sense to solve this problem?
hollow jacinth
Hm?
spice ridge
So what happens if you divide 20 by the powers of 3 (and round down). Than you count 3 is a factor of 20 and how often 9 is factor of 20.
hollow jacinth
Alright
spice ridge
I.e. 20/3 = 6 + 2/3 and 20/9 = 2 + 2/9 means the factor 3 fits in 20! 8 times.
hollow jacinth
Makes sense
spice ridge
So can you now extent this idea to the bigger problem?
spice ridge
I.e. 20/3 = 6 + 2/3 and 20/9 = 2 + 2/9 means the factor 3 fits in 20! 8 times.
Or perhaps first finish this smaller one, whichever you prefer
hollow jacinth
2023/5 = 404
2023/ 25 = 80
2023/ 125 = 16
2023/ 625 = 3
So thats 503
I did it on a sheet of paper but for 3 i got 1006
spice ridge
I did it on a sheet of paper but for 3 i got 1006
Oops maybe I went a bit quick, is it clear why this show that 15^503 is the maximum n such that 15^n divides 2023!?
odd edgeBOT
@hollow jacinth Has your question been resolved?
deep mason
💪
deep mason
you know how if you try to integrate a differential equation (e.g. dy/dx = k x) on a compooter
um
you add up the area of a bunch of rectangles with width Delta x, and, the final error in the integral is in some sense of order Delta x
since Delta x -> 0 makes the answer exact
instead, if you do the integral on a computer, but the number of steps (of size Delta x) you do follows a poisson distribution
over many repeated runs of the integral program
and you average the runs
the order Delta x error disappears
does anyone know the name for this phenomenon?
i remember seeing it (in a textbook?) but i forgot where
some relationship between poisson distributions and discrete stepping of differential equations
also happyt hanksgiving
odd edgeBOT
@deep mason Has your question been resolved?
crude skiff
ping helpers tbh @deep mason
odd edgeBOT
@deep mason Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
autumn prawn
odd edgeBOT
autumn prawn
I can't remember how, on the left equation, the partial derivatives can be simplified by dividing everything by C_c (C_c formula is in the bottom right corner)
This is from a physics class, we are calculating the relative error of C_c using the error upper bound method (probably not translating this correctly). However my question should be mathematical only I hope
odd edgeBOT
Available help channel!
candid tangle
hi i need help with understanding vectors. the one with the questions is the wrong way i did. in the other picture, i though it was using this way based on the actual answers but I do not understand why
odd edgeBOT
hi i need help with understanding vectors. the one with the questions is the wro...
@candid tangle Has your question been resolved?
candid tangle
<@&286206848099549185>
ancient rampart
zoom the question gang
candid tangle
zoom the question gang
candid tangle
i dont really understand the constant speed of 20ms-1 with the same direction with ( 3 4) part.
candid tangle
whats the problem here
i just learned about vectors so i probably dont know what unit vectors do
ancient rampart
i just learned about vectors so i probably dont know what unit vectors do
they give the direction of a vector
any vector is made up of two things
its magnitude
and its direction
unit vector gives it direction and itself has a value of 1
u cant say i wanna go 5 units u have to say which direction u wanna go in
thats what unit vector is for
and itself has magnitude of 1
ancient rampart
i dont really understand the **constant speed of 20ms-1 with the same direction ...
both are going towards same direction
candid tangle
so basically when i multiply the speed and the unit vector, im getting how far am i going with that one particular direction?
ancient rampart
also never saw that () notation people generally use it to write ncr so not sure what it represents possibly i can and j cap i guess
ancient rampart
so basically when i multiply the speed and the unit vector, im getting how far a...
yes that
candid tangle
yes that
so for the velocity vector of (8 12) this tells me the rate of change of distance in the x y coordinates?
ancient rampart
not really no vecloity seeems to be indepdent of variables so it is constant
candid tangle
not really no vecloity seeems to be indepdent of variables so it is constant
oh, then for velocity vector of (8 12), this means that it's moving 8units per second upwards and 12 units per second to the right? So the difference is from the first one and the 20ms-1 and direction of (3 4) is that velocity vectors have already accounted for the direction and the first one doesnt?
.close
odd edgeBOT
odd edgeBOT
Available help channel!
dapper ginkgo
Hi, can someone help me understand this part of euklids proof? I dont understand how we could possibly know that BDLK is twice the area as ABD, based off the altitude BK
https://brilliant.org/wiki/proofs-of-the-pythagorean-theorem/
