@restive river have you learned some general angle rules about circles and inscribed segments?
#help-27
wheat pebble
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
pallid ruin
waxen harness
Problem 1. Inverse trigonometriy.
devout snowBOT
Problem 1. Inverse trigonometriy.
waxen harness
I do not know how should I start with this.
cinder bobcat
hint: plug in some numbers for x and see if anything nice happens
waxen harness
Ohh. It comes π/3.
cinder bobcat
yep
devout snowBOT
Available help channel!
brazen star
f(x) = a^2 x + 100
f(20) + f^-1(22) = f(22) + f^-1(20)
find f(1)
brazen star
so first of all i found that
f^-1(x) = (x-100)/a^2
ok
what should i have done
:/
and yes, i asked a similar question but miswrote the question before
upper schooner
I don’t disagree with the f^{-1}, but notice how they give you that condition with f^{-1}(22) on both sides
pseudo basin
f^-1(x) = (x-100)/a^2
this is now relevant.
brazen star
do i need to substitute everything or is there an easier way to do it?
pseudo basin
if there are no tricks you can see then try doing it without any tricks.
brazen star
20a^2 + 100 + (22-100)/a^2 = 22a^2 + 100 + (20-100)/a^2
20a^2 - 78/a^2 = 22a^2 - 80/a^2
0 = 2a^2 - 2/a^2
ima just make it
2/a^2 = 2a^2
so
,,a^{-2} = a^2
woven radishBOT
help
brazen star
1 = a^4
-1 or 1 = a
nimble walrus
f(x) = a^2 x + 100
f(20) + f^-1(22) = f(22) + f^-1(20)
find f(1)
What abt the other prob 💀
brazen star
What abt the other prob 💀
uhh
asked my teacher
he's on his way home
so maybe later
devout snowBOT
devout snowBOT
Available help channel!
proud nimbus
option E correct ??
devout snowBOT
option E correct ??
proud nimbus
Why not ?
upper schooner
How did you get that?
proud nimbus
chatGPT actually
winter patrol
do your own work and see what you get
proud nimbus
i dont know how to solve these ones
upper schooner
Anyways, could you find sin(alpha) for me at least? 
proud nimbus
hate trigonometry
proud nimbus
Anyways, could you find sin(alpha) for me at least? <:catGiggle:6689487177720791...
i can do simple ones, so yes
winter patrol
compound angle identities / reference angles / right triangles
upper schooner
i can do simple ones, so yes
Cool cool, let me know what you get 
proud nimbus
$\frac{1}{\sqrt2}$
woven radishBOT
Bunnings
proud nimbus
@upper schooner
upper schooner
Hmm, how? 
Remember that you have cos(alpha) = -1/4 and also that alpha is between pi/2 and pi
proud nimbus
i am a little confused about this cos value. how can this be -1/4
dark tundra
The angle’s in quadrant 2, so having a negative cosine makes sense
do you know what the unit circle is?
proud nimbus
oh yeah i know it completely
brazen widget
Correct answer is D
upper schooner
Correct answer is D
!nosols
devout snowBOT
Correct answer is D
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
upper schooner
(but it is)
severe maple
What do I do after this
devout snowBOT
What do I do after this
proud spear
What do I do after this
I would multiply each side by the denominator to clear it.
severe maple
What's denominator
proud spear
The lower part of the fraction, in this case, x+3.
Oh wait.
I misread the image.
One is x+3 and one is x-3.
severe maple
Yes
proud spear
Bring (2x-2)/(x+3) + (x+3)/(x-3) together using a common denominator.
severe maple
Yes
proud spear
What did you get?
severe maple
Idk I don't get it
proud spear
To get a common denominator, you need to add a (x-3) to the denominator of the first fraction and an (x+3) to the denominator of the second.
You are allowed to multiply by any form of 1, so you can multiply the first one by (x-3)/(x-3). This yeilds (2x-2)(x-3)/(x^2 - 9).
Can you figure out what you need to do for the second?
severe maple
(x+3)(x+3)/(x^2+9)
proud spear
(x+3)(x+3)/(x^2+9)
Denominator should be x^2 - 9, not plus as (x-3)(x+3) = (x^2-9).
But other than that its correct!
Now that they have the same denominator, you can bring them together.
severe maple
I can't
proud spear
I can't
With (2x-3)(x-3)/(x^2-9) + (x+3)(x+3)/(x^2 - 9), you can use the fact that they have a common denominator to add them, yielding:
((2x-3)(x-3) + (x+3)(x+3))/(x^2 - 9).
So the whole expression is now ((2x-3)(x-3) + (x+3)(x+3))/(x^2-9) - 5 = 0
severe maple
What happens to 5 tho
proud spear
Right now, we're going to just sort of ignore it. It'll come into play later. For now, lets focus on getting x^2-9 out of the denominator.
To clear x^2 - 9 from the denominator, we need to multiply by it.
severe maple
What 😭
proud spear
Let me try writing this in a clearer way, sort of an amateur with TeXit though so 1s.
$((2x-3)(x-3) + (x+3)(x+3))/(x^2-9) - 5 = 0$
woven radishBOT
SleepyKitn
proud spear
Not sure how to make it do fractions, but this is our expression.
To clear this up, we need to multiply both sides by x^2 - 9. The right side is easy. The left side is a bit trickier, but the x^2 - 9 cancels with the other term and the -5(x^2 - 9) can be left in that form for now.
$(2x-3)(x-3) + (x+3)(x+3) - 5(x^2-9) = 0$
woven radishBOT
SleepyKitn
severe maple
Yes
proud spear
Now this is a bit messy as we ignored multiplying things out, so lets simplify a bit.
dark tundra
foil
proud spear
We need to multiply out the terms. Lets start with the first one, (2x-3)(x-3). Use FOIL to do that. (First, outside, inside, last).
severe maple
🧐
proud spear
So we multiply the first terms together, then the outside terms, then the inside terms, then the last terms.
severe maple
Where outside terms
proud spear
The first terms of each expression are 2x and x, the outside terms are 2x and -3, the inside terms are -3 and x, and the last terms are -3 and -3.
Multiply all of those then add them up.
severe maple
Hm
severe maple
2x in quadrat?
proud spear
2x^2, yes.
Then we repeat the process for all the other terms I laid out above, and then add them up.
severe maple
And we get?
severe maple
That's a lot of numbers
severe maple
2x^2+9x+9 idk
proud spear
x^2 + 6x + 9, as you again use FOIL.
So we can add those two now, add:
2x^2 - 9x + 9
x^2 + 6x + 9.
What do you get?
severe maple
3x^2-3x+18
severe maple
-5x^2+45?
severe maple
-2x^2-3x+63
proud spear
Yes!
One second though, I noticed I made a typo a bit back, wrote 2x-2 as 2x-3. I'll correct it and give you the corrected form at this step.
Done.
This comes out to -2x^2 -2x + 60 = 0.
My apologies for the mistake.
severe maple
Yss
proud spear
Can you solve that quadratic?
severe maple
It's okay 👍🏻😊
proud spear
Have a nice day!
west prairie
devout snowBOT
frosty cradle
!15mins
devout snowBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
dusk fractal
i m am desperately stuck
okaay now
frosty cradle
!show
devout snowBOT
Show your work, and if possible, explain where you are stuck.
frosty cradle
!nosols
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
frosty cradle
get this chatgpt crap out of here
west prairie
i promise to not copy
i have exam tom
thas y i asked
srry cwatson
cwatson could u help me ?
azure patio
whats the problem??
west prairie
ok cwatson i will do and send
frosty cradle
and note the other facts you are given
frosty cradle
well better to write what OM and MB are, I think. what would those both be
frosty cradle
yes
simple wharf
im good at maths
west prairie
im good at maths
then help me
simple wharf
ok 5z
simple wharf
yes 5z
west prairie
nm becomes median in triangle NOB
can u use vectors cause tom in exam i have to use vectors to solve ii m srry for asking for so much
azure patio
can u use vectors cause tom in exam i have to use vectors to solve ii m srry for...
ok
use vector dot products then maybe
let me try once
let angle nop be theta
then AB= abcos theta
west prairie
theta and all i dont know
azure patio
by vector dot product
west prairie
i am in 9th grade
azure patio
theta and all i dont know
and you know vector??
west prairie
going for year end exam for igcse 0580 extended mathameatics
west prairie
and you know vector??
yes
west prairie
do you know vector dot product??
no
west prairie
do you know vector dot product??
are those matrixes
azure patio
are those matrixes
no
azure patio
like if A and B are two vectors and theta is the angle between the vectors
then vector dot product says that A.B= |A||B| cos theta
west prairie
like if A and B are two vectors and theta is the angle between the vectors
umm its not there in our syllabus
azure patio
do you have euclidean geometry??
azure patio
can you send me the syllabus of vectors youve studied?
west prairie
azure patio
just join all the points possible
and use vector addition and substraction
maybe that would help
west prairie
ig
fleet loom
devout snowBOT
formal haven
what is the goal here
fleet loom
need to find mcka i think
1sec
im tryna find the word in english
area
of mcka
M is midpoint
and its a square at the bottom
<@&286206848099549185>
.close
restive river
devout snowBOT
torn vessel
which part
restive river
After dividing with cos theta
eager nova
You mean everything? xD
restive river
After this
wooden veldt
test
wooden veldt
.close
devout snowBOT
sonic smelt
upper schooner
devout snowBOT
Available help channel!
devout snowBOT
is there an order of operations for differentiating?
light quail
frosty cradle
what do you mean?
light quail
i saw this wrong at first and thought they were multiplying
but if they were
there would be exponent and product rule
frosty cradle
you mean if it was $z^{-4} \cdot -z^{1/2}$?
woven radishBOT
cwatson
light quail
yes
frosty cradle
there's no order, in the same sense as PEMDAS or whatever. you just let $f(z) = z^{-4}$ and $g(z) = -z^{1/2}$ and do the product rule for $f(z) g(z)$
woven radishBOT
cwatson
frosty cradle
well, I guess I mean there's only one order to do it (as far as I can see)
jolly marten
devout snowBOT
boreal gust
the constants are taken to the front, and the sqrt(x) is distributed into the other root cancelling with the denominator
and the integral can be done with a u=x+1, du=dx substitution
devout snowBOT
Available help channel!
jaunty bane
Hi all, here's a question I need help with:
devout snowBOT
Hi all, here's a question I need help with:
jaunty bane
"Point A is 6 cm from line m and 16 cm from line n. Point A is reflected across line m, and then its image, point A', is reflected across line n to create a second image, point A''. How far is point A from point A''?"
Here's the picture I drew:
So to find how far A is from A'', I just did 16 + 28 to get 44 cm.
However, that's somehow incorrect. Could someone please help me understand why 44 cm is incorrect?
hybrid snow
Or was it A' from A"
upper schooner
Do they say what the “actual” solution is?
upper schooner
very useful :/
hybrid snow
Maybe your teacher is being dumb
upper schooner
Maybe your teacher is being dumb
Yea wasn’t it the case the other day you had loads of errors in your solutions and stuff @jaunty bane?
jaunty bane
Yea wasn’t it the case the other day you had loads of errors in your solutions a...
yeah there were 3+ errors in the paper i did
even for simple questions like "what's the sum of the exterior angles of a polygon with n sides"
even if i did lose a point for this question, i now have the satisfaction that i actually did get the right answer
so thank you Umbra and charbit
❤️
.close
junior fiber
Help🥴What do I do with the 3 on the parentheses?
devout snowBOT
Help🥴What do I do with the 3 on the parentheses?
junior fiber
I was thinking chain rule
But like how can I go about that with an anti derivative
.close
trim shore
@junior fiber send the main question
devout snowBOT
<@554441085057761299> send the main question
orchid tulip
does lagrange multipliers give you the global maxima/minima or the local maxima/minima?
devout snowBOT
does lagrange multipliers give you the global maxima/minima or the local maxima/...
hybrid snow
It gives you extremum yielding to the constraint
orchid tulip
so it gives you the global extremum that satifies the constraint?
orchid tulip
It gives you extremum yielding to the constraint
Or does that not make sense?
devout snowBOT
@orchid tulip Has your question been resolved?
hybrid snow
so it gives you the global extremum that satifies the constraint?
It gives you the maximum value on the function that satisfies the constraint
devout snowBOT
devout snowBOT
Available help channel!
mental bay
whats the answer for this just have to confirm my answer
devout snowBOT
whats the answer for this just have to confirm my answer
frosty cradle
,rccw
woven radishBOT
gray phoenix
whats the answer for this just have to confirm my answer
We can't see the full shape so we can't determine the perimeter
mental bay
We can't see the full shape so we can't determine the perimeter
oh the wuestion below
just determine the rate
mental bay
What’s even the question?
D = a-1/ a+ 2 r=? T= a-1/a
gray phoenix
Yeah we need the full shape
mental bay
sorry my fault for the confusion
gray phoenix
The picture is cut short
mental bay
shouldve made it clear, sir @gray phoenix
this was the wuestion i neede dthe answer for
gray phoenix
Maybe it's (a-1/a+2)/(a-1/a)
mental bay
Maybe it's (a-1/a+2)/(a-1/a)
yeah i figured that out but i just need to confirm my answer
my answer is a/a+2
mental bay
<@&286206848099549185>
devout snowBOT
@mental bay Has your question been resolved?
devout snowBOT
@mental bay Has your question been resolved?
devout snowBOT
@mental bay Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
visual spire
How do i do ruffini with roots? Im just want to remember how to do it
pseudo basin
what do you mean when you say "ruffini"
visual spire
This
pseudo basin
i don't think you're supposed to do it that way
even if you're FORCED to and you substitute u := x^(1/12), the numerator will have lower degree than the denominator
instead youre supposed to break this into the sum of 3 limits of the form (x^p - 1)/(x - 1)
visual spire
instead youre supposed to break this into the sum of 3 limits of the form (x^p -...
Oh right thats seems to be right
Thanks !
.close
lost cloak
how do you know that you need to multiply both side by e^x
devout snowBOT
how do you know that you need to multiply both side by e^x
lost cloak
oh ok
supple knot
But that's also hard to do if you've never done it before
feral agate
correct
topaz beacon
yup
feral agate
maybe it'd be beneficial to write u^(-1) as 1/u
plush cairn
okay i have a recursive sequence and im supposed to prove that a_1,a_3,a_5..... is decreasing and lower bounded while also at the same time prove that a_2,a_4,a_6...... is increasing and upper bounded, that leaves a_n <a_n+2 and a_n+1>a_n+3my first though is induction but i have no clue how to go about that, any insight would be appreciated!
devout snowBOT
okay i have a recursive sequence and im supposed to prove that a_1,a_3,a_5..... ...
pseudo basin
your handwriting is kind of bad
plush cairn
i know
pseudo basin
the recurrence relation is hard to parse
magic thicket
except for the indices it's pretty good
pseudo basin
it's the indices that are the problem
i can only read it as $a_n + 1 = \frac{1}{an + 1}$
woven radishBOT
Ann
woven radishBOT
Ann
pseudo basin
no need
i think you might want to express $a_{n+2}$ in terms of $a_n$ by applying this twice.
woven radishBOT
Ann
plush cairn
applying what twice, induction?
doing the recursive loop twice in the induction, maybe?
pseudo basin
applying what twice, induction?
no, the recurrence relation.
plush cairn
(a_n + 1)/(a_n + 2) ?
but what do i put this against? a_n= or > or < ?
how does this prove that the respective sequences are increasing and decreasing
pseudo basin
,w simplify 1/(1 + 1/(1+x))
woven radishBOT
woven radishBOT
Ann
plush cairn
im kinda a big question mark rn not gonna lie what is the point of doing this?
magic thicket
you want to compare an+2 and an
hint: this is fairly complicated at first glance, because there's no apparent reason for n's parity to matter
I would therefore advise to study the function
f(x) = (x+1) / (x+2)
and see what it tells you about your sequence
plush cairn
it certainly looks like it
magic thicket
I would therefore advise to study the function
f(x) = (x+1) / (x+2)
or f(x) - x is that's more insightful
magic thicket
looks like it goes to 0.6 and something
more precisely I can tell you it's 0.618..
definitely not 1
plush cairn
f(x) = (x+1)/(x+2) would go towards 1
magic thicket
at infinity yes
but you're looking at f(an)
because an+2 = f(an) and that's the comparison you want to make
since an doesn't go to infinity, this limit of f is useless
plush cairn
okay
magic thicket
we're looking at the behavior of f on something like [1/2, 1]
where the an actually are
plush cairn
oooooh okay that makes sense then
magic thicket
are you in undergrad ?
magic thicket
then that method is something you should keep in mind cause sequences of the form xn+1 = f(xn) come up quite a bit
for instance, if the limit exists, it must be a stable point of f, i.e. such that f(l) = l (allowing infinity to be a value for generality)
you also have a way to link the monotony of the sequence to f's derivative
things that are much easier to see with the right drawing
plush cairn
okay i understand that mostly but i still dont see how i can actually prove that the respective sequences are either increasing or decreasing
magic thicket
feel free to translate pages 22-24 (big 7)
I couldn't quickly find an english ressource unfortunately
but here are the important results real quick
if f is increasing, xn is monotoneous (i.e. increasing or decreasing)
if f has a fixed point and is increasing l (i.e. f(l) = l), then xn - l doesn't change sign
this is all for continous f btw
plush cairn
ooooh i think i know what you are mean
fuck im trying to comprehend it but i feel like im close
magic thicket
first box of page 23 is very relevant here: if f is decreasing, f² is increasing and x(2n) and x(2n+1) are monotonous of opposite variations
which would be very useful taking instead f(x) = 1/x+1
then if |f'(l)| < 1, there's a stable interval I = [l-e, l+e] (i.e. f(I) is in I) and if xn is in I then f(xn) -> l
if instead |f'(l)| > 1, then there's a small interval I around l such that the values get ejected: if xn in I, then some x(n+k) isn't in I anymore
to intuit these results, it's very useful to plot both y = f(x) and y = x
and graph the algorithm of the sequence
Take a value x, and its image f(x).
To take it as an input again, send it back as an x value using the line y = x
plush cairn
okay you had me in the first half but now you kinda lost me ngl
magic thicket
take some time to think about this yeah
magic thicket
that's the visual interpretation of the case |f'(l)| < 1
I took x0 as the point in the bottom left
then above it is f(x) = x1, which I put as an x value by shifting it horizontally
plush cairn
also just saying im pretty sure im supposed to do this task with induction as it is what we learned to do so far
magic thicket
then repeat to take f(x) = x2, turn it into an x value
this is the theory
of course you can also just prove the theory
plush cairn
and how would i do that?
magic thicket
arguably by induction
magic thicket
I would therefore advise to study the function
f(x) = (x+1) / (x+2)
show that f is increasing
then f^n is increasing
therefore if x0 < f(x0), xn = f^n(x0) <= f^n (f(x0)) = f^(n+1) (x0) = xn+1
therefore if x0 < f(x0), (xn) is increasing
that's half the work done
basically the same proof for the other one and that's your exercise done
plush cairn
really sorry about this but i need 2 min to do some other urgent stuff
okay so f^n?
sorry had some puppy stuff to take care of
magic thicket
f applied n times
plush cairn
show that f is increasing
i assume i show that f is increasing my doing the derivate ?
magic thicket
most likely
plush cairn
okay i think i get it
other then one thing
how would this show that the sequences are bounded
and how would i go about finding where they are bounded
magic thicket
if f has a fixed point and is increasing l (i.e. f(l) = l), then xn - l doesn't ...
monotonous and bounded by l in the right direction
find l
plush cairn
kinda confused as to how i would that
nvm think i got it
ty so much ^^
❤️
.close
devout snowBOT
devout snowBOT
Available help channel!
muted blaze
devout snowBOT
muted blaze
I need help to solve this. Where do I start? I know have to plug in the -2x to start, but where do I plug it? I'm very new to algebra and will probably need step by step explentation
main python
g(x) = x^2+3
nova idol
plug in -2x into the x of g(x)
main python
g(f(x)) = (f(x))^2 +3
nova idol
so g(f(x)) = g(-2x)
muted blaze
g(-2x) = x^2+3
nova idol
not quite
muted blaze
hmm
muted blaze
muted blaze
(-2x)^2+3
nova idol
yes
muted blaze
oh yeah
the parentheses helps
(-2x)^2+3
so I just distribute from here
?
-2 , -2
= 4x2
and +3
is that right?
4x^2+3
nova idol
yes
nova idol
alr
devout snowBOT
@muted blaze Has your question been resolved?
supple knot
set y = f(x), then solve for x in terms of y
muted blaze
How to set y=f(x)
light quail
devout snowBOT
light quail
what should i look up to learn about this?
the notes are just labeled "what derivatives tell us about the shape of the graph"
rough night
devout snowBOT
rough night
Im not sure for b
How come it expands into cos and sin?
I dont think the question is really that relevant for this question
upper schooner
I disagree 
Looks like they're assuming that a is constant wrt t and that theta and b aren't(?)
upper schooner
Yep [the value] a is constant, whereas b isn't - it depends on time because it's increasing at a rate of 1.5cm/min
rough night
How come B isnt a constant for question b) but not for question a)
upper schooner
Well in part (a) they tell you that b is constantly 3cm, don't they?
rough night
But doesnt it say b=3 for question b)
upper schooner
It does, but note they say "when b=3" in addition to the fact that they mention that b is increasing at the rate that it is
rough night
But then it doesnt specify either the values of 1.5 or 0.2 go with cos or sin
Cause this question is super confusing to me
Because if its saying that its increasing at a rate of 1.5 I cant just assume it goes with the side value on the left if its then broken down by product rule
nvm I got it I think its more of a reading comprehension thing
thanks!
.close
restive river
how would i do comparison test for $\int_{2}^{\infty} \frac{1}{\sqrt{x^{2}+\frac{1}{x^{2}}}} dx$
devout snowBOT
how would i do comparison test for $\int_{2}^{\infty} \frac{1}{\sqrt{x^{2}+\frac...
woven radishBOT
COLOURS
clever mist
well you have to make another integral more
gray gust
or less
restive river
🗿 i tried with 1/sqrt(x^2) but it doesnt work
clever mist
🗿 i tried with 1/sqrt(x^2) but it doesnt work
isn't that 1/x
restive river
yes
clever mist
🗿 i tried with 1/sqrt(x^2) but it doesnt work
uhm why
warped relic
But does 1/x diverge?
restive river
But does 1/x diverge?
yeah i think so
gray gust
can you bound anything in the denominator from above?
restive river
1/x diverges but this integral is smaller than that so it does nothing
restive river
can you bound anything in the denominator from above?
idk im trying to figure something out ;-;
warped relic
Then compare it to something smaller
gray gust
1/x^2 is certainly greater than 0; is it less than anything here?
restive river
1/x^2 is certainly greater than 0; is it less than anything here?
x^2
gray gust
true
restive river
ok idk let me try again
gray gust
I thought you meant something else oops
You don't need it to be a good bound with these things; just one that works
a helpful thing to keep in mind generally is that if somethinf diverges, it still diverges when multipled by any nonzero constant no matter how small
restive river
You don't need it to be a good bound with these things; just one that works
i tried comparing the problem to 1/x^2 but i just get its smaller than a divergent
gray gust
so when bounding you can be super loose
restive river
oh hm uh
restive river
idk like x^2/2
gray gust
isn't that what you want?
restive river
no its inconclusive i think
gray gust
remember the difference here is we bounded in the other direction?
you just showed that the integrand is greater than 1/sqrt(2x^2) = 1/sqrt(2)x
restive river
hold on
ohhh
oh ma gawd
@gray gustat first glance did you think the integral would be divergent or convergent?
gray gust
divergent
gray gust
From an intuitive perspecrive?
oh
it's very similar to 1/x
Also the comparison test is quick
restive river
ah
gray gust
you can kinda spot it - the difficulty with a question like this comes in not trying to be clever with the bound
restive river
it's very similar to 1/x
i noticed as well but its smaller than 1/x so i wasnt sure
gray gust
I'll give more detail
When something is approximately a constant * a function, they both have the same convergence/divergence properties
restive river
ah right the 1/x^2 is almost 0?
gray gust
as in you can easily bound this function on both sides by a constant * a simple function
more that 1/x^2 is much smaller than x^2
devout snowBOT
gray gust
np
devout snowBOT
Available help channel!
restive river
question: what is the difference between limit comparison test and direct comparison test with examples please?
devout snowBOT
question: what is the difference between limit comparison test and direct compar...
supple knot
question: what is the difference between limit comparison test and direct compar...
examples 1 and 2
and 4 and 5 for limit comparison
restive river
https://tutorial.math.lamar.edu/classes/calcII/seriescomptest.aspx
are these your notes?
gray gust
no
this arises from doing a google search of wha you asked, which is all that's needed here
supple knot
are these your notes?
no. i don't see how that's relevant anyway.
restive river
ok, just to kinda of clarify in the simplest way, comparison test is removing the constant in the denominator and comparing it to the original series to see which is bigger, correct? But that doesn't seem right though. Trying to see it in the simplest way possible.
supple knot
ok, just to kinda of clarify in the simplest way, comparison test is removing th...
Understand the notes before trying to simplify
restive river
sorry but still trying to understand, I know it has something to do with whenever Bn is equal to Con or Div, An will follow the same. But that is far as I know.
devout snowBOT
@restive river Has your question been resolved?
restive river
.close
white sand
please walk me through how to solve this problem
devout snowBOT
please walk me through how to solve this problem
white sand
i have no idea what to do or where to start
clever mist
is that the whole problem
white sand
yes
devout snowBOT
@white sand Has your question been resolved?
devout snowBOT
@white sand Has your question been resolved?
wicked turtle
i have no idea what to do or where to start
hint: if x is on the line spanned by (1,2) then you want to map x to itself. If x is orthogonal to (1,2) then you want to map x to 0.
devout snowBOT
@white sand Has your question been resolved?
white sand
i understand the projection part but how do i go about finding the basis?
what does it mean by the transformation is diagonal
devout snowBOT
@white sand Has your question been resolved?
analog trellis
I can verify the exercise but I fail to see the equivalence in the final part of the problem. I feel there is something worthwhile of investigation in the exercise so I feel like I cannot just skip it as it could be used potentially for future problems to save a lot of work since this was very time consuming and messy to complete.
I find that the minimum distance to be a^2 2b^2 c^2/(2(b^2c^2 + a^2 c^2 + a^2 b^2)) which agrees with what the exercise suggest it should by computing it by the ratio it details.
devout snowBOT
I can verify the exercise but I fail to see the equivalence in the final part of...
analog trellis
My result for Exercise 3 of section 4 is:
$\frac{|Aa + Bb + Cc + Dd + E|}{\sqrt{A^2 + B^2 + C^2 + D^2}}$
woven radishBOT
stabulo
analog trellis
If we let a = b = c = d = 0 as the exercise does we obtain
$\frac{|E|}{\sqrt{A^2 + B^2 + C^2 + D^2}}$
woven radishBOT
stabulo
analog trellis
Seems like a long shot to ask as it does seem to be pulled out of absolutely nowhere.
devout snowBOT
@analog trellis Has your question been resolved?
long fog
$\frac{|E|}{\sqrt{A^2 + B^2 + C^2 + D^2}}$
Yes
devout snowBOT
@analog trellis Has your question been resolved?
sand dove
Yes what?
What is the euclidian distance in 4 dimensions?
From then you should be able to see it
analog trellis
**stabulo**
Are you referring to a proof of this formula?
I can state the result though.
The distance between two points x = <x_1, x_2, x_3, x_4> and y = <y_1, y_2, y_3, y_4> is
$\sqrt{(x_1 - y_1)^2 +(x_2 - y_2)^2 +(x_3 - y_3)^2 +(x_4 - y_4)^2}$.
woven radishBOT
stabulo
analog trellis
Eventually, I get the answer to be (although technically I've not tested that it is any kind of minimum)
$\frac{a^2 b^2 c^2}{2(b^2 c^2 + a^2 c^2 + a^2 b^2)}$.
sand dove
This result seems very weird
woven radishBOT
stabulo
analog trellis
Sorry, I made a error.
This part yield the same result.
This part is probably some high level insight the author really wants you to figure out and you'll wish you did once you do.
That exercise is the hyperplane distance.
Maybe I'm meant to consider a arbitrary tetrahedron centered at the origin a particular way.
analog trellis
For, here I considered a tetrahedron much differently.
Unless, it wants me to consider the tetrahedron to be made up of four arbitrary planes but that seems like the work will be massive.
sand dove
This is not a problem, you can recenter the tetrahedron to have its center of faces at (0,0,0)
analog trellis
No idea how to proceed other than searching random textbooks on the internet.
sand dove
**stabulo**
I think there is some insight to this result when you consider to take the square root of your answer
Where |E| is similar to abc, etc...
Seems very similar to the hyperplane bcx + acy + abz - abc = 0
analog trellis
I could set E = 1/2, A = 1/a, B = 1/b, C = 1/c, D = 0 and get that result but then a = 0, b = 0, c = 0 creates undefined fractions.
sand dove
Seems very similar to the hyperplane bcx + acy + abz - abc = 0
Maybe take values closer to this
analog trellis
Seems very similar to the hyperplane bcx + acy + abz - abc = 0
Ok. I'll look in that now.
Ok, it will yield the desired result but if we set D = 0, it seems to make the point of talking about hyperplanes unnecessary. We do yield the x, y, z-intercepts as a, b and c respectively. But I'm not sure what will be done about the required fourth vertex of the tetrahedron. If x = y = z = 0 then abc = 0. Clearly, our tetrahedron doesn't contain the origin.
Of course, it need not contain the origin.
sand dove
Of course, because we're searching for the distance between this hyperplane and the origin
analog trellis
Best lead yet though. Didn't consider rewriting how I represented the plane to be defined for a = b = c = 0.
I've also made the unfortunate mistake of using a, b and c for this problem so it's not directly applicable to the referred to exercise.
I think I might get some of it now.
analog trellis
This is not a problem, you can recenter the tetrahedron to have its center of fa...
"center of faces"
Move the tetrahedron so that it's center of faces is the origin then we need only minimise the distance from the tetrahedron to the origin. We can rotate appropriately so that we have three of the vertices at (a, 0, 0), (0, b, 0), (0, 0, c) and a final point D. I guess this is why we set D = 0 since we could make it the origin I guess.
Clearly the hyperplane is (bc)x + (ac)y + (ab)z +(0)u - (abc) = 0. Use the formula and get the desired result.
sand dove
Yes this seems correct!
analog trellis
David Widder making me think haha. At least I can try and use this technique in future problems where it seems obviously applicable. I suspect it might save some big calculations.
Because this was quite long computationally to compute.
Thank you for your help. 🙂
.close
devout snowBOT
devout snowBOT
Available help channel!
visual lark
Can someone help me spot where I lost the possible solution of 7pi /4
pseudo basin
were you asked to find f'(0) or were you asked to find all x such that f'(x) = 0...?
visual lark
All x within 0 to 2pi
pseudo basin
so you were asked to find all x in [0,2pi] such that f'(x) = 0?
visual lark
Yes
pseudo basin
then you were wrong to write f'(0) ? as if that was your goal.
pseudo basin
anyway, 3pi/4 + kpi with k=1 gets you your 7pi/4.
vale drum
Ive just learned about integrating using trig. substitution. The videos I watch explain by pointing out the similarity to pythagoras theorem and using this to figure out what to substitute, by sketching a right-angle triangle. But other than choosing which term matches up as the 'hypotenuse', the other term can take two different positions and give two entirely different substitutions for x. How is the side chosen?
e.g for sqrt(x^2 + a^2), you'd match this up as tan(theta) = x/a or tan(theta)=a/x
I've tried out both possibilities for the case the substitution is x=asin(theta) and got different answer. I couldve done it wrong, but dont think so.
devout snowBOT
Ive just learned about integrating using trig. substitution. The videos I watch ...
@vale drum Has your question been resolved?
devout snowBOT
@vale drum Has your question been resolved?
devout snowBOT
@vale drum Has your question been resolved?
devout snowBOT
@vale drum Has your question been resolved?
vale drum
Sigh
devout snowBOT
devout snowBOT
Available help channel!
graceful cedar
how can i solve this?
devout snowBOT
how can i solve this?
scarlet peak
What’s $0^1$?
woven radishBOT
lewis_f04
graceful cedar
0
graceful cedar
to the power of 1/x^2
woven radishBOT
lewis_f04
scarlet peak
$lim_{x \to 0} {cos x} = 1$ right
woven radishBOT
lewis_f04
scarlet peak
nope, you are wrong
Umm definitely correct
devout snowBOT
Umm definitely correct
scarlet peak
So then you have 1^inf therefore the limit is 1
devout snowBOT
Available help channel!
restive river
Anyone know how to find the coiffecent of kintic and static , in a pull question with just the weight of one block and the ramp measurements
devout snowBOT
Anyone know how to find the coiffecent of kintic and static , in a pull question...
devout snowBOT
@restive river Has your question been resolved?
restive river
.close
brave jolt
I need help in general trying to understand how to do quadratic functions for a study guide that’s literally due tomorrow morning
devout snowBOT
I need help in general trying to understand how to do quadratic functions for a ...
brave jolt
I need help in general trying to understand how to do quadratic functions for a ...
The study guide
I am really desperate to do this and I only have like 20 minutes before I have to go put my phone down stairs because of reasons
<@&286206848099549185>
I do remember quadratics during class somewhat and now it’s just POOF gone
devout snowBOT
@brave jolt Has your question been resolved?
vast violet
Elo i have this
devout snowBOT
Elo i have this
vast violet
so for this one i tried doing factor by grouping but its not working out for me idk
ohhhhhh i made a mistake nvm
Good or this one wrong?
thnx
ignore the first bit as i had made a mistake
weak cove
No that is not correct
woven radishBOT
AustinU
weak cove
It's best if you first factor this
Can you find two factors?
Or would you like help with that
woven radishBOT
AustinU
weak cove
Here's the hint
This factored form tells you where the graph crosses the x-axis
the x-intercepts
are x=-9 and x=6
Now secondly, because you know that this "x^2" is positive, it opens upwards
vast violet
yep
weak cove
So, in between the x-intercepts is the only place where it is less than 0
So what is the interval in between the x-intercepts then? that would be the answer
vast violet
so basically it is like -6 is less than 0 but 0 is less than 9 as it is in between?
or x i mean
weak cove
I'll try to clarify
In between the x-intercepts, the y-value of this function is less than 0. The x-intercepts of this function are x=-9 and x=6. So, in between x=-9, and x=6 the function is less than 0. Write that using interval notation to get your answer
vast violet
Hi so i got my slope as 1/6x
devout snowBOT
Hi so i got my slope as 1/6x
vast violet
and i am ready to plug in into y-y1=m(x-x1)
but it wants perpendicular
so how does 1/6x turn to a perpendicular slope
would i make it -6/1x?
devout snowBOT
@vast violet Has your question been resolved?
copper quail
You rearrange the equation to make y the subject. The gradient is the negative reciprocal of the the first line gradient.
Then use y-y1=m(x-x1)
devout snowBOT
@vast violet Has your question been resolved?
sleek estuary
where did -|a_n| come from?
devout snowBOT
where did -|a_n| come from?
dense knoll
they've taken it so that you can apply sandwich thm on the inequality
you know where |a_n| and -|a_n| tend to so you can find where the middle guy will tend to
devout snowBOT
devout snowBOT
Available help channel!
waxen harness
Question 2. I know about basic collision, SHM, adiabatic expansion.
waxen harness
I have tried but getting a different answer.
devout snowBOT
@waxen harness Has your question been resolved?
devout snowBOT
@waxen harness Has your question been resolved?
devout snowBOT
@waxen harness Has your question been resolved?
waxen harness
.close
final storm
How do I prove that the points are collinear without coordinates
devout snowBOT
How do I prove that the points are collinear without coordinates
@final storm Has your question been resolved?
final storm
<@&286206848099549185>
devout snowBOT
@final storm Has your question been resolved?
devout snowBOT
@final storm Has your question been resolved?
verbal robin
devout snowBOT
verbal robin
Please walk me through the steps to put c in terms of W and V
verbal robin
lol hello again
pearl moon
Nope buddy i am not tip top with electrostatics sorry i can't help but see you again
verbal robin
:0 ok bye lol
verbal robin
I’m in 10th the psat is next week
pearl moon
Oh all the best buddy
verbal robin
thanks TwT testing is the worst
pearl moon
Can I just go through capacitance and come back to you?
Or you will find some other person?
verbal robin
mmm I think imma close this up cause I’m going to lunch soon
pearl moon
Ok bye atb
devout snowBOT
devout snowBOT
Available help channel!
maiden zinc
p1 and p2 two projector
i have to show that q = p1 + p2 -(p2)o(p1) is a projector
so i have to do qoq = (p1 + p2 -(p2)o(p1) )o(p1 + p2 -(p2)o(p1) ) = q
but i don't know where to start because normally i just remplace the x byt the function but here how do we do
sand dove
use the fact that the linear functions space with + and o is a ring
so you can use distributive property
maiden zinc
like a "times"?
sand dove
yes
devout snowBOT
devout snowBOT
Available help channel!
azure granite
AD is parallel to BC
BAC is a right angle
length of AB = AC; DC = BC
it asks the angle of ACD
devout snowBOT
AD is parallel to BC
BAC is a right angle
length of AB = AC; DC = BC
it asks...
@azure granite Has your question been resolved?
azure granite
<@&286206848099549185>
devout snowBOT
@azure granite Has your question been resolved?
devout snowBOT
@azure granite Has your question been resolved?
devout snowBOT
@azure granite Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
wicked fractal
I really need help with this, I obtained the answers partially, but I would really appreciate a full explanation
devout snowBOT
I really need help with this, I obtained the answers partially, but I would real...
@wicked fractal Has your question been resolved?
wicked fractal
.close
wicked fractal
devout snowBOT
@wicked fractal Has your question been resolved?
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
long pasture
wicked fractal
would this help visualize the situation?
yes it does, but I'm still unsure of how to obtain that angle
long pasture
oh okay, lemme make some more markings
lol, you'll have to click on the picture to see the new markings
must be discord error
wicked fractal
nah i can see it fine
my only confusion is how do I convert this variable only problem into a numerical output
long pasture
for the ease of calculation, you can let the length of one side lets say AB, be 2a
wicked fractal
alr
long pasture
then OH will be a
wicked fractal
yea