yeah I think so
#help-27
vivid estuary
vivid estuary
but that wouldn't use the radius
radiant anvil
W=Fs for fr real
boreal helm
w=mgh+centripetal force x 2πr
vivid estuary
were probably gonna be integrating from 0 to 2pi right
radiant anvil
u just need force and displacement. the radius is not relevant
boreal helm
Bcz bro goes up and moves in a circle simultaneously
Listen his potential energy increases
So work is done
He rises by 20ft
radiant anvil
nvm use radius to find displacement
vivid estuary
is gravity acting as the vector feild here?
and him walking up the stairs is our curve navigating throught that feild?
radiant anvil
energy to move in a circle+potential energy from height gained
devout snowBOT
@vivid estuary Has your question been resolved?
thin geode
24a
woven radishBOT
thin geode
So my thinking was that the green area is 6 and white area is 3/2. i got a common factor of 1/4.
but this doesnt seem right because i use sum for geometric sequence and get 63/8
But right awnser is 819/128
<@&286206848099549185>
rose rock
but this doesnt seem right because i use sum for geometric sequence and get 63/8
Did that well but got a different answer(not the right answer either). Could you describe what did you in more detail?
thin geode
so
area of green rectangle is 8 and we remove the area of the white rectangle which is 2.
we get an area of 6. Then we do same between white and orange and get 3/2. then i divided 3/2 with 6 and got the ratio
which was 1/4, so equation was 6(1/4)^n-1
rose rock
Yep, same thing I got
thin geode
But wonder how it can be so high number
rose rock
Okay, I actually tried solving the 24b. I got 63/8 as well for 24a
thin geode
Okay, I actually tried solving the 24b. I got 63/8 as well for 24a
how was b?
6/(1/4) i reasoned but that wasnt right either
rose rock
how was b?
6 * (4/3)
thin geode
suppose to be 32/5
so i backtracked b and got 5/4 as ratio
but how does that make sense?
rose rock
Definitely doesn't
woven radishBOT
rose rock
did you try it on a)
Yh
thin geode
huh can you explain from beginning
rose rock
Ohhhhhh I'm so silly
thin geode
HUH
rose rock
The inner rectangle's side length is 1/4 of the outer rectangles side length
But the area is (1/4)^2 = 1/16
thin geode
The inner rectangle's side length is 1/4 of the outer rectangles side length
Which rectangle?
rose rock
Start with the outermost one: 6 x 2
rose rock
4 my bad
rose rock
The white rectangle area: 2 x 1
thin geode
Ya
rose rock
Then the shaded rectangle inside of it: 1 x 0.5
thin geode
Ya 1/2
rose rock
Compare the outermost area: 4x2 = 8 to the inner shaded rectangle: 1 x 0.5 = 0.5
0.5/8 = 1/16
thin geode
Oooh we never remove the 2 from the 8
rose rock
The ratios are still retained either way
thin geode
no because with 6 its smaller i think
rose rock
Assuming you do the same for the inner rectangle I mean
thin geode
Oh bruh
Why did i think 2-1/2 was 1/2 : (
That was why, yeah your right, ratio still the same
6/1.5 is 4 which means 1/4
Aight thanks bruv your a real one brudde
rose rock
No problem g
bold hornet
What would the formula to this fractal be? Can I find a formula to any fractal?
devout snowBOT
What would the formula to this fractal be? Can I find a formula to any fractal?
@bold hornet Has your question been resolved?
bold hornet
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@bold hornet Has your question been resolved?
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@bold hornet Has your question been resolved?
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lyric nacelle
What am I doing wrong?
devout snowBOT
What am I doing wrong?
lyric nacelle
I realize cos/sin=cot and I referance this
rustic jetty
what is cot(-5pi/6)?
lyric nacelle
1.732
rustic jetty
as an exact fraction, not an approximated decimal
lyric nacelle
1/(tan(-5pi/6))
rustic jetty
what is tan(-5pi/6)?
lyric nacelle
11pi/6 ?
rustic jetty
do you understand how negative angles work?
rustic jetty
$-\theta = 2\pi - \theta$
woven radishBOT
Dork9399
rustic jetty
so $-\frac{\pi}{6} = \frac{11\pi}{6}$
woven radishBOT
Dork9399
woven radishBOT
Dork9399
rustic jetty
as a positive angle
lyric nacelle
7pi/6
rustic jetty
so what is $\cot(\frac{7\pi}{6})$
woven radishBOT
Dork9399
rustic jetty
use your chart
rustic jetty
yes
lyric nacelle
But that's positive so that's wrong, right?
rustic jetty
But that's positive so that's wrong, right?
yes
any ideas on how we can find the other solution?
lyric nacelle
use 4th and 2nd quadrant?
rustic jetty
use 4th and 2nd quadrant?
keep going
lyric nacelle
7pi/6 has (-sqr3/2 , -.5)
We need one that has the same but a positive sqr3/2
or is it positive .5
rustic jetty
what are the coordinates of your other solution, 5pi/6?
thinking about those coordinates will help
just use your reference table
rustic jetty
yes
lyric nacelle
why does it say this is wrong?
rustic jetty
,w cot(5pi/6)
woven radishBOT
rustic jetty
,w cot(-pi/6)
woven radishBOT
rustic jetty
it should be easier for you to calculate it for cot now
devout snowBOT
rustic jetty
I DID IT Finally
ayy lets go
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quasi cove
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gloomy surge
Thats a fun question ahah
quasi cove
quasi cove
better now
gloomy surge
What information have you found so far on that
sand dove
The first one is to show f(0) = 0
showing f is injective can help a lot
as soon as you get f(0) = 0, you'll even get that f is bijective. And that should seal the trick pretty quickly
thin fern
as soon as you get f(0) = 0, you'll even get that f is bijective. And that shoul...
why does showing f(0)=0 mean it's bijective?
sand dove
why does showing f(0)=0 mean it's bijective?
||plug x = 0 back into the original equation||
quasi cove
(0, y) -> f(0 +f(y)) = f(0)+y -> f(f(y))=f(0)+y
thin fern
||plug x = 0 back into the original equation||
ngl I don't get it 😭
sand dove
ngl I don't get it 😭
||f(f(y)) = y, so f is bijective and f^-1 = f||
sand dove
(0, y) -> f(0 +f(y)) = f(0)+y -> f(f(y))=f(0)+y
yep. Can you now prove using "f(f(y))=f(0)+y" that f is injective?
thin fern
||f(f(y)) = y, so f is bijective and f^-1 = f||
Ohh I see
because f has an inverse it's bijective
quasi cove
(0, y) -> f(0 +f(y)) = f(0)+y -> f(f(y))=f(0)+y
with that i think F is Surjective
sand dove
with that i think F is Surjective
sure that works too
but you gotta prove it
like "for every y, y = f(x)"
tho... if you wanna prove f(0) = 0 you're gonna need injectivity, and one more thing
quasi cove
f(f(y))=f(0)+y; f(a)=f(b) -> f(f(a))= f(f(b)) -> f(0)+a = f(0)+b -> a=b, injective
sand dove
great
now
there is another property you can get from f
you haven't used the original equation fully
oh actually
going back to "f(f(y))=f(0)+y"
what happens now with a very specific value of y
quasi cove
i not understand how to continue
i test (x,0) and get f(x +f(0)) = f(x), i think have some system of equations here
sand dove
i test (x,0) and get f(x +f(0)) = f(x), i think have some system of equations he...
you can take this equation too, sure
but look
what did we just prove
quasi cove
bijective
sand dove
sure but in particular?
which property of bijectivity we said was the most important here
quasi cove
which property of bijectivity we said was the most important here
F, idk lol
sand dove
look up again
quasi cove
the zero
sand dove
?
sure
but which property I said was gonna be important
comes from bijectivity?
that you independently just proved?
quasi cove
f(0)=0
quasi cove
man you need to be clear, it really got to a point where I'm confused
quasi cove
and tell me what have we already proved
bijective
quasi cove
surjective and injective -> has only one function
sand dove
yes
surjective and injective
so
we also have f(x +f(0)) = f(x)
which property helps us simplify this?
sand dove
f(a) =0?
? no
we literally have 2 properties
surjectivity and injectivity
and we have f(x +f(0)) = f(x)
quasi cove
how i can figure how many equations using that?
quasi cove
yes, (0,0) give that
quasi cove
f(0)=0
quasi cove
i seee now
sand dove
so
now back to that original equation
f(x+f(y)) = f(x) + y
since f is bijective, we can find y such that f(y) = 1
I'll let you find more on your own...
quasi cove
I understand, but the question is, how can I find out how many functions there are, testing each number in the image?
sand dove
I understand, but the question is, how can I find out how many functions there a...
I gave you a big hint
sand dove
since f is bijective, we can find y such that f(y) = 1
use that y such that f(y) = 1
sand dove
f(x+f(y)) = f(x) + y
Apply it to the equation
then maybe you'll have a GOOD idea of what type of function f is
||linear||
quasi cove
if f(y) =1 -> f(x+1) = f(x)+y, and now what?
sand dove
if f(y) =1 -> f(x+1) = f(x)+y, and now what?
induction
compute f(0), f(1), f(2), and see the pattern... and then prove the pattern...
quasi cove
if x=k, constant, f(k +f(y)) = f(k) + y; k+f(y) = z, a variable and, f(k) is constant with y a variable; f(z) = f(k) + y ; and that is a linear equation
correct?
sand dove
right now this doesn't make much sense
if x = k constant
since y is constant too
(it's the only y such that f(y) = 1)
oh you didn't use that
still doesn't make sense
if z is your variable
then y has to vary in terms of z
so f(z) = f(k) + (something that varies in terms of z)
doesn't mean much
anyways
did you compute f(0), f(1), f(2)?
quasi cove
ok, teach me how i use that, i cant find the value of y that f(y) =1
and for f(y=y2) = 2, f(x+2)= f(x) + Y2
and that way i cant get anything
sand dove
you don't need the value of y
y is constant and unknown, we don't need its specific value
just
find f(0), f(1), f(2) in terms of y
sand dove
if f(y) =1 -> f(x+1) = f(x)+y, and now what?
and this
quasi cove
but y changes for f(y) = 1 is a different y that f(y)= 2
sand dove
we said
y is a constant
the ONLY constant
such that f(y) = 1
so sure
there might exist a different number such that f(that number) = 2
or something else
but that's not what we're interested in right now
sand dove
if f(y) =1 -> f(x+1) = f(x)+y, and now what?
we have this formula
and we're gonna use it
to compute f(0), f(1), f(2), ...
(well you already know f(0))
quasi cove
f(0) = f(x+1) -> x= -1 -> f(-1) + y = f(0) = 0
sand dove
f(0) = f(x+1) -> x= -1 -> f(-1) + y = f(0) = 0
yeah that's the only unnecessary thing to do
you know the value of f(0)
yep you can get f(-1) if you even want to
it can help you reinforce the pattern
sand dove
f(0) = f(x+1) -> x= -1 -> f(-1) + y = f(0) = 0
so f(-1) = ?
quasi cove
y= -f(-1)
quasi cove
wait, f(1) = f(x+1) -> x=0; f(1) = f(0) + y -> f(1) = y and f(2) -> x=1 -> f(2) = f(1) +y -> f(2) = 2y
f(-1) = -y ; f(1) = y ; f(2) = 2y
quasi cove
f(a) = ay
quasi cove
idk how to do that
sand dove
never done induction proofs?
quasi cove
I already did it, but it's super late in my country and I'm going to assume that's it
quasi cove
never done induction proofs?
It's been proven that this is the case, how does it help to find out how many functions there are? Is there only one?
sand dove
It's been proven that this is the case, how does it help to find out how many fu...
once you've shown f(a) = ay
only need to find the possible y...
quasi cove
ok, the possible y is 1
quasi cove
I don't understand, to me it seems like y=1 is the only value
quasi cove
is that the only one?
i think yes
Help me to complete that, that is the last question i need to do
<@&286206848099549185>
gloomy surge
I don't understand, to me it seems like y=1 is the only value
Yes it is, because a -> ay is bijective if and only if y = 1 🙂
So you have concluded that f(a) = a, so how many functions does it decribes ahaha
quasi cove
So you have concluded that f(a) = a, so how many functions does it decribes ahah...
One?
quasi cove
And the identity works as id(x + id(y)) = x + y = id(x) + y
Oh god all that work to only one function
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hasty lynx
can anyone help me with this I dont know the approach for this particular type of question? also, what is the name of these kinds of questions so that I can get further practice
devout snowBOT
can anyone help me with this I dont know the approach for this particular type o...
olive snow
What about f(3) ?
karmic umbra
Yea
karmic umbra
Oh wait nvmd
olive snow
Cuz f(5) = f(f(3) = f(f(f(2)))
hasty lynx
yea
karmic umbra
f(f(f(2)))
feral agate
f(5)=f(f(3))=f(f(f(2)))
olive snow
Yeah
hasty lynx
then we have to do it till f(777)?
karmic umbra
=4
olive snow
then we have to do it till f(777)?
No
feral agate
then we have to do it till f(777)?
No ofc not
hasty lynx
okay
olive snow
We will discover a pattern
feral agate
You need to identify a pattern and then ideally prove it
olive snow
So f(4) ?
broken ore
olive snow
Indeed
hasty lynx
f(7) is 9
olive snow
So ima write all the answers and search for pattern
olive snow
2,3,5,4,7,9,6,11,13
hasty lynx
alright
hasty lynx
every 3 terms?
every 4 terms*
olive snow
So if we need to write it as sequences ?
olive snow
How would you do it ?
hasty lynx
so it is arithmetic progression right
for even numbers, they appear at indices 1,5,9,13,..
olive snow
Yeah but depends on the parity of something
hasty lynx
so the indices is 1 + (n-1)*4
we plug in 777
we see that
n= 194
which means that it is the 194th number of these consecutive even numbers
so it should be 388
olive snow
No cuz its 1,4,7,10 ...
hasty lynx
wait
olive snow
2,3,5,4,7,9,6,11,13
Look
hasty lynx
from my calculations
f(1) = 2, f(2) = 3 f(3) = 5 f(4) = 7 f(5) = 4
olive snow
1,4 7,10
olive snow
Wait
But you cant get f(4) without f(5)
So you have to order them into the order in which they were obtain
olive snow
But how you get the 4th term ?
olive snow
Okay maybe, it confused me, since its recurrent i used to put them in order of the obtained value
hasty lynx
He is at the 388th rank ?
it is 194th rank
1 5 9 13 17 21 ,...
so it should be
1 + (n-1) * 4
plug in 777
we get the value of "n"
which is 194
so it is at the 194th position
take 194 times 2
we get the answer
388
.close
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alpine hull
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alpine hull
I dont get what to do after 8x +2y =3600
olive snow
I dont get what to do after 8x +2y =3600
Fence is the perimeter so add them to get total
autumn kite
so ur function is 4xy
alpine hull
okay
alpine hull
ohhh ok
autumn kite
so area is 4x (1800-4x)
differentiate this
i dont think i need to help more
@alpine hull did u get it
autumn kite
yeah
alpine hull
huh
autumn kite
yeah
alpine hull
we got y = 1800-4x
alpine hull
HUH
alpine hull
the expression is 4x(1800-4x)
i expanded this
autumn kite
ok
alpine hull
so then its 7200x -16x^2
autumn kite
yeah
autumn kite
yeah 2nd derivative is negative
alpine hull
theres nothing to plug it in
restive river
Hey guys, I am a French 11th grader going to 12th grade in September, I am very skilled in math, but my knowledge doesn’t extend past 11th grade, integrals seem like a very interesting and wide subject, if someone could educate me about them I would highly appreciate it
autumn kite
its that easy?
yeah lol
alpine hull
wait so if second deriv
is just a whole number
with no variables
u can just use that
alpine hull
concave down means local max right
alpine hull
wait if all
x values
would be local max
then couldnt our number be 224
and still be right?
autumn kite
no i meant there is only 1 maxima
wait
i think language barriers exist
hear me about
im saying that
there is only 1 maxima
for the whole function
which happens at x = 225
@alpine hull
autumn kite
they are asking the dimensions of the pen
such that the whole area is max
so basically x and y values
alpine hull
so all pens together?
autumn kite
yeah
alpine hull
i got y = 900
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ionic prism
how to find the area under this region using double integrals in multivariable calc?
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how to find the area under this region using double integrals in multivariable c...
@ionic prism Has your question been resolved?
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@ionic prism Has your question been resolved?
ionic prism
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karmic horizon
how would i integrate this
devout snowBOT
how would i integrate this
karmic horizon
i tried using some trig identities but im still not sure
karmic horizon
wait
faint hearth
how would i integrate this
Simplify 2sin²(x)cot(x)
foggy tusk
Just
karmic horizon
death
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restive river
Integrate the following
Integrate sqrt(sec^2x+1) dx
devout snowBOT
Integrate the following
Integrate sqrt(sec^2x+1) dx
twilit comet
dont
polar chasm
are you sure it's +1?
lost laurel
Does it even have a closed front,form if it’s +1
polar chasm
,w integrate sqrt(sec^2(x) + 1)
woven radishBOT
polar chasm
Does it even have a closed front,form if it’s +1
well, it does...
lost laurel
Maybe x=arcsec(y)
polar chasm
idt that works
restive river
Can someone just gimme a sort of a hint or something to start i mean if this is the solution i just wanna how i should start
polar chasm
wolfram's first substitution is u = sec^2(x)
lost laurel
Maybe x=arcsec(y)
This should work
restive river
Alright lemme try myself now
Thanks for the help
polar chasm
This should work
what would dx become?
lost laurel
Oh right
polar chasm
Alright lemme try myself now
Thanks for the help
Btw if this integral is part of some larger problem, its highly probable that you've made the mistake along the way. So in that case, send the original problem
devout snowBOT
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edgy nacelle
can i have help with viii) please
devout snowBOT
can i have help with viii) please
cold bone
can i have help with viii) please
what you are supposed to find?
haughty horizon
i guess proof the statement
edgy nacelle
yeah proove viii
haughty horizon
do you know how to find the point on a line closest to another point?
haughty horizon
ok the idea is to find another line through the point and through your line so that its 90° thats the shortest distance to from the point to the line
now you just need to find that line and then calculate the collision between that line and your original line to get the closest point
then if you want to reflect that point just add the distance onto the line on the other side of the 90° and you have the reflected point
you get the idea?
red is your y and your point would be 0,0
the green lines are just some other distances you can ignore that
edgy nacelle
ok cool that makes sense but y=mx so would it not go through 0,0
or is that the green lines
haughty horizon
yeah that was just for the idea
edgy nacelle
ahh ok so
i would have y=mx
then i need to do a perp line that goes through (1,0)
and this perp line has gradient -1/m
and i can come up with an equation for it with
straight line equation
then what
haughty horizon
yeah so what would it be?
edgy nacelle
y=-1/m(x-1)
haughty horizon
you got it?
cold bone
but im getting x=1/m^2+1
Yeah, it is correct
edgy nacelle
ok
edgy nacelle
yeah
haughty horizon
yeah thats your x coordinate now you need the y part
edgy nacelle
y=m/m^2+1
haughty horizon
yup
haughty horizon
so the intersection point is (1/m^2+1, m/m^2+1)
edgy nacelle
yup
haughty horizon
we have our original point 1,0 and seek lets call it x', y'
and we know (1/m^2+1, m/m^2+1) is in the middle of it
edgy nacelle
what do u mean in the middle of it
haughty horizon
we want to mirror it to the other side
and the intersection is right in the middle in between
haughty horizon
ok do you know how to calculate the middle between two points x,y and x',y'
e.g. 2,3 and 5,9
haughty horizon
plus but yeah
haughty horizon
so we have our original point 1,0 and the middle (1/m^2+1, m/m^2+1) and we seek x',y'
we know the middle between 1,0 and x',y' can be calculated like above
and the result is (1/m^2+1, m/m^2+1)
then solve for x' and y'
rose rock
can i have help with viii) please
You could do this with relative ease using vector projection
haughty horizon
got it?
edgy nacelle
hm not yet
so we have the middle
sorry this sounds dumb
and this is the halfway point
basically that’s what we have
and we need the full way
haughty horizon
yeah so try to find the middle for 1,0 and x', y' like with the formula above
edgy nacelle
did we not just find the middle
rose rock
edgy nacelle
haughty horizon
plus but yeah
edgy nacelle
would it be minus or plus
haughty horizon
x'+1
edgy nacelle
cos it is going backwards when u draw the graph
rose rock
opps my bad
devout snowBOT
haughty horizon
np 🙂
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fleet moth
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fleet moth
I just need a quick solution
lusty sapphire
I just need a quick solution
!status
devout snowBOT
I just need a quick solution
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
wicked turtle
write out an equation that captures what you are given
it should just involve p (the probability of heads on a single toss)
then solve for p
fleet moth
Huh
lusty sapphire
So, can you help
I would let p be the probability of heads, and 1-p be the probability of tails, and then I would draw a probability tree to get the probability of the four outcomes it mentioned : 3 heads, 3 tails, 2 heads one tails, and one heads two tails
fleet moth
I would let p be the probability of heads, and 1-p be the probability of tails, ...
What would that do
wicked turtle
Huh
P(exactly 3 heads) + P(exactly 3 tails) = P(exactly 1 head) + P(exactly 2 heads)
work out what each of those four terms is
and then solve
lusty sapphire
P(exactly 3 heads) + P(exactly 3 tails) = P(exactly 1 head) + P(exactly 2 heads)
It would let you solve this
fleet moth
But how would I know the probabilities
wicked turtle
the coin tosses are presumably independent
so it's a bernoulli trial
with unknown parameter p = probability of heads on a single toss
fleet moth
This sounds rly complicated
fleet moth
it's really not
Then what's the answer...
wicked turtle
i'm not gonna just give you the answer, that's now how it works
happy to guide you to the answer tho
fleet moth
How to do a bernoulli trial
wicked turtle
start with the easy ones
suppose p = the probability of heads on a single toss
then what is P(exactly three heads)?
fleet moth
p^3
fleet moth
(1-p)^3
wicked turtle
right
ok cool, that's half the equation done
for reference: P(exactly 3 heads) + P(exactly 3 tails) = P(exactly 1 head) + P(exactly 2 heads)
now how about P(exactly 1 head), how can you calculate that?
fleet moth
p
wicked turtle
no it's more complicated than that
there are actually three outcomes involved there
fleet moth
😕
wicked turtle
it could be any one of:
HTT
THT
TTH
"exactly 1 head" means "exactly 1 head in 3 attempts", not just 1 head in 1 attempt
wicked turtle
yea that's the probability for any one of those outcomes
HTT for example
but there are three possible outcomes with exactly 1 head
so you need to sum those probabilities
fleet moth
for reference: P(exactly 3 heads) + P(exactly 3 tails) = P(exactly 1 head) + P(e...
p^3+(1-p)^3=3(p(1-p)^2+p^2(1-p)) ??
wicked turtle
almost
on the right hand side each of the terms should be multiplied by 3
because each one of these has probability p(1-p)^2:
HTT, THT, TTH
fleet moth
K
wicked turtle
so when you add them up you get a factor of 3
ok cool so now you just have a polynomial to solve
the bad news is that it's 3rd order
fleet moth
K thx
wicked turtle
those are usually not much fun
the good news it that the p^3's will all cancel
so it's really a quadratic in disguise haha
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lone stirrup
.
lone stirrup
In here I have to find a equation for a
So for now I've filled in all variables
A = (2+2)*2 / 2
glacial wyvern
what have you tried?
lone stirrup
A = 4
That's how far I've come, my solution that I've not found yet, but tried is to backtrack the number
small jackal
In here I have to find a equation for a
What?
glacial wyvern
If you'd like a problem-solving approach then notice that you get A by
- taking the quantity a
- adding b to it
- multiplying by h
- dividing by 2
- wow now you have A
To get from A to a, you can just do the steps backwards, reversing them
glacial wyvern
very good!
lone stirrup
that's actually a very logical approach of solving it
lone stirrup
Sometimes it's hard to see the trees through the forest once you've come to a road block
But thanks! I'll try to apply it once I get such a question again
glacial wyvern
very cool! well done! ^^
lone stirrup
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plush field
I have a question to transforms. I defined myself a differential operator $(\nabla \times \vec{e})^T=\left(\begin{matrix}0&-\partial_z&\partial_y\partial_z&0&-\partial_x-\partial_y&\partial_x&0\end{matrix}\right)$ that operates on scalar Funtions $w_i : \mathbb{R}^3\rightarrow\mathbb{R}$. How do I have to transform the operator under a transformation of the form $r = \vec{a} + B \hat{r}$ ?
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woven radishBOT
Felix.5
plush field
I want to know how $(\nabla \times \vec{e})^T w_i$ is related to $\widehat{(\nabla \times \vec{e})^T} \hat{w_i}$
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final mica
So far I’ve gotten the formula average speed = (distance uphill + distance on flat ground + distance downhill)/(time uphill + time on flat ground + time downhill)
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So far I’ve gotten the formula average speed = (distance uphill + distance on fl...
final mica
I’ve also assigned the distance f from the cafe to the boba shop as X so the total distance is 2x
I don’t really know what to do from here
tough parrot
So far I’ve gotten the formula average speed = (distance uphill + distance on fl...
i thought the average speed of the entire round trip is same as the speed going from cafe to boba shop
unless i am missing something ??
depends on how big the downhill and the uphill ._.
final mica
depends on how big the downhill and the uphill ._.
It doesn’t say :(
final mica
i thought the average speed of the entire round trip is same as the speed going ...
She has different speeds when walking in uphills, flat grounds, and downhills
tough parrot
She has different speeds when walking in uphills, flat grounds, and downhills
look the formula doesn't change, as y said...
(distance uphill + distance on flat ground + distance downhill)/(time uphill + time on flat ground + time downhill)
or
you could also add the speeds on each condition and divide by 3.
which is (100 + 120 + 150 )/3 = 123,3... that should be the speed for going and for going back and for the entire round...
tough parrot
She has different speeds when walking in uphills, flat grounds, and downhills
but overall, when she go back, those speeds doesn't change...
final mica
look the formula doesn't change, as y said...
(distance uphill + distance on ...
Uhhhh
Well
The hint says
tough parrot
🥲
final mica
The answer is not 125 meters per hour, nor is it 123 1/3 meters per hour
tough parrot
thats the hint ? 🥲
sharp axle
I think the fact that the required speed is roundtrip is key
Maybe you get some cancellation between downhill and uphill
Because one way it's up but when coming back it's down
tough parrot
that wouldn't make sense... you can't cancel because she went the opposite way... (i think, kinda confused me there xd)
it depends on distance. and speed on each condition...
overall she went 2 uphills 2 downhills and 2flat ground...
altho the problem doesn't mention the route condition from cafe to boba. ?
tough parrot
altho the problem doesn't mention the route condition from cafe to boba. ?
@final mica
final mica
altho the problem doesn't mention the route condition from cafe to boba. ?
Ya
It doesn’t
tough parrot
x)
final mica
.
tough parrot
trick question with the answer of 0m/s as overall she from the start to the difference positions is 0 ? x)
how could we know xd
unless i go to google maps and check the conditions of all routes from all cafes to all boba shops x)
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final mica
No
orchid sierra
If we assume the ground was flat the whole trip, then 2*(120m/hr)/2 = 120m/hr
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final mica
I think I figured it out
But
I don’t know why it works
Also is it possible to do latex here
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@final mica Has your question been resolved?
final mica
Ok so I know how to do it but I don’t know why it works
And that’s kinda what I need to know
So I know that you can use the harmonic mean formula to find the rate
tough parrot
So I know that you can use the harmonic mean formula to find the rate
and how can you use it ?
chrome heron
trick question with the answer of 0m/s as overall she from the start to the diff...
average velocity would be 0m/s, not average speed
tough parrot
average **velocity** would be 0m/s, not average speed
yeah you're right then, but other than that, the speed here depends on how big the uphills and downhills and flat grounds from cafe to boba shop, which it doesn't say that...
warm karma
the distance uphill is equal to distance downhill
i mean if there is answer it is 120 meters per hour
because for the answer to exist it should be independent of how much hilly and flat sections there are
which means you can assume it's all flat
but every meter of hill would take (1m / 100m/h + 1m / 150 m/h)/2 = (3 + 2)/600 h = 5/600 h = 1/120 h which means the average would in fact be 120 m/h
So the answer does in fact exist
tough parrot
the distance uphill is equal to distance downhill
how did u know that ? unless u meant the distance of uphill when going is same as the distance downhill when returning
warm karma
how did u know that ? unless u meant the distance of uphill when going is same a...
because you return to the same point (that has the same height). But if you don't like that you can always say that the path has sections of total length A going uphil, sections of total length B flat, and sections of total length C going downhill
but going back uphill and downhill are reversed
so you have A+C uphill, C+A downhill and 2B flat
and then you can calculate the average
And A, B, C actually all cancel out
tough parrot
lemme show u an example...
lets say the route condition from cafe to boba is just downhill,, then the speed will be 150, and when she is returning the route will be an uphill, and the speed will be 100
the average speed will be (150+100)/2 = 125
lets say the route is just flat, then in returning it will be flat as well, and so same average speed = 120
lets say 2 uphills and 1 downhill and a flat ground when she went from cafe to boba shop,
and in returning it will be 1 uphill and 2 downhills and a flat ground
and so the average speed will be
(150 x 3 + 100 x 3 + 120 x 2)/6 which is 123,75
there are 3 possible average speeds on this problem. and 2 more possibilities
lets say 1 uphill and 1 flat ground
in total it will be 1 uphil 1 downhill and 2 flat grounds
(150 + 100 + 120 x 2)/4 = 122.5
lets say 1 uphill and 2 flat grounds
(150+100+120 x 4)/6=121.66
actually there are infinite possiblities @warm karma
warm karma
lemme show u an example...
lets say the route condition from cafe to boba is jus...
no it won't be
that's not the formula for the average speed
average speed = total distance / total time
tough parrot
oh, apologies
warm karma
np
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restive river
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restive river
what does the question want
a lot of chemical things are said i dont like chemistry
someone explain please
frozen aurora
let N be the number of isotopes of carbon-14 originally
this means that after some time t, we have 0.0625*N isotopes of carbon left
small jackal
a lot of chemical things are said i dont like chemistry
Do you know about the formula $N=N_0 $ (½)^ ${t/t_½}$
restive river
Do you know about the formula $N=N_0 $ (½)^ ${t/t_½}$
what
this is the way the ms solved it
i dont think what u said is in our syllabus
if it is im cooked
woven radishBOT
The procrastinator💯
Do you know about the formula $N=N_0 $ (½)^ ${t/t_½}$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.49 Do you know about the formula $N=N_0 $ (½)^
${t/t_½}$
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
restive river
let N be the number of isotopes of carbon-14 originally
number of isotopes?
tough parrot
its radioactive thingy...
he meant N the number of C14s present if i am not mistaken
small jackal
N0 is the number of C14 at the beginning
tough parrot
like all atoms of C14s
small jackal
N is the the number of c14 after time t
tough parrot
N is the the number of c14 after time t
altho in the answer they did explain it without using N
restive river
wait i thought that there was 1 isotope that had a half year of 5600 year
btw what is a half year
tough parrot
wait i thought that there was 1 isotope that had a half year of 5600 year
at the beginning there are N atoms of C14
after 5,600 years.. there are N/2 atoms of C14
restive river
at the beginning there are N atoms of C14
after 5,600 years.. there are N/2 ato...
ohhh
tough parrot
btw what is a half year
the necessary time for the object to lose half its atoms..
or as i say from N atoms to N/2 atoms
restive river
damnn
small jackal
btw what is a half year
The time it takes for half of a sample of radioactive substance to decay
tough parrot
yup
restive river
how should i put all of that in an equation
small jackal
we have 6.25% left right?
Yes N=0.0625N0
restive river
ohhh i kinda get it
so 100/2/2/2.... until its 6.25
then the times u divided by 2 multiply by 5600
but isnt there an easier way?
tough parrot
hhhh okay xd 👌
restive river
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halcyon depot
Hii can anyone help me with this lim
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Hii can anyone help me with this lim
tough parrot
u can try one thing which is annoying
multiply by the conjugate of the upper part
from both sides if u know what i mean
OR
i advice u use hopital
since the limit of the upper part is 0 and the bottom part is also 0
just use hospital rule @halcyon depot
basically its the same limit, but the derivative of the upper part and second part
halcyon depot
Lik that?
halcyon depot
since the limit of the upper part is 0 and the bottom part is also 0
It's not allowed 😔
To use the hopital rule
tough parrot
then just use its demonstration
don't mention hopital just use its demonstration (2 extra lines thats it)
halcyon depot
don't mention hopital just use its demonstration (2 extra lines thats it)
How , can u show me??
I'm really stuck I don't see anything...
halcyon depot
wait lemme look at this... it shouldn't be 0
Yeah but it always comes to 0
I just want that numerator to be different than 0 then it's going to be so easy...
tough parrot
Lik that?
in the last part...
its not 0.. its still unindentified x)
if i am not mistaken...
ok lemme try hopital wait
halcyon depot
in the last part...
its not 0.. its still unindentified x)
Yes I'm stuck in that point
I Don't know why I wrote that
'=0' in the end 😭
tough parrot
i think my solution is bit long x)
i was gonna use hopital twice xd, i don't think that's how it's done even tho its possible yet very long ...
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halcyon depot
i was gonna use hopital twice xd, i don't think that's how it's done even tho it...
Can I see how ???
tough parrot
i am doing it wait
halcyon depot
Kk
tough parrot
sorry this is all i could've thought of xD
7/4
but yeah no hopital mentioned just the demonstration
(i used the demonstration twice, i didn't expect this function will be this wierd)
@halcyon depot
halcyon depot
I'm going to review it now
Btw Ty so much
tough parrot
ok yw... i believe there is another way (idk it), cuze hopital is just the last resort ._.
halcyon depot
ok yw... i believe there is another way (idk it), cuze hopital is just the last ...
Yeah definitely
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humble gazelle
So my doubt so far is whats the difference beetwen A and B? Because i think in B i would need to put 4 since is the number up in the Y also yeah im spanish so im sorry if it takes me a bit to understand but ik english ^^
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So my doubt so far is whats the difference beetwen A and B? Because i think in B...
iron sun
So my doubt so far is whats the difference beetwen A and B? Because i think in B...
What did you answer for a)?
frozen aurora
between these two?
humble gazelle
What did you answer for a)?
I havent, idk how to do it but based on the video i watched i thought B would be 4 but dont know how to do A
humble gazelle
between these two?
Yeah
frozen aurora
I havent, idk how to do it but based on the video i watched i thought B would be...
b is 4
this should give you a hint as to what a is
iron sun
So for b) that is correct, when we talk about limits, we avoid what happens precisely at the point of interest, but rather around it
humble gazelle
Yeah that dot confuses me, like idk what it means but also i may have forgot since i havent been able to go to school in a while, like for me A and B look similar
humble gazelle
So for b) that is correct, when we talk about limits, we avoid what happens prec...
What that means? Like i know the point of limits is getting infinitivly close to a number but never reaching it but that you get the number even if you dont reach it
iron sun
While in a) you’re asking what happens precisely at x = 0.
The value f(0) is the functions output for x = 0
humble gazelle
So in A it asks where the point its actually but on B you just need the answer of where the lines go infinite close to?
iron sun
What that means? Like i know the point of limits is getting infinitivly close to...
So limits intuitively like you say is getting closer to a number without reaching it, the need to specify that we don’t reach it is because we don’t care what happens precisely at that point.
Take for example the expression x/x.
In this case the expression is undefined for x = 0, but the limit let’s us reason about what happens around this problematic point, since we don’t want to directly look at x = 0
humble gazelle
So i did this to kinda explain what i got
In A we take the 1 since its where the line is
But in B we take where the line gets infinitily close to?
humble gazelle
So limits intuitively like you say is getting closer to a number without reachin...
I never heard the expression x/x i think and i think i kinda get the last part
iron sun
Yeah, so for B look at what happens around the point you’re interested in.
Imagine looking closer and closer around the point x=0, and seeing what values we get
humble gazelle
I think i understand it, i'll try to do more excercises and if i get stuck i'll ask again, ty ^^ appreciate the explanation and not only the answer
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cold bone
What are the different methods to solve this problems?
devout snowBOT
What are the different methods to solve this problems?
iron sun
One is by considering a quartic polynomial that satisfies the first 4 conditions
cold bone
By expanding all the parentheses
hmph... okay I guess
iron sun
That’s why the polynomial method is probably the best in this instance
cold bone
That’s why the polynomial method is probably the best in this instance
Yeah but I was curious if there is any other method
tyvm
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