Sure 
#help-36
tulip coyote
half forum
I see ty
pearl bane
final saddleBOT
pearl bane
How to approach the ladder question?
This is what I’ve done but I can’t confirm or know if it’s correct
final saddleBOT
@pearl bane Has your question been resolved?
warm python
given an arbitrary curve, how do I determine if it's closed or not?
final saddleBOT
given an arbitrary curve, how do I determine if it's closed or not?
warm python
say $x^2+y^2=x^6+y^6$
soft zealotBOT
WhyAmIHere?
vital surge
given an arbitrary curve, how do I determine if it's closed or not?
normally, they aren't
but you can find a few points that lie on the curve then check asymptotic behavior, i guess
(this is fine because by looking at the curve here you can kind of tell that it should be continuous for most points if defined)
alternatively, in this case, x^6 + y^6 is factorable
(i can't offer you a rigorous proof as to why this would be acceptable, but it might make sense in an intuitive sense)
final saddleBOT
warm python
.reopen
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warm python
**WhyAmIHere?**
for this curve, how would I find where it intersects the axes?
vital surge
for this curve, how would I find where it intersects the axes?
more or less how you'd expect
set x = 0 and solve for y
then y = 0 and solve for x
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uncut totem
List all abelian groups of order 1000.
final saddleBOT
List all abelian groups of order 1000.
muted prairie
Do you know the fundamental theorem of finite abelian groups?
uncut totem
Do you know the fundamental theorem of finite abelian groups?
prime factor ya
seems like alot to list out tho
@muted prairie
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@uncut totem Has your question been resolved?
uncut totem
.close
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pearl wraith
guys can someone help me remember how to find this angle right here
final saddleBOT
guys can someone help me remember how to find this angle right here
pearl wraith
angle theta
fluid bay
ig use sine rule
pearl wraith
ig use sine rule
hmm not sure how to use sine rule to get theta but I can get this angle tho using sine rule
fluid bay
hmm not sure how to use sine rule to get theta but I can get this angle tho usin...
you see that triangle
with
18.4
-y axis
and blue line
??????//
pearl wraith
yeah I see it
pearl wraith
ah yeah I see
fluid bay
??//
pearl wraith
thanks
final saddleBOT
@pearl wraith Has your question been resolved?
lost token
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lost token
does the pair need to be like (1,20) or (1,1) like similar numbers or no
tranquil pine
n and k can be any integers except that there is an upper bound for k
lost token
n and k can be any integers except that there is an upper bound for k
what
so how i do i solve
final saddleBOT
@lost token Has your question been resolved?
tranquil pine
k values are [1,2,3,4,5]
write 2024^k = (253^k)(8^k)= (253^k)(2^3k)
calculate n
and then calculate pairs
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rugged fiber
for part e can i use this argument
final saddleBOT
for part e can i use this argument
wheat lynx
hey is there an easier way of doing this other than sketching the graph
tranquil pine
hey is there an easier way of doing this other than sketching the graph
,, y = a(x-\5rh)^2 + \5bk \tqs{where} (\5rh,\5bk) \tsx{is the vertex}
soft zealotBOT
tranquil pine
so u can use that
wheat lynx
ok and we sub in y with 0 right?
tranquil pine
yes
wheat lynx
and what about A?
tranquil pine
find out a thats your first goal
tranquil pine
no
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wheat lynx
.reopen
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wheat lynx
@tranquil pine hi i am back ahah how do I find A?
if we are trying to find x how do we find A
or anyone can help
tranquil pine
if we are trying to find x how do we find A
like you have y = a(x-2)^2 -6 right?
wheat lynx
then find the other x intercept with that
final saddleBOT
tranquil pine
lmao you too
final saddleBOT
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jade fable
a
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crude plover
are my two answers the right way to think about the problem?
also when the fair amount to be raised is outside the domain does that mean that we should just raise it at the domain restricted value instead of what ever the maximum point is (which will be out of the domain)??
final saddleBOT
are my two answers the right way to think about the problem?
also when the fai...
@crude plover Has your question been resolved?
crude plover
<@&286206848099549185>
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@crude plover Has your question been resolved?
loud sundial
b. I think they just want the domain to have a positive number of people
c. Find the ||vertex of the graph|| (Note that ||this is halfway between the roots||)
crude plover
b. I think they just want the domain to have a positive number of people
c. Find...
for part b how come i shouldnt consider the decrease in price if they mention an upper limit of pasangers on the train?
loud sundial
Ig it depends on if you consider the price increases as reversible
It doesn’t explicitly state it but it’s a reasonable assumption to make
crude plover
<:catshrug:563818735085944843>
😭 why do word problems have to be so ambiguous
crude plover
b. I think they just want the domain to have a positive number of people
c. Find...
the part a formula looks right though? (just double checking)
loud sundial
Yes.
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fickle gate
29, 60, 64
final saddleBOT
29, 60, 64
rocky tusk
get a common denominator
fickle gate
On 29?
fickle gate
Ok one sec
fickle gate
-2?
fickle gate
-2/sec ² x - 1
fickle gate
That's an iddntity?
fickle gate
I dont have that one written down
rocky tusk
it comes from sin^2+cos^2=1
fickle gate
That's why I was lost
rocky tusk
dividing this equation by cos^2
rocky tusk
tan^2+1=sec^2
gives ^
because sin^2/cos^2 is tan^2
cos^2/cos^2 is 1
and 1/cos^2 is sec^2
fickle gate
Yea I get it
rocky tusk
!occupied
final saddleBOT
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).
fickle gate
Already occupied
rocky tusk
Yea I get it
ok so what’s ur final answer for that one
fickle gate
-2/tan ²x
fickle gate
-2 cos²x /sin²x
rocky tusk
which is what
fickle gate
Cot²x
rocky tusk
yes
fickle gate
2cot²x
fickle gate
-2cot²x
rocky tusk
good
fickle gate
There
fickle gate
Sin/cos
fickle gate
Tan
rocky tusk
mhm
fickle gate
X
rocky tusk
for 64 get a common denominator
fickle gate
Yea
rocky tusk
ok
fickle gate
27 was easy
rocky tusk
this is a difference of two squares
fickle gate
Ohhh
fickle gate
Sec ² x - tan² x times sec² x + tan ² x
rocky tusk
Sec ² x - tan² x times sec² x + tan ² x
forget that it’ll be easy
rewrite them
in terms of sin and cos first
fickle gate
1/cos⁴
rocky tusk
mhm
fickle gate
Sin⁴/cos⁴
rocky tusk
Sec ² x - tan² x times sec² x + tan ² x
this also works but i think a common denominator is easier
notice they have the same denominator
fickle gate
1-sin⁴/cos⁴
rocky tusk
mhm
fickle gate
That's where I got stuck
fickle gate
The answer is F btw or sec² x + tan² x
rocky tusk
The answer is F btw or sec² x + tan² x
ok maybe my first method works better then
because sec^2-tan^2 is just one
so one times sec^2+tan^2 is one
does that make sense
because 1+tan^2=sec^2
subtract tan^2
fickle gate
Yea I see
rocky tusk
ok 64
fickle gate
Yes
rocky tusk
what’s the common denominator
fickle gate
(1+sec ²x)(tan x)
fickle gate
Wdym
rocky tusk
like
fickle gate
1 is the numerator
fickle gate
Yea I see that now
rocky tusk
expand 1+sec
fickle gate
1+ 2 sec + sec²
fickle gate
Sec²
fickle gate
2sec( 1 + sec)
fickle gate
1+secx
rocky tusk
so 2sec/tan
fickle gate
Yea
rocky tusk
oh yea
wait
yea that makes sense
so
2sec is 2/cos
divide that by sin/cos
using keep change flip
(2/cos)(cos/sin)
cos cancels
2/sin
2csc
rocky tusk
ur welcome
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terse folio
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muted ore
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autumn geode
what about it?
muted ore
what about it?
I need help for question B
From what I can tell, the expression is already determined as -2x^2 - 2y^2...
In matrix form, it is basically A if you do (x,y,z) * A * (x,y,z)^T
Im not sure how to reduce it
autumn geode
I need help for question B
did you finish question A
muted ore
did you finish question A
Yes
Matrix([[sqrt(3)/3, sqrt(2)/2, sqrt(6)/6], [-sqrt(3)/3, sqrt(2)/2, -sqrt(6)/6], [-sqrt(3)/3, 0, sqrt(6)/3]])
determinant is 1
<@&286206848099549185>
.close
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tranquil pine
I'm looking to prove that [
\dv[\vj r]s = \4{\vj v}{\norm{\vj v}} = \vj T
]
where $\vj r$ is a position vector, $s$ is a smooth curve that is traced by $\vj r$, $\vj v$ is the velocity vector corresponding to that position vector, and $\vj T$ is the unit tangent vector to the curve
final saddleBOT
I'm looking to prove that \[
\dv[\vj r]s = \4{\vj v}{\norm{\vj v}} = \vj T
\]
wh...
soft zealotBOT
tranquil pine
its clear that dr/dt = v
ocean lintel
differentiate wrt the curve ?
stone wagon
what is ds/dt, then?
tranquil pine
so the chain rule tells you that [
\dv[\vj r]s = \dv[\vj r]t\cd\dv[t]s
]
so this becomes proving that [
\dv[t]s = \41{\norm{\vj v}}
]
soft zealotBOT
tranquil pine
hmmge
,, \6st=\int_{t_0}^t\3{\9{\6{x'}\tau}^2 +\9{\6{y'}\tau}^2 + \9{\6{z'}\tau}^2} \dd\tau =\int_{t_0}^t\abs{\6v{\tau}}\dd\tau
soft zealotBOT
tranquil pine
so i guess it does make sense for the derivative of this to be t
so [
\dv[t]s = \41{\dv*[s]t}
]
soft zealotBOT
tranquil pine
but like idk how to prove this
i mean they need to be inverses but how do i prove s is one-to-one 
vital crag
where do you need one-to-one
tranquil pine
for this to be true
ocean lintel
locally one-one is fine
Which simply means nonzero derivative
Which is obvious
vital crag
yea i guess physics always sweeps under the rug that you can always shrink your domain sufficiently enough
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unique hawk
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unique hawk
How do I solve this ?
hardy yew
the line farthest should be the perpendicular to the line that joins the intersection of those and (7,4)
unique hawk
Ok so first I have to find the equation of the perpendicular line ?
hardy yew
yes
hardy yew
Ok so first I have to find the equation of the perpendicular line ?
first find the intersection
unique hawk
Ok and then the equation , and through that equation the equation of the required line , then compare it with the given equation to get value of lambda ? this is how it goes ?
hardy yew
not really. once you find the equation, find the slope of it. since we need a line perpendicular to it, the slope would be the negative reciprocal. so if your line joining (4,7) and the intersection was x + 3y = 5, then the slope of that is -1/3, which means the slope of the line we need is -1/(-1/3) which is 3. now simplify the expression we have in terms of lambda so that all the coefficients of x are together and find the slope, and equate it to 3
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solid acorn
hi!! this is weird but if you have the sequence (2n-1)!... why does this work hold up let me get a screenie
final saddleBOT
hi!! this is weird but if you have the sequence (2n-1)!... why does this work ho...
solid acorn
you get (2n-1)(2n-2)(2n-3)(2n-4)(2n-5)(2n-6)
wooden plover
ye?
solid acorn
and then you can make it look like (2n-1)2(n-1)(2n-3)(2(n-2)(2n-5)2(n-3)
but I don't get how then you can turn all those terms with a 2
into 2^(n-1)
wooden plover
you factor a 2 from them
wooden plover
xd np
solid acorn
so u have
desert mantle
solid acorn
I guess I heard someone in my class say there were (n-1) twos
but I didn't rlly understand why
aren't there an infinitr number of twos
wooden plover
@solid acorn not all terms go to 2^(n-1)
solid acorn
yeah half of them do right
wooden plover
they are 2^(n-1);2^(n-2);2^(n-3)
wooden plover
it's just times i just copied yours Xd
wooden plover
you divide the monomial by 2
to "simplify it
and the ones dividable by two are two multiples 2/4/6
only half of all monomials is dividable by two
solid acorn
wait so we're at
wooden plover
do you know what factoring is?
solid acorn
yes but they aren't exponents
wooden plover
okay can you factor x^2 - x = 0 for me please?
wooden plover
nice so you divided both terms by x and multiplied by x
now can you factor 2x^2 - 2x = 0
wooden plover
great
now we replace x with n
and don't have = 0 just a polynomial
2n-1
can you factor that?
no common variables and you can't divide 1 by anything
solid acorn
no
solid acorn
2(n-1)
solid acorn
yeah
wooden plover
and this works in between terms because it's just multiplication
solid acorn
yeah
wooden plover
2n-3 or 2n-5 and all other odd terms are not factorable
but 2n-4 or 2n-6 and so on are because they are divisable by two
so you have a chain of factored non factored terms
solid acorn
yeah
but how do the even ones become 2^(n-1)
that was what tripped me up
why 2(n-1)2(n-2)2(n-3)... = 2^(n-1)
solid acorn
that was what I'm confused about
wooden plover
you wrote a different thing initially
wooden plover
yeah
solid acorn
so we were writing an expression for this
and I understand everything except how he knows the 2^(n-1)
because obviously you want to keep the negative terms but cancel the even ones
wooden plover
right but on your question you are missing half
it's not just 2^n-1
it's 2^n-1 * (n-1)!
solid acorn
oh yeah sorry I just meant how do we know that's how many "twos" there are
ike some kid in class was like "we raise it to the power of (n-1) because there are (n-1) twos"
and I didn't get that at all 😭
solid acorn
how do we know there are n-1 "twos"
wooden plover
can you make out why that is?
wooden plover
there are infinite n
solid acorn
so there are n/2 twos??
wooden plover
so there are n/2 twos??
apperant n/2 twos
the whole equation says
2^n-1 * (n-1)!
wooden plover
2^n-1 * (n-1)!
expand this
wooden plover
yes now distrubute infinte twos to each term
solid acorn
2^(n-1)(n-1) * 2^(n-1)*(n-2) ...
wooden plover
no no i meant
2^n-1 is in itself 2*2...
n-1 times
you don't distribute 2^n-1 to each term
it's multiplication
solid acorn
n2^(n-1)-2^(n-1)
I'm bad with factorials
wait may I ask a weird question
you know how earlier we had
just the evens: 2(n-1) 2(n-2) 2(n-3) etc
does that equal 2((n-1)(n-2)(n-3))
wooden plover
if you see subsctaction and addition inside brackets
consider them like a single unit when multiplying dividing outside them
solid acorn
yeah sorry that was silly on my end
wooden plover
as in (n-1) = k
it's fine it's very confusing
specially when you type in discord the brackets and a misstype makes you more confused xd
solid acorn
cus I get that you would pull out the 2 ^ however many twos there are
wooden plover
exactly
let N = n-1
if N = 3
you have
2^N(N)(N-1)(N-2)
this is very important to understand and it's the part everyone gets confused
there is a 2 for each term
not 1 less
because we are starting at n-1
not n
factorial ! ends when N reaches 1
solid acorn
how did u pull out the exponen 😭
wooden plover
wdym?
wooden plover
what you typed is correct
you are just worked up on n-1
but you solved it for n-1 = N
solid acorn
there are no exponents yet
right
cus when u typed it here too there was an exponent
oh ur trying to show they're the samr thing??
wooden plover
yeah
you are just expanding the exponent
into many twos
put on each term
n-1 = N was to show that you have as many 2's as terms
solid acorn
so if n = 3 N = 2
wooden plover
yes
it's just for you to grasp it
cause the counting starts from n-1
basically 2^N * N!
solid acorn
wait if you just like
wooden plover
you don't replace that on the original one tho
wooden plover
sure
solid acorn
because we are starting at n-1
u were saying this is why there are n-1 terms and not "n" terms
or something
wooden plover
u were saying this is why there are n-1 terms and not "n" terms
exactly
nobody said there n terms but from prior problems you just assume
so from the problem everyone be like huh why is a 2 missing
also thinking of 2^n-1 and (n-1)! as infinite is also wrong and messes up the intuition even more
what you should do is replace n with a small number
so you actually see what goes on
expand the terms
and witness how the numbers check out
solid acorn
so the 1st term = 0
wooden plover
nobody will understand the problem if you keep on saying n-1)(n-2)(n-3)(n-4) to infinity
wooden plover
so the 1st term = 0
if n = 1
but you gotta get a bigger number so you can actually have some terms xD
solid acorn
so if n = 1 there are 0 twos
if n = 2 there is 1 two
if n = 3 there are 2 twos
and so you know the number of "twos"
= n-1
OMGOSH
I LOVE YOU
I THIBK THAT'S IT
was that valid??
lmao
wooden plover
was that valid??
YEAH
solid acorn
YAAAAAAAAY
wooden plover
teachers do such a poor job explaining breh
good luck slapo and type .close if you are done
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tranquil pine
Having trouble with 23
final saddleBOT
Having trouble with 23
tranquil pine
I got x+ sqrt(3)y -6 = 0
But there should be x+sqrt(3)+6=0
Let me send in my work
pastel cosmos
Both are answers
tranquil pine
You mean like y-intercept
pastel cosmos
hmm
practicing a lot?
solve lots kind of math problems
damn I can't fall asleep since I'm helping other people\
😂
It's 4:44 am in my country
tranquil pine
Oh sorry! I understand now though. thank you for your help:) I really appreciate it
Have a good night
pastel cosmos
thanks
tranquil pine
.close
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fair sedge
whats the mathematical logic behind Sinh(ln x) = x^2 - 1/2x
final saddleBOT
whats the mathematical logic behind Sinh(ln x) = x^2 - 1/2x
fair sedge
every video i watch just skips over it like im supposed to know it
trail crest
Do you know what sinh is?
fair sedge
yes we went over it in class and the graph too
if anything in this problem confuses me it's more or less where we get the x^2 from
trail crest
$\sinh(x) = \frac{e^x - e^{-x}}{2}$
soft zealotBOT
casework
trail crest
You know this?
fair sedge
Yes I know that and that cosh(x) is just that with a plus
soft zealotBOT
casework
trail crest
Or if you prefer $\frac{x - \frac{1}{x}}{2}$
soft zealotBOT
casework
fair sedge
oh do both work?
trail crest
Same thing
fair sedge
ah ok i guess im lacking in simplification
fair sedge
**casework**
i got confused seeing this
how do you simplify it in that case
im sorry for the stupid questions but this really confuses me
oh my god nevermind.
sorry for wasting your time like this
.close
final saddleBOT
plain mural
Im in Intermediate Alg, so I don’t how to do that. My apologies
I could still try if you can walk me through
final saddleBOT
@thorny folio Has your question been resolved?
plain mural
Ah I'm sorry
final saddleBOT
@thorny folio Has your question been resolved?
final saddleBOT
@thorny folio Has your question been resolved?
cyan kayak
@thorny folio to solve a least squares regression by hand you need to find the mean of your data, then the covariance between x and y divided by the variance of x.
And then using the means of x and y and the slope you can get the intercept. You'll be left with an equation: y = ax + b where a is the covariance/variance ratio, and b is the intercept you solved for using the mean and the covariance.
The formula for the slope is $\sum_i \frac{(x_i - \overline{x})(y_i - \overline{y})}{(x_i - \overline{x})^2}$
soft zealotBOT
全能の存在
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@thorny folio Has your question been resolved?
thin leaf
Find a cubic equation in x-intercept form where the line touches the x-axis at 3, the y-intercept is 18 and it passes through (1,20)
final saddleBOT
Find a cubic equation in x-intercept form where the line touches the x-axis at 3...
thin leaf
ill send a pic of my work so far
im so close
i just can't get it
it's everything in the bottom part
where it says #5 B
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@thin leaf Has your question been resolved?
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thin leaf
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quasi plinth
,tex
\begin{flalign*}
& \text{Given the plane } \boldsymbol{\Pi}: 2x - 2y - z = 5 \text{ and the line } \mathbb{L}: \mathbf{X} = \lambda(1, 0, 1) + (1, 1, 2). \text{ Find all lines } \mathbb{L}' \text{ that simultaneously satisfy:} &\
& \text{i) } \mathbb{L}' \cap \mathbb{L} \neq \emptyset \quad \text{(non-empty intersection with } \mathbb{L}\text{)} &\
& \text{ii) } \mathbb{L}' \perp \mathbb{L} \quad \text{(perpendicular to } \mathbb{L}\text{)} &\
& \text{iii) All points of } \mathbb{L}' \text{ are at a distance of 2 from } \boldsymbol{\Pi} &
\end{flalign*}
final saddleBOT
,tex
\begin{flalign*}
& \text{Given the plane } \boldsymbol{\Pi}: 2x - 2y - z = ...
soft zealotBOT
レナト (renato , ping if reply)
scarlet sequoia
!status
final saddleBOT
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
how do I get this started?
scarlet sequoia
Let line L' = av + w
signal vector
Can you see that there will be 2 such lines only?
scarlet sequoia
Let line L' = av + w
try to find all vectors v that can satisfy ii) and iii)
(hint : if all points of L' are at a constant distance from Pi, where does v lie?)
final saddleBOT
@quasi plinth Has your question been resolved?
quasi plinth
if all of L' are at a constant distance of 2 from the plane,
the line L' must be parallel to the plane with a constant distance of 2 from it, meaning that the direction vector of L' lies within the plane parallel parallel to $\Pi$, the normal vector of $\Pi$ is (2,-2,-1)
To satisfy condition iii) L' should be parallel to the plane,
which means the direction vector v should be orthogonal to the normal plane vector
soft zealotBOT
レナト (renato , ping if reply)
final saddleBOT
@quasi plinth Has your question been resolved?
scarlet sequoia
yep
you have v orthogonal to (2,-2,-1)
and L' is perpendicular to L so v and (1,0,1) are orthogonal too
with this you quickly have a single value of v possible (up to a multiplicative constant)
next, you find w using i) and iii)
misty umbra
In activity 2, when I tried to isolate x on one side I got x=radicaly +1 , but in the answer key (second picture) it says the equation is x=-radicaly+1 why?
final saddleBOT
In activity 2, when I tried to isolate x on one side I got x=radicaly +1 , but ...
@misty umbra Has your question been resolved?
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lilac estuary
A random sample of size n = 18 drawn from a normal distribution had a sample variance
of s
2 = 27.64. Construct a 98% confidence interval for σ
2
.
final saddleBOT
A random sample of size n = 18 drawn from a normal distribution had a sample var...
lilac estuary
I have found no table that gives me information for a significance level of 0.44 for chi squared dsitributions
I'm trying to find k1 and k2 such that P(X<k1)=P(X>k2)=0.44
floral nova
Either use software like R or just linearly interpolate between values on the table and accept the error
I'm not sure where you are getting 0.44 if you are trying to construct a 98% confidence interval
lilac estuary
I'm not sure where you are getting 0.44 if you are trying to construct a 98% con...
I belive P(X<k1)=P(X>k2) = alpha/2
if I'm trying to build a 98 percent confidence interval then alpha = 0.98
so I have 0.44
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limber marsh
HEY
limber marsh
I NEED HELP REALLY BADLY
oops sorry for caps
can someone explain what its asking im kinda dumb rn
variations what it means?
and any suggestion how could I find for any real number that is strictly positive
signal vector
Do you know what the expansion of e^x is?
signal vector
Right, so try using it for the question b
limber marsh
alr
plush merlin
do you mean expansion using taylor series ?
limber marsh
Right, so try using it for the question b
wait hold on
signal vector
Or you can show that it is >0 for x=0 then show it is increasing
plush merlin
why will you do that
plush merlin
Or you can show that it is >0 for x=0 then show it is increasing
exactly thats easier
find the derivative
limber marsh
alright
plush merlin
show that it is increasing
plush merlin
then let g(x)=e^x-x and find g(0) you know that for all x>0 g(x)>g(0) and you are done with b
limber marsh
and solve o find
limber marsh
then let g(x)=e^x-x and find g(0) you know that for all x>0 g(x)>g(0) and you ar...
ohhh k
ty
what about a?
a is confusing me mostly
plush merlin
for a you just need to find when g is increasing, when it is decreasing and when it has critical points
plush merlin
solving a will put you on half the road to solve b
bc notice that the derivative of the given function is the same as that of the derivative of e^x-x
so they have the same variations
plush merlin
thats why they gave you both questions as parts of the same given
bc you gotta relate them somehow otherwise they will give separate questions like 1,2 instead of 1a,1b
limber marsh
alr
jovial crane
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jovial crane
Work incoming one sec
I think my solution is correct to what I wrote so I think the process is wrong
If that helps any
I just can't find where
gentle aspen
How you cancelled that tan theta with tan theta?
jovial crane
ahhhh
Okay nevermind I made a small oopsie
So it should just be 6tan^2theta
over what I have for denom
gentle aspen
Ya
jovial crane
Ahh thanks
gentle aspen
nvm
jovial crane
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manic helm
is this histogram unimodal, bimodal or trimodal?
final saddleBOT
is this histogram unimodal, bimodal or trimodal?
@manic helm Has your question been resolved?
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fast salmon
is this histogram unimodal, bimodal or trimodal?
How many modes does this chart have?
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forest lodge
can someone help with me this one
final saddleBOT
can someone help with me this one
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vital crag
can someone help with me this one
,tex .transformation rules
soft zealotBOT
riemann
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riemann
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wise light
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wise light
so i got have a pretty clear idea of how to graph the first problem
i forgot how the second one is solved
wise light
would it be okay to see how someone would solve this
specifically the
1/2x if x <0
and
3 if 0 =< x < 1
west berry
first draw the graphs of y=x/2 and y=3, and then based on the values x can take try narrowing the graph
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gray acorn
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west berry
sin becomes negative in quadrant 3
Since there's a modulus, it'll be -sinx in quadrant 3 to make it positive
west berry
Wdym
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west berry
Np
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neon bear
im actually stupid or something
final saddleBOT
im actually stupid or something
craggy plank
im actually stupid or something
!status
final saddleBOT
im actually stupid or something
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
I got an answer but I was told that it's wrong.
neon bear
1/2
craggy plank
What was your progress?
craggy plank
(pi)(r^2)(1/2pi)
Then angle is t, not 1
craggy plank
yes
shut mantle
Question iii - resistance
final saddleBOT
Question iii - resistance
west berry
,rccw
soft zealotBOT
west berry
Question iii - resistance
Is C for capacitance?
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warm python
$\left(x^2+y^2+1\right)dy+xydx=0$
final saddleBOT
$\left(x^2+y^2+1\right)dy+xydx=0$
soft zealotBOT
Why am. I here
warm python
Other than this answer here, is there any other way to solve this https://math.stackexchange.com/questions/1756959/solve-x2y21dyxydx-0?noredirect=1
I was thinking maybe x/y=u
or something like that
soft zealotBOT
NEON
gritty solar
maybe
warm python
though when I tried this last the $1/(xy)$ caused problems
soft zealotBOT
Why am. I here
gritty solar
$\frac 12 \dv{x^2}{y} + x^2 \frac 1y = - y - \frac 1y$
soft zealotBOT
NEON
warm python
huh, dx^2/dy?
gritty solar
its a linear differential equation 😱
gritty solar
huh, dx^2/dy?
yeah
soft zealotBOT
NEON
strange shore
ah this
gritty solar
yeah sorry
gritty solar
Ive gottan into a habit of writing it like that
gritty solar
and not x^2/y
huh?
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warm python
.reopen
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warm python
oh, yeah, ok
gritty solar
but yes youre right in principle
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fluid bay
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fluid bay
how to approach?
craggy plank
Same method
fluid bay
hmm
craggy plank
2a+3b+4c=6
How many sets of (a,b,c) are there?
craggy plank
List down all of them
fluid bay
umhum
craggy plank
It’s like pick one from two selections
fluid bay
and add
craggy plank
yes
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craggy plank
Np, gl
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warm python
$\frac{dy}{dx}=\frac{\left(y-x-1\right)}{y+x-2}$
final saddleBOT
$\frac{dy}{dx}=\frac{\left(y-x-1\right)}{y+x-2}$
soft zealotBOT
Why am. I here
warm python
to solve something like this , I pressume, I divide by y, and then sub x/y=u?
or do I divide by x
The problem is
that gives
$u+\frac{xdu}{dx}=\frac{\left(u-1-\frac{1}{x}\right)}{\left(u+1-\frac{2}{x}\right)}$
soft zealotBOT
Why am. I here
warm python
which is kind of a pain to solve
warm python
so maybe x+y=u
cold gorge
Might wanna find their intersection
warm python
or something like that
warm python
Might wanna find their intersection
how does that help me solve the ODE
cold gorge
That's one way to do it.
You can then use a new X and Y system.
If the intersection is (a,b) you can use x-a = X
dy/dx is still dY/dX
But then once you do that, you can activate use Y/X or X/Y = u
I think?
Didn't try that yet but yeah.
warm python
You can then use a new X and Y system.
wait, what?
cold gorge
well of x = X + a
(A new variable)
dx is still dX
Isn't it?
You'll get a homogeneous equation in the new variables afaik.
warm python
yeah, and a is a constant?
cold gorge
You'll get a homogeneous equation in the new variables afaik.
Which is also when you can use that y/x = u thing.
Only then, not randomly whenever.
rustic wedge
**Why am. I here**
Adding and subtracting x-1 might help too
cold gorge
It does not. I think.
warm python
hmm, would a trig sub be more useful here?
warm python
well of x = X + a
hmm, thanks!
signal vector
well of x = X + a
No, this is the way
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faint locust
Find a differential equation with solutions $1, x, x^2, e^{-x}, xe^{-x}, \sin(x), \cos(x)$.
final saddleBOT
Find a differential equation with solutions $1, x, x^2, e^{-x}, xe^{-x}, \sin(x)...
faint locust
So I came up with the following characteristic polynomial
Does that look fine to you?
faint locust
lambad - i is wrong
oh
faint locust
rest is ok
Wait, my instructor had this example
faint locust
$y_1(x) = e^{-2x}\cos(x)$ comes from $y_1(x) = e^{(-2 + i)x}$ and $y_2(x) = e^{-2x}\sin(x)$ comes from $y_2(x) = e^{(-2 - i)x})$, right?
lyric summit
to jest uklad fundamentalny ktore go wrosnkian jest rozny od zera means, that is fundamental ssytem which its wronskin si not zero