If we set $\cos^2 v=0$ we get $$y=\frac{(2n+1)\pi}{2x^2}$$ which also satisfies the original equation
#help-13
lyric narwhal
wraith daggerBOT
kheerii
lyric narwhal
My question is, is this truly an extra solution? Or is it included in the intended solution?
cedar kilnBOT
@lyric narwhal Has your question been resolved?
lyric narwhal
<@&286206848099549185>
cedar kilnBOT
@lyric narwhal Has your question been resolved?
cedar kilnBOT
wraith daggerBOT
leycors
formal nest
if z=2-x^2, and you can graph it
cedar kilnBOT
if z=2-x^2, and you can graph it
cosmic steppe
Can't be a function if x takes on two values for one input, z
formal nest
tf
formal nest
Can't be a function if x takes on two values for one input, z
it doesnt take 2 values for one input
cosmic steppe
The +-
formal nest
even then
cosmic steppe
If z = -2, then x is 2 and -2
formal nest
x=sqrt(2-z) is not graphable
formal nest
If z = -2, then x is 2 and -2
tf
cosmic steppe
,w graph x = sqrt(2-y)
wraith daggerBOT
cosmic steppe
Focus on the real part
formal nest
if E is the volume inside those 3 functions what is J1 ?
@cosmic steppe could you help me with this ?
my work:
teacher's answer is 48/35
cosmic steppe
Multi var calc is not my forte im gonna br completely honest
But if you crush dimensions
cedar kilnBOT
@formal nest Has your question been resolved?
cedar kilnBOT
@formal nest Has your question been resolved?
frigid sinew
cedar kilnBOT
livid crescent
idle tusk
maybe put the C outside of the bracket
frigid sinew
maybe put the C outside of the bracket
It was that
Wtf
Is C always outside of bracket
idle tusk
yes
i mean technically no but it's a convention
(it makes no difference in 99.9% of cases)
sharp lotus
Is C always outside of bracket
C is an arbitrary constant, 7C is just as arbitrary, so you may as well turn 7C into a new C
idle tusk
precisely
cedar kilnBOT
prime bison
r^n would tend to 0
Because when the absolute value of r is less than 1, exponentiation makes it smaller not bigger
0.5^2 = 0.25 and so on, it approaches 0
:)
cedar kilnBOT
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frigid sinew
cedar kilnBOT
frigid sinew
I think everything here makes sense but
It feels kinda cursed
Is mathrespected jere?
nova snow
What do you mean is math respected
frigid sinew
What do you mean is math respected
Like did I majorly screw up somewhere
Also is -ln|cosx|
nova snow
That’s a weird way to ask lol
frigid sinew
The same as lnsecx
frigid sinew
That’s a weird way to ask lol
Sometimes I break 9 laws of math omw to the answer
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marsh brook
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marsh brook
Wait wrong file
For #9, why is it not diagonizable? My work is shown, but the answer key said it’s not diagonizable
(Linear algebra)
Oh wait they need to be distinct, got it
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stoic thorn
cedar kilnBOT
stoic thorn
Hello may someone help me find the exact value of this?
that answer is apparently -(2rad10)/3
I got stuck midway
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
stoic thorn
is it possible you walk me through using the double angle formula?
I got stuck when trying to calculate sorry
stoic thorn
okkokk thank you
timber oak
ok so $\tan 2\theta = \frac{2 * \frac{\sqrt{10}}{2}} {1-\left(\frac{\sqrt{10}}{2} \right)^2}$
wraith daggerBOT
Waffloid
wraith daggerBOT
Waffloid
timber oak
which simplifies to $\sqrt{10} * \frac{4}{4-10}$
wraith daggerBOT
Waffloid
timber oak
$\sqrt{10} \frac{-4}{6}$
wraith daggerBOT
Waffloid
timber oak
$=\frac{-2\sqrt{10}}{3}$
wraith daggerBOT
Waffloid
timber oak
which is indeed the answer you gave
stoic thorn
**Waffloid**
for this part
timber oak
mhm
timber oak
we replace $\tan \theta$ with $\sqrt{10}/2$
wraith daggerBOT
Waffloid
timber oak
yep yep
stoic thorn
is that also for other trig functions?
timber oak
the double angle formula is a way of finding $\tan 2 \theta$ given the value of $\tan \theta$
wraith daggerBOT
Waffloid
timber oak
yeah we have identities for other trig functions that work exactly the same
we have $\sin(2\theta) = 2 \sin(\theta)\cos(\theta)$
wraith daggerBOT
Waffloid
timber oak
and $\cos(2\theta) = \cos(\theta)^2 - \sin(\theta)^2$
wraith daggerBOT
Waffloid
timber oak
no worries :)
stoic thorn
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cedar kilnBOT
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hot python
cedar kilnBOT
regal oak
What do b, h and k represent?
austere hull
this seemed too easy
h means horizontal translation? or what
austere hull
What do b, h and k represent?
I believe b means base
regal oak
Ok
hot python
<@1132371071975309322> your answer is wrong
alright so
all options are pos 5
for b
base
hot python
ok
this is
what i just covered
so its about as solid in my brain as custard
i barely understand it
austere hull
ok
if the horizontal shift is moved to left, what that will be?
negative or positive?
hot python
ohh
i picked the one option that could be wrong based off that
lol
that leaves me with
a and b
-1 or 1..
up or down
hot python
-1 is a neg int
austere hull
yep
austere hull
exactly!
austere hull
np
hot python
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quick ember
ik Y is 7 but what is X?
uncut quarry
ik Y is 7 but what is X?
could you find some relation between the two angles?
quick ember
could you find some relation between the two angles?
they are parallel right ?
both angles r 90?
uncut quarry
think about it again
quick ember
they add up to 180?
uncut quarry
yeah 👍
uncut quarry
correct
uncut quarry
9.4 thats weard number to get
quick ember
I agree
uncut quarry
however now u got it right
cedar kilnBOT
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chrome musk
How do you get these two steps?
cedar kilnBOT
How do you get these two steps?
uncut quarry
How do you get these two steps?
first he grouped some numbers with each other into one group like the first one:
1/3 + 1/4
now he replaces the numbers with smaller numbers, here we replaces the 1/3 with 1/4 (which is smaller than 1/3)
and he do it also for the other groups to infinity
is there something not clear up until now?
chrome musk
I think I can understand
so it doesn't matter if you replace it, because the series is endless?
chrome musk
Oh Ok
lost gyro
so it doesn't matter if you replace it, because the series is endless?
He's pretty much saying: we create this sequence that we know diverges. The original sequence is bigger, so the original sequence also diverges
uncut quarry
yeah, if thats what he meant
cuz after that you will find out that the new series you formed is going to be samller the original since we replaced each number with a smaller number
cedar kilnBOT
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lunar chasm
Hello, could anyone break this down for me? It's from a video about the Pi Function and I know they're using integration by parts but I'm struggling to understand how they got to that last expression
shell smelt
Hello, could anyone break this down for me? It's from a video about the Pi Funct...
Search DI method on youtube
lunar chasm
Thanks 🙌🙌🙌
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cedar kilnBOT
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vague musk
how do i get this answer
cedar kilnBOT
how do i get this answer
digital cliff
a combo of chain and quotient rule
vague musk
a combo of chain and quotient rule
how do i use the chain rule tho
digital cliff
you have a square root, thats your outer function
cedar kilnBOT
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hollow basin
figured out 11a, which is 128, stuck on 11b
what i have tried:
subsets with size 1: there is only 1 selfish subset where its complement is also selfish: {1}
size 2: the subset must be {2, n} where n is NOT 6. the number of combinations you can get would be 6C1, because there are 6 possible numbers to choose for n (1-8, excluding 2 and 6)
size 3: the subset must be {3, n, m} where n and m are not 5, so the number of combinations for this would be 6C2. possible numbers to choose for n and m would be 1-8, excluding 2 and 5
continuing this pattern up to a subset with size 7, you get 6C0 + 6C1 + 6C2 + ... + 6C6 = 2^6 = 64
however, the answers say it's 44, and i don't know where to go from here
fair geyser
that's all correct
just read it again carefully and find a mistake
no wait
i don't even see a mistake
hollow basin
hmm
fair geyser
it shouldn't work because you can't make anything with size 4
fair geyser
i'm confused because my program says 45
hollow basin
did it count {1, 2, 3, ..., 8} maybe?
fair geyser
it's 6C3
fair geyser
yes, it counted {1..8} as valid thank you
cedar kilnBOT
solid juniper
🥪
honest torrent
squeeze theroem?
solid juniper
solid juniper
look it up 
coral jewel
look it up <:MelodyCreepySmile:1142931460932767864>
oh hey you got helpful back
solid juniper
yep
cedar kilnBOT
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umbral roost
for this problem
cedar kilnBOT
for this problem
umbral roost
This is the solution they offered:
I don't understand it tho
why do they assume (A+B)^T is symmetric?
gusty forum
they did not
digital cliff
it hinges on the fact (A+B)^T=A^T+B^T
solid juniper
they don’t
umbral roost
it hinges on the fact (A+B)^T=A^T+B^T
but why does that matter?
umbral roost
so A^T+B^T=A+B
I understand this
digital cliff
yeah so whats wrong
umbral roost
yeah so whats wrong
I understand that this equation is true:
A^T+B^T=A+B
I don't understand why because this equation is true means that the LHS is symmetric
delicate elm
If (A+B)^T=A+B, then A+B is symmetric. Those steps are just to show that the if statement is true
digital cliff
I understand that this _equation_ is true:
A^T+B^T=A+B
I don't understand why b...
because that whole thing = (A+B)^T
it shows (A+B)^T=A+B which satisfies 👇
upper abyss
A matrix is symmetric if:
M^T = M
A + B is then symmetric, because
(A + B)^T = (A + B)
cedar kilnBOT
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cedar kilnBOT
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weak hazel
hi, does sb here has a course about heap (in informatic) with if it's possible an implementation in C or in oCaml
cedar kilnBOT
hi, does sb here has a course about heap (in informatic) with if it's possible a...
@weak hazel Has your question been resolved?
icy sage
cedar kilnBOT
late lotus
so first assume that for k its true
then 6k + 6 < 2^k
and then check for 6(k + 1) < 2^(k + 1)
which is just 6k + 6 < 2^k * 2
then u get 3k + 3 < 2k
which u know is true since k is positive and is already greater than 6k + 6
hence it must be greater than 3k + 3
@icy sage
icy sage
ok
icy sage
then u get 3k + 3 < 2k
3k+3<2k or 3k+3<2^k
icy sage
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magic solar
cedar kilnBOT
magic solar
how do we go about this geometrically
cedar kilnBOT
@magic solar Has your question been resolved?
pearl junco
how do we go about this geometrically
what have you tried
magic solar
tbh I forgot how to skecth complex locus but I've been told to sketch the locus
and try a circle geometry approach
pearl junco
and try a circle geometry approach
i see, how much do you know about circle geometry and complex
magic solar
I know circle geo a fair bit, complex locus I dont really remember
but i'll probably understand once you explain
pearl junco
try to draw the problem out once ig ?
cedar kilnBOT
pearl junco
draw it?
yeah, let take xy plane, take random point p from first quarter since its 0 < arg z < pi/2
try approach from there
pearl junco
<@558568705630404609>
ofc they have been half if you extend the smaller circle to larger one, but i wanna let her figure it out after drawing herself
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peak prism
Can anyone help me with an example for a cylinder V, which is parallel to the Z axis and it's volume is exactly $4\pi$ that satisfies:\
$\int\int\int_V xdxdydz = -2\pi$\
$\int\int\int_V ydxdydz = 2\pi$\
$\int\int\int_V zdxdydz = 2\pi$\
wraith daggerBOT
mtr123
cedar kilnBOT
@peak prism Has your question been resolved?
cedar kilnBOT
@peak prism Has your question been resolved?
peak prism
anyone?
sweet fossil
What have you tried so far? What is your thought process?
peak prism
What have you tried so far? What is your thought process?
Couldn’t get too far
I meant z \leq h there
But this give 0
peak prism
What have you tried so far? What is your thought process?
how do i rotate it?
cedar kilnBOT
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south terrace
i need help
cedar kilnBOT
i need help
south terrace
- why must the base of a logarithm be positive?
- why can we not calculate the logarithm of a negative number?
hiiii barbie
focus on studying for your exam LOL
crimson sedge
2) why can we not calculate the logarithm of a negative number?
Basically because it generally might give imaginary solutions
like lets say a = log x (b)
so if x <0 and if a is not a positive value like if x = -6 and y = 3 then x^y would give you a solution that isn't real
mortal grove
so it makes sense logically to say that since (-3)^2 = 9, then log base -3 of 9 is equal to 2. HOWEVER what if you take log base -3 of 2? then you're saying (-3)^x = 2, and that doesn't make much sense
basically we want logarithms to be well defined, and just bc they make sense for a few numbers doesn't mean they do for all numbers
crimson sedge
true
rain cloud
1) why must the base of a logarithm be positive?
first you need to understand what a function is. A function for an X value gives a unique Y value. Let's imagine a log with base -2 such that log_-2(X) = Y. from this we would get to -2^Y = X. Now we must consider that Y is a rational number so it can be represented in p/q form. so you will get -2^p/q. This means q\sqrt{-2^q}. Now if q was even you would get a real answer. But if q was odd you would get an answer that is imaginary. Hence a Y value can only be determined at specific X values.
crimson sedge
Are you cbse or icse?
rain cloud
focus on studying for your exam LOL
😭 i am trying
south terrace
Are you cbse or icse?
whats that
crimson sedge
whats that
nevermind I thought you were Indian sorry
south terrace
i am, but idk what does short forms stand for
crimson sedge
basically education boards
cedar kilnBOT
crimson sedge
cbse for central board of secondary education and icse is indian certificate of secondary education
rain cloud
i am icse 
crimson sedge
i am icse <:thumbsupanimegirl:1203420374243610665>
icse i believe is good upto 10th
like a lot of my icse friends switched to cbse post matriculation
rain cloud
icse i believe is good upto 10th
yea i was in icse only upto 10th
now i am in state board
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novel cloak
can anyone help me solve this limit
lim (2x-3) ( pi - 2arctgx )
novel cloak
as x -> infinity
untold torrent
$\lim_{x \to \infty} \frac{2x-3}{\pi - 2\arctan x}$
wraith daggerBOT
RedstonePlayz09
untold torrent
?
Oh
Multiplication is probably what you meant
Yeah mb
$\lim_{x \to \infty} (2x-3)(\pi - 2\arctan x)$
wraith daggerBOT
RedstonePlayz09
cedar kilnBOT
@novel cloak Has your question been resolved?
wraith daggerBOT
RedstonePlayz09
novel cloak
im not sure how to use that here...
warm crescent
l'hopital or without l'hopital?
novel cloak
l'hopital or without l'hopital?
l'hospital
cedar kilnBOT
l'hospital
novel cloak
i did do that
warm crescent
what did you get
sage forge
That notation hurts
sage forge
infinity* 0 -> infinity* 1/infinity
sage forge
The convention is infinity*0 = 0
dreamy sail
cedar kilnBOT
dreamy sail
How do I go about this?
can i use squeeze theorm like this -1 <= cos(npi) <= 1
then divide each side by 8n-5
so I get -1/8n-5 <= cos(npi) / 8n-5 <= 1/8n-5
then limit as n approches infinity of 1/8n-5 is 0 since 1/inf = 0
so can I then conclude lim as n approches infinity of cos(npi)/8n-5 = 0 therefore it is divergent?
whoops I mean convergent
Not sure any help would be gr8
<@&286206848099549185>
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paper grail
cedar kilnBOT
paper grail
Hello I got this question, it's asking if y=1 and y=-1 are horizontal assyntotes
but when I tried doing what my teacher taught, dividing everything by the highest degree
I get 1
for x-> negative infinite or positive infinite
idle tusk
how do you get that for negative infinity case?
paper grail
I honestly don't know how to get it for negative infinite specifically because
doing the math it just gives me 1
idle tusk
show the steps
i am 99% certain the error lines in the fact that the numerator is negative while denominator is always positive
idle tusk
yes but you divide the denominator by x
which is negative
then you put it into the square root but it removes the roots
paper grail
which is negative
that would make it the square root with x^2/x^2 + 2/x^2
idle tusk
then you put it into the square root but it removes the roots
^^^^^^
you need to be more careful
paper grail
I don't get, my math isn't correct?
idle tusk
yes
$\lim_{x\to -\infty} \frac{\overbrace{x}^{\text{negative}}}{\underbrace{\sqrt{x^2 + 2}}{\text{positive}}} = \lim{x\to -\infty} \frac{\overbrace{\frac{x}{x}}^{\text{positive}}}{\underbrace{\frac{\sqrt{x^2 + 2}}{x}}{\text{negative}}} = \lim{x\to -\infty} \frac{\overbrace{1}^{\text{positive}}}{\underbrace{\sqrt{\frac{x^2}{x^2} + \frac{2}{x^2}}}_{\text{also positive}}}$
wraith daggerBOT
artemetra
idle tusk
so in the first one the whole thing is negative, then it's still negative, but the third step makes the whole thing positive
austere hull
woah cool latex
paper grail
so the math is correct, but it can ruin the sign
idle tusk
essentially
idle tusk
woah cool latex
thank you thank you
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cedar kilnBOT
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frozen umbra
hey guys quick one here i found a graph the other day that looks a bit like this quality recreation, cant remember the equation though. Any ideas?
frozen umbra
pretend it's symmetrical
muted bear
,w sinx/x
frozen umbra
thats it, thanks a bunch
frozen umbra
.close
cedar kilnBOT
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icy sage
cedar kilnBOT
main needle
where are you at? the main part is (n+1)^2-n^2 = 2n+1
tribal basin
cedar kilnBOT
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merry temple
can anyone help on this?
cedar kilnBOT
can anyone help on this?
merry temple
this one is testing continuity
what I know is to find each equation test it if f(x) exist or not
then after that Im not sure what to do next
next hornet
So what have you tried
merry temple
f(0) = 0
cos x is not equatl 0
cos 0 = 1
while 1 - x^2 is x = 1
all the function exist ye on the corresponding piecewise function?
Im not sure what to do with the if x<0 x=0 and x>0
oh nvm
lmao
cos 0 = 1
cedar kilnBOT
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heady spindle
Hello, could you please help me. I have no idea how to proceed. Find the particular solution of the initial value problem.
cedar kilnBOT
Hello, could you please help me. I have no idea how to proceed. Find the particu...
@heady spindle Has your question been resolved?
maiden ruin
Can I get some help on this?
cedar kilnBOT
Can I get some help on this?
runic moth
yep
subtle harbor
maiden ruin
Can’t sorry
runic moth
ok
runic moth
try to do somthing withidentities
maiden ruin
I guess
flint plinth
worst case i guess you can just take another point on the graph
runic moth
reamarkable identities
runic moth
or try on chat gpt
maiden ruin
How did you know that
cedar kilnBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
subtle harbor
well, they appear to be at a number slightly greater than 3. Now, typically with these sorts of conic sections you want to think about square roots, so what's a square root that's slightly bigger than 3
flint plinth
that's some big brain reverse engineering there haha
subtle harbor
lmao
maiden ruin
sqrt10?
subtle harbor
yeah, thats a good guess
now assuming the x-cord of the is foci=ae
and e^2=(1+b^2/a^2)
10=1+b^2
i think you can just derive this from the definition of a hyperbola
maiden ruin
Isn’t a^2=1
subtle harbor
yea
maiden ruin
So then b^2=9
maiden ruin
That’s probably right but it’s just annoying that I would have to assume the sqrt10 yk
subtle harbor
yeah, it would've been nicer if they labeled it
maiden ruin
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cedar kilnBOT
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quaint dome
I need a little bit of help with integration. Please keep in mind that the question is not a homework question, rather just an innocent little circuit I randomly drew up, and tried to solve it, only to realize that I cannot solve it :/
quaint dome
here is the circuit for proof:
Here is the math involved:
@wraith dagger
,tex $0 \text{A} = \sin \left( t \right) + \frac{V_{\text{A}} \left( t \right) }{10 \Omega} + \frac{1}{1 \text{mH}} \int_0^t V_{\text{A}} \left( t \right) \text{dt}$
wraith daggerBOT
FuzzyPenguin
quaint dome
The goal? Solve V_A(t)
I have no idea where to even begin because I have not taken Calc 4, highest Calc I've taken is Calc 2
cedar kilnBOT
@quaint dome Has your question been resolved?
warm crescent
I don't know about circuits
but maybe you want to solve $0 = \sin t + \frac{V}{10} + \int_0^1 V dt$
:c
quaint dome
It is v(t)
wraith daggerBOT
svc20060505
wraith daggerBOT
svc20060505
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
quaint dome
,tex $0 = \cos t + \frac{V'}{10} + V$
wraith daggerBOT
FuzzyPenguin
warm crescent
yes that thing
quaint dome
well, the problem is that you have 1/1/1000 on the left of the integral
so more like...
,tex $0 = \cos t + \frac{V'}{10} + \frac{1}{\frac{1}{1000}}V$
wraith daggerBOT
FuzzyPenguin
warm crescent
ok i don't know about diff equations maybe just wolframalpha or idk
,w solve for y diff eq 0 = cosx + y'/10 + 1000y
wraith daggerBOT
warm crescent
maybe ping helpers
quaint dome
maybe ping helpers
the answer is here:
I'm trying to reverse engineer that function (essentially)
but also try to find out how to solve for it
warm crescent
in what units you want V
warm crescent
t is in what units
quaint dome
seconds
warm crescent
do you know any voltage at some t?
like voltage at t=0
okay know what
i mean the V variable idk the name of it
warm crescent
,w solve for v in d/dt(0) = d/dt( sint + v(t)/10 + int from 0 to t of v(a) da )
ok i give up
,w solve for v in 0 = cost + v'/10 + 1000v
wraith daggerBOT
quaint dome
is the amplitude close to pi/500
warm crescent
**FuzzyPenguin**
are you sure this eq is correct
idk a dumb guess I would do is try to match a sine function with that amplitude and that stuff
something like v(t) = 7/1000 sin(2π t) but don't trust me
cedar kilnBOT
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finite badger
hey guys, can anyone explain to me what they did in the red rectangle ?
finite badger
if its something basic i need to refresh please give me titles so i can look it up
calm sierra
which rectangle?
finite badger
both of them
unclear to me how they got to =1/x
and where the ln`s went in the second one
calm sierra
$\int\frac1xdx=\ln x+c$
wraith daggerBOT
e
finite badger
how they turned xt` to integral of 1/x
finite badger
yes
calm sierra
you agree it has the form $x\dv{t}{x}=f(t)$?
wraith daggerBOT
e
calm sierra
f(t)=right side
calm sierra
i simply rewrote my screenshot
finite badger
**e**
is that something i should accept as is?
or its specific for this case scenario
calm sierra
and im defining f(t) as the right hand side
finite badger
alright
calm sierra
so i get $x\dv{t}{x}=f(t)$
wraith daggerBOT
e
finite badger
yeah i do 100%
now i just need to figure out the other red rectangle thing. unclear to me if they got rid of the ln(x)
finite badger
done
wraith daggerBOT
e
calm sierra
good?
finite badger
yup
calm sierra
c is a constant so e^c is another constant
we can make this look nicer by giving e^c a name
technically the name should be smth not used before, like d
but its no big deal to use c again
finite badger
ahhh okay
but i can leave it as is in my final answer?
or i need to get it back to e^c
calm sierra
no need to change back, but you should make it clear when you relabel
calm sierra
another example, say you get 2c. since c is a constant, so is 2c
say smth on the side like "im rewriting 2c as c"
in general, any expression that only depends on c is just another constant and can be relabeled as such
calm sierra
the original problem is a differential equation
the goal is finding an unknown function y
finite badger
oh okay got it, just got this marathon video and i feel like she assumes ppl watch it knowing certain details beforehand lol
i will manage from here
thank again! @calm sierra
.close
cedar kilnBOT
cedar kilnBOT
✅
calm sierra
i have some notes which may clarify some of the introductory concepts
finite badger
please send them my way if possible
calm sierra
eg what solving a differential equation means (VERY important)
in particular you should read the intro https://www.math.umd.edu/~immortal/MATH246/lecturenotes/ch0-1.pdf
finite badger
and this one as well? https://www.math.umd.edu/~immortal/MATH246/lecturenotes/ch1-8.pdf
calm sierra
theres also lots of practice problems in the first link (groupwork/homework)
i dont think so, that section covers a different type of problem
finite badger
alrighty
hope i will have the luxury of getting to those problems but probably just gonna solve exams from past years in my uni
got a very limited time window
youre an ME student?
calm sierra
mech eng?
finite badger
yeah
calm sierra
actually i was NE but switched to phys+math
calm sierra
year 1+2 is fine since both majors just require calc, year 3+4 is where they split a lot
finite badger
i usually crumble when physics ask me to use calc
but we dont have that much calc in physics
mainly ask us to understand and use the correct equations
anyway gl man
calm sierra
thats interesting, most college phys requires calc (thats what separates it from high school phys)
calm sierra
got it, and the goal of this question is finding the constant, correct?
btw i wanted to point out what part of the notes addresses this
finite badger
we have some, but very basic, although when i think about it last semester we had some double integral going on in the test but managed to get through it
calm sierra
my answer was we're finding an unknown function, this is exactly what i mean
all clear?
finite badger
give me a min, kinda need to look at few questions and their answers to understand what youre saying in your paper
calm sierra
sure
cedar kilnBOT
@finite badger Has your question been resolved?
finite badger
one sec
@calm sierra still cant get my head around the goal of differential equations sadly
here is an example for a question from out test
how exactly i can use your paper to understand what is needed to be done here?
calm sierra
i was answering this
the goal of this question is finding the constant, correct?
calm sierra
lets look at the examples to understand what that means
ex 1, let f(t)=e^t
then f'(t)=e^t yes?
finite badger
fuck me forgot about the e^x always stays the same
yeah okay im with you
i get the first line now as well
okay i get the theme now
calm sierra
right so another example to make sure
ex 4, let f(x)=x^2
then xf'(x) and f(x) are not equal yes?
calm sierra
ya, so in this example f is not a solution to the DE
now many times we see a DE along with an "initial condition" (IC), like f(2)=3
DE+IC is called initial value problem (IVP)
solution to IVP means solving DE and satisfying IC
that brings me to this
this is shown in your problem
when we solve this DE theres a c in the solution
c can be any number. for each value of c we get a solution
hence we have infinitely many solutions
but if we have an IVP, once we solve the DE we can use the IC to lock down the value of c to get a "specific" solution
this is shown in the other problem
finite badger
i think i got it but i feel like something is missing here
so technically since we dont have an IVP here, the c is the "solutions"
and thats how a final answer for a DE from the "genre" should look like?
me finding the c?
@calm sierra
ah you what i think im trying to pick to many puzzle pieces at once, i need few more hours or learning before i should nag you on this lvl 💀
calm sierra
so technically since we dont have an IVP here, the c is the "solutions"
theres no IC so once we find a solution (which should have c in it) we're done
it may help to think of a much easier example
solve this DE: $y'=2$
wraith daggerBOT
e
finite badger
y=2x?
finite badger
dy=2dx?
im honestly guessing im way too early into this course, i just came here for the basic math i couldnt get
calm sierra
the integration constants can be different so be careful
calm sierra
now we can move a constant to the other side so that theres only one constant yes?
so in practice when we integrate both sides we really only need one constant
y=2x+b-a, let c=b-a so y=2x+c
in the future we can just shortcut to having c on one side
finite badger
<@150414892225134592> still cant get my head around the goal of differential equ...
it makes sense now but then u got this^, where the general answer has x on both sides
what exactly is achieved there @calm sierra
because the x on the left side of the answer is in the original form of the equation of y` its alright for the x to be on the other side too?
or technically the c should be alone
calm sierra
ah thats a separate point
finite badger
oh no
calm sierra
sometimes its easy to get y=... in which case we call it an explicit solution
if we leave it in the form F(x,y)=c we have an implicit solution
many times when its impossible or we're too lazy to get an explicit solution we settle for implicit
finite badger
gonna use implicit as a default 
@calm sierra
anyway thanks a lot
from here i must press on solo with hopefully no major hiccups
thanks!
light pagoda
how does this even work???
cedar kilnBOT
how does this even work???
light pagoda
i know they intersect at a 90° angle, but what do i do after that
light pagoda
so is it 56
toxic edge
how u got 56
light pagoda
180-82-42
toxic edge
no
ur ABC is is the angle that covers two triangles
so u gotta divide by 2
to only get the 1 triangle
light pagoda
so your saying that this whole triangle is 164
toxic edge
what are u saying
light pagoda
ur ABC is is the angle that covers two triangles
👆
light pagoda
82 times 2
since BAD is 82
i just need help bro im stuck on this geometry bull crap
82 degrees
it gives that
light pagoda
would that be 21
light pagoda
so would that be 159 im confuse
hidden vapor
According to kite's property angles opposite to main diagonals are equal, bad = bcd
Equate sum = 360 question over
toxic edge
According to kite's property angles opposite to main diagonals are equal, bad = ...
girl what 💀
hidden vapor
Who girl 💀
toxic edge
yep!!
light pagoda
wrong
toxic edge
💀?
hidden vapor
Check 154
light pagoda
so would that be 159 im confuse
i was close 💀
toxic edge
???????????????????????????
OH MY BAD G
yo i misread the question ngl
but its twice that angle
hidden vapor
Indeed adc looked obtuse and answer yall got was 77
hidden vapor
According to kite's property angles opposite to main diagonals are equal, bad = ...
this here too
Shortest way possible
light pagoda
so on this its 107 for a side
15 for the angle on each
and equals 180
this here is the part i struggle with
the teacher did NOT explain well
i just need some help on the actual math part
dreamy thicket
15 for the angle on each
Which angle?
cedar kilnBOT
@light pagoda Has your question been resolved?
swift saffron
2011^2011^2011 mod 14
brazen cove
would it be valid for me to say that cos(a) simply returns the length of the size of the leg adjacent to a, then divides the number by the hypotenuse in order to get the base ratio between them which removes the sizes of the legs from the equation
I feel that I'm missing something with this understanding
brazen cove
like maybw its not just about removing the size of the legs from the equation but it's also about how the adjacent side relates to the hypotenuse? But I'm not sure what that means
cedar kilnBOT
@brazen cove Has your question been resolved?
brazen cove
<@&286206848099549185>
kindred storm
86
kindred storm
i think so
kindred storm
The sum of the angles of a quadrilateral is 360, but the main angle is 107 and the single angle is 30, so 360-107*2-30=116.
brazen cove
how does that help me understand the relationship between the adjacent leg and the hypotenuse leg of a right triangle
brazen cove
how does that help me understand the relationship between the adjacent leg and the hypotenuse leg of a right triangle?
I'm not asking about quadrilaterals
<@&286206848099549185>
it's been past 30 minutes now
kindred storm
Can’t we just ask for an answer?
unique gulch
answer: 360-107-107-30 = 116. right?
brazen cove
what are you two on about
brazen cove
.close
white fable
cedar kilnBOT
white fable
Can someone please explain what i got wrong?
digital cliff
in b you were subbing things into f rather than f'
also f(-1) does exist
you need to be mindful of your brackets
it was (-1)^2 not -1^2
in c, you got them the wrong way around
in d, the maximum is not 4/5, you wrote yourself that f(1)=1>4/5 so thats a direct contradiction in of itself
the issue with the DNE follows from your earlier errors
it does have a minimum
at x=1 there is a max, at x=-1, a minimum
you can sub those into f to get said values
im not sure what you did in e since you offered no explanation
same for f, though i note those are not coordinates
cedar kilnBOT
@white fable Has your question been resolved?
white fable
Thank you!
azure ridge
I been doing derivatives for half a year but I think I finally understand the difference. d/dx is doing the derivative of the given function, but it doesn't "change" / "mutate" the function
azure ridge
Whereas dy/dx is doing all the above but also "mutating" the y function
cedar kilnBOT
@azure ridge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dense locust
Lol im having troubles differentiating this
cedar kilnBOT
Lol im having troubles differentiating this
cedar kilnBOT
cedar kilnBOT
Available help channel!
random grove
am I interpreting this definition correctly?
s(x) is a step function and I believe that f is continuous
