#help-0
pale kestrel
huh, I am talking about this
xa + yb = 0
x and y are scalars
x = y = 0 is the only solution
buoyant breach
Oh
I think I started to get it
I got itt
Ahh you get m = 1/2
K = 2
sorry if I took so long
AG = AC/2
BC =2IG
I didn't understand you at first
This was a new way to prove using vectors for me
Thanks a lot mann
.close
slim stag
lone heartBOT
slim stag
I can't understand how Theorem 2.41 directly implies that every bounded subset of R^k lies in a compact subset of R`k
warped jolt
The theorem states that if a,b, or c is held for a set E, the other two also hold. So, if there is a subset E that is bounded, according to the theorem it should also be compact and every infinite subset of E should have a limit point in it. Hence, a bounded subset is also compact.
merry depot
If E was closed then E would also be compact itself. If you take the closure of a bounded set E, then you have a closed bounded (and therefore compact) set that contains E
slim stag
Oh, makes sense, thanks
near lagoon
Other than the theorem, indeed, you also need the observation that the closure of a bounded set is bounded
eager shale
lone heartBOT
eager shale
What is the area of the colored region?
merry depot
I assume those shapes are all semi-circles?
eager shale
Yeah
merry depot
you know how to find the area of a circle?
eager shale
pi r ^2
merry depot
yep
So you have 3 half-circles there. Find the area of the larger half-circle and subtract the area of the two smaller half-circles
eager shale
I got something, but the exercise asks me to give an answer 2 pi without any of the decimals
not really sure how to do it so
eager shale
pi 6 ^2
merry depot
the diameter is 6, not the radius
eager shale
pi32
merry depot
so 9pi is the area of the larger circle. What's the area of smaller circles?
eager shale
how did you get the 9 pi
merry depot
what you said, radius is 3, so area is $3^2\pi$.
ocean sealBOT
Zybikron
eager shale
diameter is 6 is how can the radius be just 3 tho
merry depot
radius is half the diameter
merry depot
so what are the areas of the smaller circles
eager shale
6pi and 3pi I think
merry depot
whats the radius of the smallest circle?
eager shale
1.5
merry depot
no. the smallest circle has diameter 2, so what is the radius
eager shale
1
merry depot
so with radius 1, what is the area of the smallest circle?
eager shale
16pi
merry depot
diameter is 4, not the radius
eager shale
then the area has to be 4pi
wary stream
I havent slept for 2 days and corona so my brain is lagging very badly rn
Tbh that's not healthy and you should sleep. Sleep helps you function
merry depot
So the area of the largest cricle is 9pi, the area of the smaller circles are 1pi and 4pi, so subtract the smaller areas from the larger one
lone heartBOT
Available help channel!
merry locust
lone heartBOT
merry locust
Is there a reason why I cant use perfect square trinomial method for 6A
When I use that method I get (2x-3)^2
wary stream
Because it's not a perfect square trinomial
echo socket
And nor is -13 the same as 2 * 2 * (-3)
wary stream
When I use that method I get (2x-3)^2
Expand this out and it doesn't match the problem, meaning it wasn't a perfect square trinomial
lone heartBOT
@merry locust Has your question been resolved?
rapid nova
Prove that
[ -\sum_{i=0}^{k-1} \binom{n+i-1}{i} \binom{n}{k-i} \cdot (-1)^{k-i} = \binom{k+n-1}{k} ]
ocean sealBOT
rept1d
blissful whale
@rapid nova What do you know about the binomial coefficient?
rapid nova
<@!586955478529998860> What do you know about the binomial coefficient?
many things
blissful whale
I would try proof by induction.
rapid nova
by k?
blissful whale
yeah I think that is the most natural choice.
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
https://hig.app.box.com/s/ll9o8vofnb0hwltjf89uq1yfpl2duzcz i need to solve (number) ab and (number)ac for AT anyone?
lone heartBOT
https://hig.app.box.com/s/ll9o8vofnb0hwltjf89uq1yfpl2duzcz i need to solve (numb...
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Not yet
wind pumice
any here?
dense sleet
Can you use trig?
wind pumice
Trig?
dense sleet
Trigonometry
dense sleet
Well..... this just became a little harder
wind pumice
can you help me ?
hazy rune
dense sleet
Shouldnt ne
Seems like simple decellaration
Decelaration is 22 - 44 / 11
So -2m/s
,w plot 44 - 2x from 0 to 11
ocean sealBOT
wind pumice
Kinetic formulas probably
yup
ocean sealBOT
bleak ridge
I mean the kinetic formulas are basically calculus wrapped up in a nice formula
Do you know which one you would use here?
wind pumice
vf=vi + at
bleak ridge
Id prob go with the first one
wind pumice
v = x/t i think
wind pumice
whats the solution ?
dense sleet
,w integrate 44-2x from 0 to 11
ocean sealBOT
dense sleet
This
dense sleet
I mean if graph i ploted is correct this is as well
ocean sealBOT
bleak ridge
👁️
dense sleet
Unless the graph i plotted is incorrect the solution it should be correct
bleak ridge
It looks right
wind pumice
use kinematics
dense sleet
,calc 2211/2 + 2211
ocean sealBOT
Result:
363
Yeah thats it
dense sleet
Actually absolute(delta(v))t/2 + vt
bleak ridge
I mean theres several ways to go about it
The two kinematic equations related are uhh
$\Delta x = \frac{v+v_0}{2} t$
wind pumice
yes the answer is 363
ocean sealBOT
PapaBread
bleak ridge
$\Delta x = v_0 t + \frac12 at^2$
ocean sealBOT
PapaBread
bleak ridge
One of which is def easier than the other
bleak ridge
I mean its just plugging in the numbers
bleak ridge
What does v0 represent
wind pumice
idk
ocean sealBOT
PapaBread
bleak ridge
And $v_f$
ocean sealBOT
PapaBread
wind pumice
i think the formula is wrong
bleak ridge
It should be right
Lemme try writing it with diff notation
$\Delta x = \frac{v_f+v_i}{2} t$
ocean sealBOT
PapaBread
bleak ridge
Is that more what you learned?
bleak ridge
Well for how long was he decelerating?
bleak ridge
I mean technically VF is 22
Since thats the velocity the cab ends at
But its not important to this problem
Since addition can be reordered
bleak ridge
Just keep that in mind for future problems where it might matter more
bleak ridge
Youre sure youre not supposed to use trig for those angles?
bleak ridge
Well the first step is to find the slope of each line probably
wind pumice
ok
bleak ridge
So whats the slope of the one in the top right for example
lone heartBOT
@wind pumice Has your question been resolved?
sick crest
lone heartBOT
dense sleet
Couldve used formula s = at²/2
alpine sable
we don't have a though?
sick crest
why not just v=d*t
dense sleet
,w 1500 = a*25^2/2
ocean sealBOT
pulsar aspen
Because the plane does not move in constant speed
dense sleet
,w 24/5 * 25
ocean sealBOT
dense sleet
,w plot 24/5x
ocean sealBOT
dense sleet
This would kinda be accelaration maybe
merry depot
why do u need to use vi+vf/2
you're finding average velocities. One way is to take the distance/time. The other is to take starting and final velocities and average them
merry depot
yep
sick crest
right?
dense sleet
Basically you have a vt graph that looks something like
merry depot
it started at rest, so you know the initial velocity was 0
dense sleet
,w plot 24/5x from 0 to 25
ocean sealBOT
dense sleet
This should be it
When x is 25. Aka 25th second v is 120
You can look at this mathematically or physically
merry depot
ok
if your question is answered you can type .close to close the channel and open it up for someone else.
lone heartBOT
@sick crest Has your question been resolved?
honest smelt
HEY
supple tundra
question?
lone heartBOT
@honest smelt Has your question been resolved?
supple tundra
screenshot
supple tundra
dude
lone heartBOT
supple tundra
you''re supposed to post your questions here
so people can help you
🤦♂️
@honest smelt type '.reopen'
honest smelt
.reopen
lone heartBOT
✅
wary stream
Is your friend allowed outside help?
lone heartBOT
@honest smelt Has your question been resolved?
merry locust
merry locust
Can someone help me with B
merry locust
at which points of h does the flare hit the water?
0
covert agate
now apparently, the graph starts at t = 0 which happens to be a root
can you find another root?
the answer will be their distance
merry locust
now apparently, the graph starts at t = 0 which happens to be a root
doont i have to like
factors n stuff
covert agate
kinda yea
merry locust
yea i have to do that cuz my teacher said to show my owrk like that
covert agate
yea shoudn't be hard
covert agate
t = 0 or 150 - 5t = 0
whenever you got a few things multiplied and turns out to be 0
at least one of those things is 0
merry locust
how do i determine which one it is
covert agate
wdym which
covert agate
how do i determine which one it is
at least one
in general, if $a_1 a_2 ... a_n = 0, a_1 = 0 \enskip \text{or} \enskip a_2 = 0 ... a_{n - 1} = 0 \enskip \text{or} \enskip a_n = 0$
ocean sealBOT
Chromium
fiery adder
just want to double check a thought but this is wrong right? cuz it's assuming commutativity?
fiery adder
by this i mean the claim is wrong
pliant ingot
yes, (a . b) . c being associative does not imply that it equal (a . c) . d
but the claim is correct
fiery adder
oh 
fiery adder
oh wait yeah i see it
merci! i did most of the right work but the wrong conclusion lol
this was a friend's work but i thought the opposite of the claim was true
fickle kayak
fiery adder
fiery adder
a counter example is e(e(2,3),2) vs e(2,e(3,2))
is this good enough scratch work for a pf by contradiction?
ignore the shit on the right
pliant ingot
yeah that seems okay, but you didn't finish your counterexample
pliant ingot
if its obvious those are different numbers then the original question is also obvious lol
but yeah, basically "assume phi is associative => contradiction"
therefore phi isn't associative
fiery adder
very epic, merci!
one more thing! is 0 usually taken to be both negative and positive or neither
idk if it's a prof choice thing, like whether or not it's in N or not
lone heartBOT
@fiery adder Has your question been resolved?
pliant ingot
you just have to specify usually
fiery adder
bleh
pliant ingot
'non-negative integers' includes 0
fiery adder
these likely dont have 0 though right
pliant ingot
yeah
steady otter
can someone help find the second alternate exterior angle? i have to find an alternate exterior angle for angle 8 but i only found one
lone heartBOT
can someone help find the second alternate exterior angle? i have to find an alt...
@steady otter Has your question been resolved?
steady otter
<@&286206848099549185>
pliant ingot
8 doesn't have an alternate exterior angle, since it's interior of the parallel lines, right?
steady otter
sorry i don’t understand your question 🥲
pliant ingot
the 'exterior' part means that the angle is on the 'outside' of the two parallel lines
steady otter
oh yes
pliant ingot
can you screenshot the question
steady otter
oh nvm it says interior (my bad sorry 😭)💀 so basically i have to find two alternate interior angles for angle 8 but only found 1
pliant ingot
is there any more to the question?
do you know anything about the two non-parallel lines crossing? ( in the center)
steady otter
it says “consider the line l and m intersected by 2 transversals”
and then find alternate interior angles for angle 8
but that’s it besides the picture
pliant ingot
yeah, 8 and 15 are alternate interior angles
I don't think there's anything else to it
steady otter
hm it says to find 2 and i can’t find the other one
pliant ingot
8 and 15 is two, lol
steady otter
two as in besides 8
pliant ingot
I don't see any others, so I'm guessing it's a poorly worded question?
steady otter
there’s two spaces for answers tho🤔
pliant ingot
did you put 8 as one of the answers?
pliant ingot
that's very weird
it doesn't even say that l and m are parallel
makes me wonder if you're supposed to assume that 17 is the same as 8
even though in general it isn't true
steady otter
it doesn't even say that l and m are parallel
yeah i’m just assuming lol T-T
steady otter
makes me wonder if you're supposed to assume that 17 is the same as 8
hm ok
pliant ingot
ohh
steady otter
what happened?
pliant ingot
so 'alternate interior angles' don't have to apply to parallel lines
but when they are parallel lines they are equal
steady otter
ohhhh
pliant ingot
so I'm guessing that the other alternate interior angle is 9
pulsar grotto
I'm not sure if i'm doing the math wrong or if it wants the answer in a different format
pulsar grotto
here es my work
ancient saddle
here es my work
Hello, you don't need the absolute values because 8+y^2 and 1+x^2 are always positive. Then you can solve for y, considering that y(0) = +√3
pulsar grotto
Hello, you don't need the absolute values because 8+y^2 and 1+x^2 are always pos...
I'm having difficulty seeing how that changes my answer, since i evaluated it that way
Do you mean the C value would be osmething else?
ancient saddle
I'm having difficulty seeing how that changes my answer, since i evaluated it th...
You have to isolate y, that's what I mean by solving for y
ancient saddle
Do you mean the C value would be osmething else?
No, I mean that in this form y could be + or - √3
Because of the square
Try it, you will get C = 1/2 ln11 for both cases
You have to find a function y(x)
ancient saddle
Yes, but first get rid of the 1/2 that is on both sides so the next steps are easier
tacit ferry
lone heartBOT
Available help channel!
raw citrus
So I'm a bit confused on how to do this problem. I was told to use Saccheri-Legendre Theorem twice
raw citrus
The theorem states: The angle sum of any triangle is ≤180
lone heartBOT
@raw citrus Has your question been resolved?
silver adder
The theorem states: The angle sum of any triangle is ≤180
wouldn't that mean the interior angles of any quad is ≤360 ?
silver adder
im honestly not sure where a lot of the letters come from
raw citrus
The letters?
silver adder
what is m
raw citrus
Measure
The measure of angle ....
CPCF is "corresponding parts of congruence figures are congruent"
lone heartBOT
@raw citrus Has your question been resolved?
chilly inlet
Can you guys help me with intergers like for adding subtracting multiplying and dividing pls
placid zinc
You can't add integers?
chilly inlet
No
placid zinc
What's 2 + 3?
placid zinc
Are you perhaps confused about what an integer is?
chilly inlet
No
I just need the part for multiplication and division
Because i forgot about it
Nvm
.close
lone heartBOT
placid zinc
chilly inlet
Ok thank you
lone heartBOT
Available help channel!
rocky ledge
i dont understand how to do the circled questions
lone heartBOT
i dont understand how to do the circled questions
alpine sable
i dont understand how to do the circled questions
First one
All of them are in the form a^2 +2ab+b^2
The first one a=t, b=1/2
(t+1/2)^2
(x-2/3)^2
(3y+1/5)^2
(x+1/x)^2
rocky ledge
ye
rocky ledge
Like this?
alpine sable
Basically
Put the 2ab in the middle
Not exactly how you should show
t^2+t +1/4
=t^2+ 2(t)(1/2)+ (1/2)^2
= (t+1/2)^2
That’s how you show it
rocky ledge
why did u put a 2t?
alpine sable
a^2+2ab+b^2=(a+b)^2
rocky ledge
do u just get rid of 2ab and let the (t+1/2)^2 be by itself since that equation will make the 2ab?
alpine sable
do u just get rid of 2ab and let the (t+1/2)^2 be by itself since that equation ...
Let me explain
When you expand (a+b)^2
That’s he same as (a+b)(a+b)
Which expanded is a^2+ab+ba+b^2
alpine sable
Which is
rocky ledge
Like this?
^
lone heartBOT
@rocky ledge Has your question been resolved?
rocky ledge
why are there 2 -> 1/2s?
tbh I got the answer right for that one so I think I'll just stick to the way I was doing it
can you help me with q.20 tho?
quiet delta
"You need to select two candidates for cthe council - one boy and one girl. There are 12 boys and 16 girls to choose from, how many possible combinations are there?"
quiet delta
I thought, since there are 12 possible elements and 16 other possible elements
the answer should be 12*!6 = 192
However, the answer is 192*2 = 384
Where did the extra factor of 2 come from?
hasty elk
it should be 12 * 16, as you said
quiet delta
Yeah, since the order doesn't matter
hasty elk
nope
hasty elk
np 🙂
covert agate
lone heartBOT
covert agate
why do we write the remainder as $h_k(x) (x - a)^k$ instead of $h_k (x) (x - a)^{k + 1}$?
ocean sealBOT
Chromium
hasty elk
the Taylor polynomial is a polynomial up to (x-a)^k
but notice that this is an approximation to what f actually is
the error term needs to be a function with respect to the same power (x-a)^k, i.e. that Peano form, because if you assume it's a function h(x)(x-a)^{k-1} with h(x) \to 0, you may lose some information about the error
covert agate
wdym lose info
hasty elk
in particular, you lose the cases "h(x)(x-a)^{k-1} where h(x) does not go to 0"
hasty elk
think about it
if you want to say that $f(x) = \sum_{n=0}^k a_n(x-a)^n + h(x)(x-a)^{k+1}$ where $h(x)$ goes to $0$, you're effectively saying that you can have a so-called jump at the $(x-a)^{k+1}$ term, cause you're ignoring those functions that can be approximated further than order $k$ (which most definitely have \textit{non-zero} coefficients for the order $k+1$ term)
ocean sealBOT
Camilleone
hasty elk
the important part is the h(x) goes to 0
covert agate
is there an example?
hasty elk
without it i don't care what your function or order is, but you need specifically h(x) goes to 0
and that forces it to be $h(x)(x-a)^k$
ocean sealBOT
Camilleone
hasty elk
probably $e^x$ works, but someone else has to work through the details
ocean sealBOT
Camilleone
hasty elk
i'm tired and i have a headache so i'm not doing it
lone heartBOT
@covert agate Has your question been resolved?
hasty elk
i saw that, and i laughed
drifting hull
@covert agate The whole point of this approximation is that h(x) tend to zero, because that is the thing that says that this is a good approximation. If i don't have this property, i can do something like: Let f(x)=x then $f(x)=0+0x+0x^2+h(x)*x^2$ where h(x)=1/x. So you approximate f(x)=x by 0, which is pretty useless
ocean sealBOT
Alexander42
covert agate
i dont get it
drifting hull
Ok, we can do it the other way around. Suppose you write the remainder as h(x)*(x-a)^{k+1}. Can you show any properties for h(x) or is it just a function you know nothing about it?
drifting hull
what is a remainder function?
covert agate
the thing we omit
since we're doing a k-degree taylor approximation
everything from k + 1 we dump
drifting hull
and why can you just dump it? it might be important
covert agate
since we're doing a k-degree taylor approximation
?
drifting hull
if you approximate f, the thing you dump has to be small, otherwise its not an approximation, right?
covert agate
yea
drifting hull
and taylors theorem tells you how small the thing is, that you are dumping
covert agate
and taylors theorem tells you how small the thing is, that you are dumping
ok..?
drifting hull
namely, it is of the form h_k(x)*(x-a)^k with h_k(x) tending to 0
covert agate
**Chromium**
are you leading up to this 
drifting hull
it less less information, if you just say its of the form h_k(x)*(x-a)^{k+1} without any restrictions on h_k, because what if h_k(x) would be 1/(x-a)^{k+1}. Then the thing you dump is 1, so the approximation is bad
covert agate
**Chromium**
as to why this is convention
drifting hull
,w plot |x|^(3/2)
ocean sealBOT
drifting hull
suppose we taylor this f in 0.
The f'(0)=0
so we get $f(x)=0+0*x+h_1(x)*x$ with $h_1(x)=\sqrt{|x|}$
ocean sealBOT
Alexander42
drifting hull
and $h_1(x)$ tends to 0 for x to 0
ocean sealBOT
Alexander42
drifting hull
If we write it you way, we get $f(x)=0+0*x+g_1(x)*x^2$ with $g(x)=\frac{1}{\sqrt{|x|}}$ which tends to infinity for x to 0
ocean sealBOT
Alexander42
covert agate
i thought |x| isn't differentiable at 0
drifting hull
it isn't, but |x|^(3/2) is once differentiable in 0
$lim_{h\rightarrow 0} \frac{|h|^{3/2}}{h}= lim_{h\rightarrow 0} sgn(h)*\sqrt{h}=0$
ocean sealBOT
Alexander42
covert agate
$\lim_{h \to 0} \frac{|h|^{\frac{3}{2}}}{h}$
drifting hull
with a - in the exponent this limit doesn't exist, but with a + it exists
ocean sealBOT
Chromium
drifting hull
did it get clear what i try to say?
covert agate
still not really 🤦
covert agate
did it get clear what i try to say?
could you do one with, say, e^x?
lone heartBOT
@covert agate Has your question been resolved?
covert agate
yea, still not sure why that’s true
covert agate
apparently this generalises to higher degrees?
covert agate
<@&286206848099549185>
lone heartBOT
@covert agate Has your question been resolved?
covert agate
.close
leaden tiger
is this correct?
lone heartBOT
is this correct?
leaden tiger
i needed to shade the region that satisfies both inequalities
im a little unsure how to do it and just went with a guess
here is the question if needed:
.close
weak elbow
Im baauuuuuughck, just to recheck, X is = 9 - 6 right? or im wrong and theres another way of solving for either X or Y
lone heartBOT
Im baauuuuuughck, just to recheck, X is = 9 - 6 right? or im wrong and theres an...
@weak elbow Has your question been resolved?
weak elbow
sorry <@&286206848099549185>
alpine sable
Apply Pythagoras theorem to triangle whose hypotenuse is 6 express x in terms of y or vice versa then use geometric mean property of right angle triangle
dull lily
Hey so for a problem like this, I need to use the chain formula to find the derivative
dull lily
The issue here is I can’t find out which is the outter value and which is the outter-Er value
Does it matter which is which?
Cuz I’ve been doing two shell problems for a while but now that I’m on three shell problems my brains kinda going bonkers
glass lichen
$g(t)=(2t+1)^{-2}$
ocean sealBOT
Mosh
glass lichen
there's only 1 composition not 2
lone heartBOT
lone heartBOT
Available help channel!
cinder egret
Hi need somw help
lone heartBOT
Hi need somw help
cinder egret
How can i check that:
Z^101 - 1 = (Z-1) sigma Z^n
glass lichen
expand the RHS
glass lichen
what don't you understand from those 2 words and 1 acronym...?
glass lichen
Right hand side
glass lichen
Distributive property
lone heartBOT
@cinder egret Has your question been resolved?
lone heartBOT
https://hig.app.box.com/s/eibsc9fr5j9sjbdmuozm5gos3x74rfd6
alpine sable
hello i dont understand this how did i get a 7 and why is 1-a-b(lambda) positive
tacit arch
just screenshot your question
alpine sable
its mac i havent got used to it, how do i get 7 ? or how does this work?
and how does 1-a-b(lambda)=0 gets to be a+b(lambda)=-1
for clarity i got this one too
AT should be described with coordinates as AB and AC
lone heartBOT
@alpine sable Has your question been resolved?
tacit arch
its mac i havent got used to it, how do i get 7 ? or how does this work?
did you try getting the inverse of the matrix?
this matrix's inverse
lone heartBOT
@errant moss Has your question been resolved?
fathom tapir
how do I do this type of problem?
lone heartBOT
how do I do this type of problem?
dense sleet
I guess you could use tan
dense sleet
,w tan(45°)
ocean sealBOT
dense sleet
,w tan(11°)
ocean sealBOT
dense sleet
Close enough to 1/5
fathom tapir
how do you get that?
dense sleet
Ok imma explain
ocean sealBOT
fathom tapir
also I now have to find out how long the base of the triangle is
fathom tapir
sin , cos , tan are trigonometry functions
oh
dense sleet
Ok so you see this right triangle and lets take the lower right angle for example
sin of that angle is opposite over hypothonus , cos is adjective over hypothonus and tan is opposite over adjective or just sin/cos
That basically gives you ratio of 2 sides
@fathom tapir anything unclear?
You can ask. Im not best at explaining things
fathom tapir
sin of that angle is opposite over hypothonus , cos is adjective over hypothonu...
I dont understand a word of this im so sorry
hh
ocean sealBOT
dense sleet
,w right triangle with angles 30° and 60°
ocean sealBOT
dense sleet
@fathom tapir ok so look ar this triangle
Hypotenuse is 5 and we got angles 30° and 60°
Lets call the unknown sides a and b
How do you think we get a and b just with 1 side and an angle?
I mean we dont have to go into trigonometry if you dont want to
You can just memorise right now the table and you will later learn about relation of slope and angle
thin urchin
lone heartBOT
thin urchin
am I setting up this problem correctly?
just want to make sure my differentation is on point
lone heartBOT
stoic ember
what is the question?
wary stream
What's the goal?
dense sleet
The domain?
robust phoenix
yeah
dense sleet
Any number except zero ig
dense sleet
Oh i see the sqrt
glass lichen
yes, x in [1,inf) is right
dense sleet
Yes then thats correct
dense sleet
X cannot be 0 and
x-1 must be more or equal to 0
Therefore x can be more or equal than 1
azure rain
whats this someone plz help
lone heartBOT
whats this someone plz help
azure rain
yes
azure rain
kinda but its kinda hard for me to understand how
wanton junco
well what do you have in mind
Try to list the law of sines on paper on this particular triangle and that might nudge you towards the right direction
azure rain
i did sin(30) times 12 to get 6
thats is x
then i did
tan(40) times 6 to get 5.04
wanton junco
Oh
okay that works as well
I was referring to the extended law of sines
for all triangles
but using the right triangles is just as good lol
yea seems right
azure rain
kk thanks
lone heartBOT
@azure rain Has your question been resolved?
tacit arch
is your question for your friend ?
stark ivy
-
I have a DE equation of the form
$$
A(x) y'''' + B(x) y''' + C(x) y'' + D(x) y' + E(x) =0
$$ -
I have found how x should behave at certain boundaries, x=0, and x=x*. I.e.$ y(near 0) = \alpha x^3 + \beta x + \gamma$, and another of different powers at the other boundary.
-
I numerically have the constants $A,B,C,D,E$
-
A(x) has roots at 0 and x*
-
I know that $y(0) = 0$, and that y(x*) should diverge not faster that 1/(x-x*)
With all of this, if someone told you to "find 2 more boundary conditions y(x)" what would that entail? I have a single boundary condition at y(0), but as for the other two I'm not sure how I would find them?
ocean sealBOT
Andrew
lone heartBOT
@stark ivy Has your question been resolved?
south yarrow
Hi, trying to solve an ODE in the form dy(x)/dx. Is this just the same as dy/dx with different notation?
tacit arch
yes
supple elk
Question number 6. I don’t even know where to begin. I was hoping someone could set me off on the right track
tacit arch
"combine waves of equal period" is pretty vague
are you supposed to use sum formula for sine?
supple elk
The previous question called for suing sum formula but I think this one is asking for something different
tacit arch
i think you should just use this
can't find anything else that can be useful
https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.02%3A_Sum_and_Difference_Identities#:~:text=The sum formula for sines,sine of the second angle.
$cos \theta=sin (\pi/2−\theta)$ can also work if you start with the right hand side and then use the sum of sines formula
ocean sealBOT
riemann
distant surge
Hey, so im very stuck here
lone heartBOT
Hey, so im very stuck here
distant surge
this is what the memo says, i just dont understand how it got there
celest storm
How do you find roots of such an equation?
distant surge
How do you find roots of such an equation?
im at a loss...
wary stream
Hey, so im very stuck here
Apply concept of the discriminant
celest storm
Do you see why it would help to you find the roots of $2x^2+(m-5)x-8$?
ocean sealBOT
BenFire
distant surge
Do you see why it would help to you find the roots of $2x^2+(m-5)x-8$?
ohhh i see now
ok great thanks
.close
lone heartBOT
celest storm
Np
lone heartBOT
Available help channel!
thick flame
I'm looking to get the position of a point C from 2 points A and B. C is one of the points where unit circles around A and B intersect. Specifically the point that is the smallest clockwise rotation from B about A. (Reference image below)
I'm hoping to do this without trig functions and the fact that triangulation is possible without trig functions gives me hope XD
near lagoon
I'd suggest Heron's formula
@thick flame
On the triangle ABC, whose sides have length 1.5, 1, 1
So if C = (Cx, Cy)
Cx = 2 (Area of ABC found by Heron's formula)/1.5
Cy = sqrt(1-Cx^2)
solemn grove
I'm looking to get the position of a point C from 2 points A and B. C is one of ...
i was thinking about using the fact that y of c is mid between a and b
because of the symmetry of the problem
and then subbing it into the eqn of a circle
thick flame
That doesn't work in all cases
solemn grove
either
solemn grove
because of the symmetry of the problem
^^^
solemn grove
That doesn't work in all cases
this specific one
thick flame
I need all cases XD
solemn grove
ah,
thick flame
.close
lone heartBOT
thick flame
.reopen
lone heartBOT
✅
thick flame
Cx = 2 (Area of ABC found by Heron's formula)/1.5
This is what happens when I move a point
H is your method using Heron's @near lagoon
OH
Cy is relative to (0,0) when it should be relative to the points XD
But then the x coordinate makes no sense XD
It seems to not work at all when I move B on the X axis
(aside from keeping H on the red circle)
I'm guessing your formula for x only works when A and B are on the y axis
.close
empty canopy
hi
solemn grove
I'm guessing your formula for x only works when A and B are on the y axis
consider the vector ab as the y axis. if exactly one point is translated, it’s the equivalent of rotating it theta degrees from the centre of the other circle as centre of rotation, idk just a thought
but then again, it has trig
frigid hatch
i got 14.9 is it correct?
yes
solemn grove
2x altitude /sqrt(3) = side length
alpine sable
Yo help I need maddddd helpppp
solemn grove
and 3 times that is perimeter
alpine sable
I beg
frigid hatch
bro is begging
solemn grove
so 2root3 altitude i think
solemn grove
find x?
alpine sable
Oh wtf
solemn grove
(x+15 )/x = 13/8
empty canopy
and 3 times that is perimeter
yes i got 14.9 it matches my answer thanks
solemn grove
This *clearly* isn't their channel.
apologies
solemn grove
yes i got 14.9 it matches my answer thanks
sweet
solemn grove
yeah,
alpine sable
How’d u get that
solemn grove
any rearrangement of that works
alpine sable
Did u need to factor
glass lichen
@alpine sable Get your own channel.
solemn grove
i’ve done them way to many times that i can spot them
glass lichen
@solemn grove again, stop promoting rule breaking
alpine sable
<@456226577798135808> Get your own channel.
Alr my bad bro
solemn grove
yes i got 14.9 it matches my answer thanks
they forgot to close my friend
alpine sable
@solemn grove dms?
empty canopy
how do i close
solemn grove
sure
glass lichen
.close
solemn grove
.close
empty canopy
.close
lone heartBOT
tacit arch
.close
lone heartBOT
Available help channel!
open folio
A 4kg object moving at 5m/s collides elastically with a 6kg object moving at -2m/s. calculate final velocity of each object.
open folio
V1i + V1f = V2i + V2f
5 + V1f = -2 + V2f
V1f = V2f - 7
4(5) + 6(-2) = 4V1f + 6V2f
8 = 4V1f + 6V2f
8 = 4(V2f - 7) + 6V2f
8 = 4V2f - 28 + 6V2f
8 = 10V2f - 28
36 = 10V2f
3.6 = V2f
Thats one of the answers
8 = 4V1f + 6V2f
8 = 4V1f + 6(3.6)
8 = 4V1f + 21.6
-13.6 = 4V1f
-3.4 = V1f
Thats the other answer
This is what I got, but my friend used a diff formula and got a diff answer... did I make an error, or is my formula wrong?
Cmon physics nerds
<@&286206848099549185>
lone heartBOT
@open folio Has your question been resolved?
open folio
.close
wanton tinsel
"test the series for convergence or divergence"
lone heartBOT
"test the series for convergence or divergence"
wanton tinsel
i want to use the alternating series test
but can that be used with oscillation like this that isnt (-1)^n?
the terms definitely go to 0
and i suppose | a_n | <= pi/(1+sqrt(n))
is that enough to satisfy the condition the other condition of ast?
<@&286206848099549185>
are there maybe other tests that could work?
limit comparison seems unlikely since 1/sqrt(n) diverges
raven rover
Is the π inside the sin?
It's normally found inside the sine function
If so, then there maybe a way you can rewrite the sum
raven rover
If not, I'm not super sure what you'd do
Yeah
Maybe sin sum identity?
What if you expanded that out?
wanton tinsel
oh maybe
raven rover
Could you use a limit comparison, and maybe compare it with something?
wanton tinsel
still seems strange because theres no (-1)^n
this converges so we would need a series that converges to compare it with
raven rover
Oh, you know the answer?
raven rover
Right
Oh - because sin alternates signs, I wonder if that is similar to using the alternating series test
Because the terms go to 0 and there is a sign change every once in a while.
wanton tinsel
also its in the alternating series section so id figure theres a way to use alternating series test on this
raven rover
This isn't the exact same as using the AST, but the idea is there
Maybe rewrite sin(n + 1/2) as a power series?
Not sure
wanton tinsel
yeah i see intuitively how it would apply but
raven rover
Never really took that approach for a series like this before
wanton tinsel
lol using power series before even learning ratio test
raven rover
That'd be wack - I'd agree
wanton tinsel
same ive never seen something that oscillates in a series without (-1)^n
raven rover
$\sum_{n = 0}^{\infty} \frac{\sin \left( n + \frac{1}{2} \right)}{1 + \sqrt{n}}$
wanton tinsel
i want to say that this counts as decreasing since |a_n| <= pi/(1+sqrt(n)) which is decreasing
ocean sealBOT
Shen
raven rover
i want to say that this counts as decreasing since |a_n| <= pi/(1+sqrt(n)) which...
I mean that makes sense