now that since all edges are of the same length
#help-27
wicked fractal
yea alr
got that far
long pasture
then using cosine, we can find the angle👍
(tbh, i didnt do the math, so i don't know the final answer :P)
wicked fractal
DV = CV = BV = AV = y
VH = sqrt(y^2*-a^2)
VOH = 90 degrees
but thats as far as I get
long pasture
lets see
wicked fractal
then using cosine, we can find the angle👍
then why I applied the cos rule as you suggested, I get a/(sqrt(y^2-a^2)
long pasture
now that since all edges are of the same length
Note: ALL edges
including DV,CV,BV,AV
get it? XD
wicked fractal
no
I'm a very slow person 
wicked fractal
AB=BC=CD=DA=VA=VB=VC=VD=2a
one of my only super reactions
🙂
thanks a lot man
byeee
.close
low fossil
Is this proof by induction fallacious?
T(n) = T(n-1) + n. Prove that T(n) = O(n^2)```
loud light
if we have a group, call it G that is not necessarily finite, and we have that H is a subgroup of G and |G:H|=m, can we conclude that G is finite since |G:H| would be infinite if G was infinte?
devout snowBOT
if we have a group, call it G that is not necessarily finite, and we have that H...
loud light
from the definition, |G:H|, which is the number of (left) cosets of H in G. this doesnt make intuitive sense to me as H is finite
long fog
from the definition, |G:H|, which is the number of (left) cosets of H in G. thi...
H is finite?
loud light
hhhhhmmmmm
not stated, so not necessarily
So the whole question is.
Let G be an abelian group(possibly infinite) with subgroups H and K such that H is a subgroup of K. Suppose |G:K|=n and |G:H|=m where n|m. Find |K:H|.
all i need to finish the proof is to prove that G is finite
if it is finite, then I can use Lagranges theorem and be done
Note: I used the third isomorphic theorem, simply stating for clarity
devout snowBOT
@loud light Has your question been resolved?
devout snowBOT
long fog
So the whole question is.
Let G be an abelian group(possibly infinite) with subg...
Think of Z
long fog
all i need to finish the proof is to prove that G is finite
That's not a proof question
devout snowBOT
Available help channel!
half cape
calc help
half cape
I found h''(x) = f''(g(x)) * (g'(x))^2 + f'(g(x)) * g''(x).
Since f is concave down, that means f''(x) < 0. So does that mean that f''(g(x)) is < 0?
<@&286206848099549185>
digital knot
Yes it does
half cape
hmm
also
it says f is increasing
So we know that f''(g(x)) is < 0 and (g'(x))^2 > 0 so the product of that is negative. Also, f'(g(x)) > 0 and g''(x) < 0 so the product of that is also negative. Since the sum is negative we have shown h''(x) < 0 and thus concave down.
My only concern is that is f'(g(x)) > 0 or >= 0?
digital knot
It also says the first derivative is nonzero
digital knot
I see your concern. I don’t think there are any functions meeting the criteria where that actually happens, but really you don’t need to check
half cape
Because for this part of h''(x): f'(g(x)) * g''(x) would I then say that the product is always < 0
digital knot
Break it down into two cases, f’(g(x)) = 0 and f’(g(x)) > 0
half cape
because if f''(x) >= 0 then this product would be 0
digital knot
Right, the first term is less than 0 and the second term is at most 0, so the sum is less than 0
half cape
Yes but
lol
this question is so dumb
u get what my problem is tho right?
I don't want to say that f'(g(x)) * g''(x) is < 0
cuz f'(g(x)) could be 0
which would make the product 0
digital knot
Right. But that’s not the only part of h(x). I gtg hope you figure it out
I meant h’’(x)
half cape
<@&286206848099549185> can anyone help?
lusty sapphire
cuz f'(g(x)) could be 0
No it can't
The problem states that f' is never zero
Do not consider f'=0
Perfect answer right here
half cape
calc
half cape
,w points of inflection x\left(\ln\left(x^{2}\right)\right)^{\frac{2}{3}}
woven radishBOT
half cape
,w intervals increasing x\left(\ln\left(x^{2}\right)\right)^{\frac{2}{3}}
woven radishBOT
half cape
,w what is y when x = 0.9 x\left(\ln\left(x^{2}\right)\right)^{\frac{2}{3}}
woven radishBOT
half cape
,w intervals decreasing x\left(\ln\left(x^{2}\right)\right)^{\frac{2}{3}}
woven radishBOT
lusty sapphire
@half cape are you trying to find an example function?
half cape
No I have this function:
Don't know where is it decreasing
Can't seem to find that out
lusty sapphire
and did you calculate f'' at those points yet?
lusty sapphire
x = 1/e^2/3
e^(-2/3)
half cape
and did you calculate f'' at those points yet?
that isn't need to check increasing or decreasing
only first derivative is
lusty sapphire
Oh duh I did it backwards
You are right
No wait..
f'=0 will give you critical points, local max or min
Intervals between critical points will be either increasing or decreasing
use f''>0 or f''<0 to determine increasing or decreasing between critical points
lusty sapphire
it has decreasing points
half cape
hmm so is wolfram trolling?
half cape
which decreasing intervals did u get?
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.
lusty sapphire
sorry
half cape
I got between -1 and 1 not inclusive
lusty sapphire
best advice I can offer is ^(2/3) is being interpreted as a complex root
do cbrt(^2) to keep it as a real root
This is a tricky problem
Lots of parts
devout snowBOT
@half cape Has your question been resolved?
half cape
.close
devout snowBOT
devout snowBOT
Available help channel!
scenic surge
devout snowBOT
scenic surge
for this series
im suppose to use
limit comparison
but
idk what
b_n is suppiose to be
apparently the answer key says b_n = 1/n^(3/2)
wanton temple
you're asked to show whether this series is divergent or convergent, right?
or are you to compute the actual values?
scenic surge
you're asked to show whether this series is divergent or convergent, right?
yes
and i am to use limit comparison test here
but like
I dont even know how to get started because
I dont know what $b_n$ is here
woven radishBOT
Calc II Victim
scenic surge
apparently the answer key says b_n = 1/n^(3/2)
and I dont know how they got this either
sick fulcrum
try comparing it to 1/n^2 lol
scenic surge
but why 1/n^2
sick fulcrum
if that doesnt work tune the p in n^p
scenic surge
what do u mean by tuning?
sick fulcrum
Like mess with it
scenic surge
ngl doe Idk how I would get to 1/n^(3/2) from there doe
sick fulcrum
If you calculate a few terms you see it would converge
So you just find a few terms of like
1/n^2 and friends
Yeah if 1/n^2 doesnt work I'll go to 1/n^(3/2) as my next try
Or 1/n^(5/2)
scenic surge
OHHH
wait so like
lets say I were to start with
1/n^5 right
not for this series
but like sum other series
and that didnt work
then I would try
1/n^4.5 and 1/n^5.5
as my next b_n right
sick fulcrum
Usually I start with 1/n^2 because its the first thing I know that converges
1/n doesnt
wanton temple
mfw basel problem
scenic surge
what that mean
scenic surge
Usually I start with 1/n^2 because its the first thing I know that converges
I get u now
tysm
sick fulcrum
np
wanton temple
what that mean
just the name of the sum 1/n^2, which was proven by euler to converge to pi^2/6
sick fulcrum
No
You get used to it
Kmm if you're not going to contribute to the help don't randomly talk
sick fulcrum
Yeah of course
sick fulcrum
Calculate a few terms and find some other series to look at
scenic surge
Calculate a few terms and find some other series to look at
wont the limit always reach infinite still
no matter what I compare it with
sick fulcrum
What
scenic surge
(a_n * 1/b_n)
sick fulcrum
What is a_n
scenic surge
last question
.
sick fulcrum
I have to go now sorry
But you actually have the tools you need to figure it out yourself
median stratus
can someone help me with this question?
devout snowBOT
can someone help me with this question?
wispy hare
can someone help me with this question?
since they gave you 2 roots, you can directly let b and c be equal to them
that'll make the equations easier to solve
median stratus
yes! i have done that
let me show u
i dont understand how to get the dialation though
wispy hare
hmm is there missing info? like the question says it passes through point A and (10, -15/4)
whats point A
cuz you need 2 equations to solve for a and b
wispy hare
yup
wispy hare
all the best!
devout snowBOT
@median stratus Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
maiden zinc
i have a function f such as f : Rn[x] -> Rn[x]
f is invective
Since dim Rn[x] < +infinite
So f bijective
I have some doubt about that and if it's really true, then why?
i don't get it
magic thicket
Try to prove it
maiden zinc
then (e1, ... e(n+1)) a basis of Rn[x]
f(e1) have the same degree of e1 because it's Rn[x] -> Rn[x]
so (f(e1), ... f(e(n+1)) a basis
magic thicket
what's the degree of a vector ?
maiden zinc
degree of what?
magic thicket
then (e1, ... e(n+1)) a basis of Rn[x]
f(e1) have the same degree of e1 because ...
f(e1) has the same degree as e1
maiden zinc
yes
magic thicket
that means you've defined what the degree of a vector is
I'm asking you what that is
maiden zinc
e1 € Rn[x]
so the same meaning as a polynomial
magic thicket
f(e1) has the same degree as e1
so X^k -> X^(k+1) if k != n and 1 if k = n
is injective
does it preserve the degree ?
maiden zinc
hum
magic thicket
i have a function f such as f : Rn[x] -> Rn[x]
f is invective
Since dim Rn[x] <...
also let's try and make a proof that holds for any vector spaces, not just Rn[X] -> Rn[X]
maiden zinc
ok
then f :E -> E
with dim E < +infinite
we have to show that if f injective then f bijective
maiden zinc
ok
f injective so f(e1) is not a linear combination of any f(e(i))
so (f(e1), ... f(e(n)) a basis?
magic thicket
f injective so f(e1) is not a linear combination of any f(e(i))
why ?
maiden zinc
well that's no true
f injective so f(e1) is not equal of any f(e(i))
but that's not sufficient
i have to show that it's not a linear combination of any other f(e(i))
don't know how to do that
maiden zinc
don't have idea
magic thicket
i have to show that it's not a linear combination of any other f(e(i))
that works as well actually
maiden zinc
have any advice? x)
magic thicket
what's easier to use
as a characterization of injectivity
f(x) = f(y) => x = y
x != y => f(x) != f(y)
maiden zinc
f injective so f(e1) is not equal of any f(e(i))
that what i saw
magic thicket
one of the strengths of the proof by contradiction is that it gives you a starting point if you otherwise have none
maiden zinc
if n = dim E
then there's n f(e(i)) so it's a basis since the cardinal is equal to the dimension
maiden zinc
hum
magic thicket
i have to show that it's not a linear combination of any other f(e(i))
which is really just a rephrasing of this
which you may have seen as saying that a linear combination of them can't be 0 unless it's actually an empty sum
which amounts to saying one can't be a LC of the others
maiden zinc
it's remind me nothing
magic thicket
i have to show that it's not a linear combination of any other f(e(i))
suppose it is
maiden zinc
ok
magic thicket
i have a function f such as f : Rn[x] -> Rn[x]
f is invective
Since dim Rn[x] <...
cause even though you didn't mention it, surely it was implied
magic thicket
write it out
did you do that
devout snowBOT
@maiden zinc Has your question been resolved?
maiden zinc
write some sort of equality
i don't see what kind of equality
magic thicket
what does it mean for f(e1) to a linear combination of the f(ei) ?
maiden zinc
of the e1?
magic thicket
of the f(ei), i.e. (f(e2), ..., f(en+1))
magic thicket
of the f(ei), i.e. (f(e2), ..., f(en+1))
the contradiction is to say it's a combination of the others
need to point that out somehow
so wlog f(e1) is a CL of the others that way it's just [2, n+1]
magic thicket
without loss of generality
magic thicket
suppose f(e1) is a CL of the others
maiden zinc
ye
magic thicket
the others are the f(ei), i in [2, n+1]
which is more convenient than [1, n+1] \ {i} for a fixed i
maiden zinc
i don't get why inside a set with max n+1 honestly
but it's not the main point
so here you showed what?
you wanna show that it's a free family right
magic thicket
yes
by contradiction
to have a starting point
since you otherwise couldn't find one
maiden zinc
ok but don't see where's the contradiction
woven radishBOT
mateo713
magic thicket
that's what we assume to reason by contradiction
maiden zinc
ok and how can i find a contradiction, we just have the information that f is linear and injective
magic thicket
use linearity
maiden zinc
$f(e1) = \sum b_k e_k = \sum a_k f(e_k)$
magic thicket
$f(e1) = \sum b_k e_k = \sum a_k f(e_k)$
_ don't get copy pasted because they are special characters
magic thicket
**Max.cc**
that in physics, we would call not homogeneous
i.e. the units are wrong
because the ek and f(ek) don't exist in the same space
maiden zinc
not true since e(i) is a basis
magic thicket
**Max.cc**
the ak don't suddenly become bk that aren't defined
maiden zinc
$f(e1) = f(\sum a_k e_k )= \sum a_k f(e_k)$
maiden zinc
that f is injective so e1 != sum of ak*ek
so contradiction
the family is free
so the familie is free and the cardinal is equal to the dimension so it's a basis
maiden zinc
we have to show that if f injective then f bijective
so i have to show that
magic thicket
you just did
magic thicket
so contradiction
you contradicted f's injectivity by assuming it wasn't a basis
magic thicket
note: you actually showed something a bit more general:
linear injective functions preserve linear independence
magic thicket
but i have to show the bijectivity
what can you say of n independent vectors in an n-dimensional vector space
they're a basis
but now I gotta go
hopefully you'll be able to convince yourself without me
maiden zinc
ye thx a lot
devout snowBOT
Available help channel!
orchid glade
how do i go about looking for sum of this series
devout snowBOT
how do i go about looking for sum of this series
magic thicket
that's the sum of the (n choose k) for k ranging from 0 to n
which is known to be 2^n by the expansion of (1+1)^n using the binomial theorem
Feel free to look up any term you've never heard before
(n choose k) being a binomial coefficient (to look it up more easily)
devout snowBOT
@orchid glade Has your question been resolved?
scenic surge
devout snowBOT
scenic surge
can someone explain how to approach this
devout snowBOT
@scenic surge Has your question been resolved?
vast rain
probably should try using some test on it
trail eagle
Or could it be possible by comparison to the geometric series (7x)^n?
devout snowBOT
@scenic surge Has your question been resolved?
scenic surge
probably should try using some test on it
what test would be appropriate
maiden zinc
i have E a subspace at finished dimension, let's call n = dim E
and u a linear function of E -> E
i have ker u^k include in ker u^(k+1)
(u^k = it's the combination meaning. ie u^3 = u(u(u(x)))
i have to show that it exists a p€N such as ker u^p = ker u^(p+1)
devout snowBOT
i have E a subspace at finished dimension, let's call n = dim E
and u a linear f...
maiden zinc
i think that what make this expression true is that the dimension of E is finished
since ker u^k is growing the dimension of ker u^(k+1) is at least +1 grower
so it'll arrive a time when dim ker u^k will be equal to dim E and so the next one will be 0 because it can't be bigger than E
is my reasoning true?
devout snowBOT
@maiden zinc Has your question been resolved?
maiden zinc
<@&286206848099549185>
magic thicket
Yes
Exercise: prove/disprove the property for infinite dimension
Hint/answer: ||it's false||
vast rain
infinite dimensions don't exist
infinity is fake news
all numbers are less than 2^128
clever mist
why 2^128
maiden zinc
i don't get it, it works for finite dimension right?
vast rain
yes
maiden zinc
since ker u^k is growing the dimension of ker u^(k+1) is at least +1 grower
ok i just don't know how to prove ^
magic thicket
so it'll arrive a time when dim ker u^k will be equal to dim E and so the next o...
That's the idea, it just needs some fleshing out
devout snowBOT
Available help channel!
kindred sedge
devout snowBOT
restive river
factor numerator
kindred sedge
is the factor 2x^2-x+3
restive river
yeah
winter patrol
,w expand (x-2)(2x^2-x+3)
woven radishBOT
kindred sedge
so if i factor it it will turn into (x-2) (2x^2-x+3)??
restive river
yeah
kindred sedge
then i substitute the limit
restive river
then cancel out x-2
restive river
,w lim as x-> 2 of (2x^3-5x^2+5x-6)/(x-2)
woven radishBOT
restive river
yeah ur correct
little onyx
Somebody tell me how OK= csc in the picture
devout snowBOT
Somebody tell me how OK= csc in the picture
@little onyx Has your question been resolved?
lusty sapphire
csc=1/sin
HO=1
OA=1
OG=sin (by definition)
triangle OGA similar to tirangle OHK
Thus, OK/OH=OA/OG
@little onyx
sage socket
devout snowBOT
sage socket
So, the value I got for c was an imaginary number.
So, I'm not sure why that conclusion is wrong
summer flower
It has to do with the definition of MVT
sage socket
is an imaginary number a value we can use for c?
summer flower
Think of continuity
sage socket
okay
pseudo basin
the right conclusion would be that mvt is inapplicable
since your function isn't even defined at x=3, and if it was, it would be guaranteed discontinuous there
summer flower
The C is irrelevant given that your function doesn’t meet the first requirement of MVT.
sage socket
because it's not continuous on that interval?
summer flower
Yes
sage socket
gotcha
cause it is differentiable
but it fails the first one
yeah okay okay
alrighty
ty everyone
.close
finite briar
What's the general procedure to solving functional equations? For example, f(0.8) = 7/3, f(2) = 13/3. How would I solve this one?
devout snowBOT
What's the general procedure to solving functional equations? For example, f(0.8...
winter patrol
depends if you're given more information
magic thicket
That's not quite a functional equation I think.
That's more like "how do I extrapolate that"
finite briar
depends if you're given more information
Nope
finite briar
That's not quite a functional equation I think.
That's more like "how do I extra...
Well i have to find f(x), so i think it's a functional equation
magic thicket
It's so far from unique
violet wind
There's no simpler description of the set of functions that satisfy those equations
pseudo basin
f(x) = 7/3 if x=0.8, 13/3 if x=2, 42069 otherwise
magic thicket
You've got an infinity of polynomials, of trig functions, etc
pseudo basin
@finite briar are you 110% certain that you are given zero further information
finite briar
<@717652530061901855> are you 110% certain that you are given zero further infor...
Yeah..well i am given 2 or 3 more values for f(x) but that's about it
pseudo basin
"about"?
okay, no, this won't do.
show us the problem exactly as it was stated.
screenshot or picture.
or tell us you are unable to do this.
finite briar
"about"?
The entire question is an integral question, have to find the area under a graph
But the function or its derivative haven't been stated
Wait a sec
winter patrol
show everything under the question number regardless of whether you think its relevant
devout snowBOT
@finite briar Has your question been resolved?
finite briar
Wait a sec
<@&286206848099549185> sorry i went afk 😞
sage burrow
i cant see a task where you should determine a function. you should shade an area and select a part of the graph which represents something
sage burrow
What's the general procedure to solving functional equations? For example, f(0.8...
no one asked you to do something like this.
finite briar
Find how far the travels in the first 4 seconds..
Isn't that the integral from 0 to 4 of this graph?
finite briar
i cant see a task where you should determine a function. you should shade an are...
Yeah, but that doesnt help find distance, does it?
sage burrow
it is the integral, yes. but you are not asked zto calculate it. you are asked to shade the area which represents this.
finite briar
Oh...oops ig
pseudo basin
in the future be mindful of the xy problem
finite briar
But okay, say they asked me to calculate it, how would I do so?
finite briar
in the future be mindful of the xy problem
Okay ma'am 🫡
sage burrow
But okay, say they asked me to calculate it, how would I do so?
you cant - without further information. What you could do is to estimate the integral by counting the shaded squares - for example.
finite briar
Ah..is there no way to derive the function using the graph?
pseudo basin
no
finite briar
Sad 😦
sage burrow
not exactly. you could assume it looks like a log (or something else) and fit the log, but this is alos an estimation.
finite briar
not exactly. you could **assume** it looks like a log (or something else) and fi...
Okay.. Tysm Ann and ThM
.close
spice saffron
Hey! a^2 + 8a + 12, solve by splitting middle term
devout snowBOT
Hey! a^2 + 8a + 12, solve by splitting middle term
spice saffron
Kindly help
rotund heron
!status
devout snowBOT
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
Does that say “solve” ??
spice saffron
I'm on 2
rotund heron
Okay, show what you’ve done so far. But wdym “solve”
It’s not an equation
Do you mean factorise
rotund heron
Alright can you Show your work?
woven radishBOT
Shady
spice saffron
$-3x -2 = -5, +6$
woven radishBOT
Shady
rotund heron
wrong question
Oh lmao
spice saffron
rotund heron
Why are you using ‘y’
spice saffron
uhh
rotund heron
Should that not be 6a and 2a
rotund heron
Okay so $a^2 + 6a + 2a + 12$
woven radishBOT
Deol
spice saffron
but like
I can't take common in everything
which is how we are told to factorize
rotund heron
I can't take common in everything
Wdym?
rotund heron
And what about 2a and 12?
spice saffron
i get it now
rotund heron
So what do you get as answer?
spice saffron
(a+2) (a+6)
rotund heron
Yess
spice saffron
gg thx but
rotund heron
Nice work
rotund heron
gg thx but
Yes?
rotund heron
Lol nice
rotund heron
Show me what you mean
woven radishBOT
Shady
rotund heron
You can do that
woven radishBOT
Shady
spice saffron
really
spice saffron
**Shady**
but here
its manipulating -2
why?
soo
The answer to a^2 -5a +6
is?
winter patrol
factoring -2 out of -2a - 6 gets you -2(a+3) and not -2(a-3)
rotund heron
factoring -2 out of -2a - 6 gets you -2(a+3) and not -2(a-3)
They changed the question mid way
winter patrol
they're both factorable, in slightly different ways
spice saffron
I see
Eh lets get to the last question here
y^2 +18y +17
I see I can't like split the middle term here
rotund heron
Can
woven radishBOT
ℝamonov
winter patrol
yes
devout snowBOT
@spice saffron Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
safe turret
Indices
safe turret
Need help with B part
devout snowBOT
@safe turret Has your question been resolved?
safe turret
im gonna fail math
devout snowBOT
@safe turret Has your question been resolved?
safe turret
.close
light quail
devout snowBOT
light quail
ok so i got to here
should the bottom 2 look different?
after i found that my function is = to 0 at x=6
i plug in numbers on either side of 6 into my original function to figure out if its a maximum or minimum
<@&286206848099549185> invite me your private chat
i dont understand why im being targeted
@frosty cradle is a good man, maybe he can help
light quail
i plug in numbers on either side of 6 into my original function to figure out if...
i
and that gave me my picture up top with the black boxes
im not sure if i set it up correctly
frosty cradle
your picture isn't very clear, the writing is pretty light
frosty cradle
well what's the original problem?
frosty cradle
what is the green box?
light quail
the derivative
they wrote it differently but the graybox is my answer which is also correct
frosty cradle
ok then N=6 seems right. is it actually wrong?
light quail
nope n = 6 is correct
so i plug in a 7 and 5 into original function to determine if its max or min
light quail
and that game me my 2 things in my picture here
at the bottom
im curious if its done wrong or if i just dont know how to interpret it
to know if it goes from negative to pos or vice versa
frosty cradle
the "proper" thing to do is calculate the second derivative and see whether it is positive or negative
but you have to square the whole denominator, anyway
light quail
hmm that would be a very big quotient rule setup i think?
oh ur right
ok so i got k5/3,721 and k7/7,225
now what does this mean for my min and max?
light quail
the "proper" thing to do is calculate the second derivative and see whether it i...
is the way im doing it valid as well? i did remember to include that ^2 on the outside the ( )
they are both positive
what does it mean if they are both positive?
light quail
but you have to square the *whole* denominator, anyway
afk?
devout snowBOT
@light quail Has your question been resolved?
frosty cradle
sry
light quail
thats ok
frosty cradle
both positive? then perhaps N=6 is an inflection point
so you'd need to verify with the 2nd derivative
woven radishBOT
light quail
what do i do next if i assume its an inflection point?
frosty cradle
,w plot (2N) / (36 + N^2)
light quail
im not sure how you were able to plot that
woven radishBOT
light quail
hmmm
frosty cradle
,w plot (36 - N^2) / (36 + N^2)^2
woven radishBOT
frosty cradle
according to this, at N=7 the derivative is negative, not positive
(for k=1)
,w plot (72 - 2*N^2) / (36 + N^2)^2
woven radishBOT
frosty cradle
ok, I see where you went wrong. You have to evaluate $f'(5)$ and $f'(7)$, whereas it looks like you evaluated the original functions
woven radishBOT
cwatson
light quail
oh
frosty cradle
$f'(N) = \frac{k(36 - N^2)}{(36 + N^2)^2}$
woven radishBOT
cwatson
light quail
can i also just plug in 5 and 7 into
frosty cradle
into what?
light quail
the derivative of the original function
frosty cradle
yes, that's what I'm saying
light quail
ok so i got f'(5) = 11k/3,721 and f'(7) = -13k/7,225
so its positive when its approaching 0
and the negative after
which means its a maximum
frosty cradle
yes
frosty cradle
is it not just n=6?
frosty cradle
I don't know, seems confusing
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magic dust
I was given
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I was given
magic dust
and asked to prove
I proved that it is correct
but now I'm asked to prove given what I found previously that
and I've been trying for like an hour but I can't seem to grasp where to even begin
magic dust
the problem is the goal is they want me to get to exactly the same inequality
and I'm not sure how cause for all I know they chose random number to fill in and I will be lucky to find them
prime basin
i'm a bit confused as to what you mean
magic dust
What I'm expected to do is prove this inequality for those specific numbers
and not just say that it's true cause 0.1 is less than 1/6
or wait
that actually makes no sense when I think about it
Okay I think I got it hate my language
thanks.
.close
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graceful jackal
I need help with this
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I need help with this
gusty sparrow
!status
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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
@graceful jackal
graceful jackal
Ya
gusty sparrow
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
.
graceful jackal
1
gusty sparrow
Do you know the formula for area of trapezoid?
gusty sparrow
umm no
graceful jackal
Idk than
gusty sparrow
$$ A = \frac{a+b}{2}h $$
woven radishBOT
gusty sparrow
where a and b are the sides of the trapezoid and h is the height
graceful jackal
So I plug the numbers in Using that formula?
gusty sparrow
So I plug the numbers in Using that formula?
exactly
naive comet
Ye
pearl moon
Subtract the area of rectangle in between
graceful jackal
Need help with this one
graceful jackal
Idk what that is
graceful jackal
So N is 5
graceful jackal
No
pearl moon
Then how can n be 5
graceful jackal
Sorry it’s 12
pearl moon
Ok correct
Now do the formula
And divide it by number of angles
Which is 12 too
1800/12
Tag me when you reply
graceful jackal
@pearl moon 150
pearl moon
Ok 150/2is the angle between radius and segment
Ami right?
Do you know trigonometry reply with tag
graceful jackal
@pearl moon yes Ik trig but not expert at it
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@graceful jackal Has your question been resolved?
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@graceful jackal Has your question been resolved?
restive river
can a differentiable function exist with no local minima between two local maxima
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can a differentiable function exist with no local minima between two local maxim...
@restive river Has your question been resolved?
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pine plinth
In how many ways can you fill 36 tiles with 2 white pieces , 3 black pieces and an infinite number of purple pieces ?
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In how many ways can you fill 36 tiles with 2 white pieces , 3 black pieces and ...
pine plinth
I don't know how to aproach this one. My first guess would have been 12* 36! but apparently that isn't among the answers by a long shot
proud perch
hmm
does order matter?
like is white then purple different from purple then white?
topaz axle
you choose where white pieces are, and choose where purple pieces are, accounting for some empty space filled by white
so not e, not f
pine plinth
A refers to non repeating permutations in this textbook, and C to non repeating combinations
topaz axle
no clue lol
topaz axle
it's maybe A
nope
ok i'll calculate all of them just in case
oh right it's a
10 is 5C2
pine plinth
oooooooooooh
topaz axle
you choose 5 non purple spots, and then choose 2 white
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sage socket
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clever mist
!status
devout snowBOT
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
sage socket
what
So, I'm still struggling with these concave questions
and inflection points
I've watched a few videos and read from different books
clever mist
ok what is concave
sage socket
oh, like concavity
clever mist
yeah
sage socket
well most examples just talked about this
and the second derivative
But here, I don't have the equation
So, I'm really not sure how I'm supposed to apply it other than just looking at the shape of the graph
sage socket
yeah not super sure what I'm supposed to get from this.
sage socket
sure
magic pine
i see concavity as where the function “opens up to”
don’t know if that helps
sage socket
yeah my professor made a similar statment
here is where the graph holds water and where it empties it
I get the idea
sage socket
but I don't think I'm sure where the intervals are supposed to start and end I guess?
clever mist
concave?
sage socket
concave downward ?
sage socket
if it's above the graph it concaves upward yeah
clever mist
wha
sage socket
the tangnet line
isn't that what you drew
oh wait
it's the second deriv
not the tangent line
clever mist
i just drew the thing
sage socket
okie
clever mist
clever mist
thats how i would solve it
sage socket
well
okay
If I wanted to use the intervals, would I said, it concaves down at (0,1),(1,2) ?
clever mist
yeah
sage socket
how about the inflection point?
here
I thought it would be at x = 2
so the coordinates would be (2,3)
oh the inflection point was correct
I just didn't need the ()
sage socket
wait, actually, idk if this helped me
sage socket
cause like what is the blue line supposed to be again
clever mist
just a line
sage socket
okay it's just a line
sage socket
ohhhhhh
clever mist
lol
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pine fox
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pine fox
i'm a little unsure how to start this question
should i just apply the transformation to the basis vectors in B
how do i ensure that the range ends up being a linear combination of vectors in the set D
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@pine fox Has your question been resolved?
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@pine fox Has your question been resolved?
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@pine fox Has your question been resolved?
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@pine fox Has your question been resolved?
restive river
Not sure how to solve this.. something about telescoping rule?
devout snowBOT
Not sure how to solve this.. something about telescoping rule?
upper schooner
Swear down every time that keisuke posts something, it gets asked by someone else moments later 
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indigo zinc
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indigo zinc
just 25)c
I took values of x in the range: -2, 1, 0, 4, 5
ans indicates that 4 is the best possible value for x, since I get y as 5
clever mist
??
chrome girder
I took values of x in the range: -2, 1, 0, 4, 5
take values of x really close to 3, like 3.01 or 3.001 or 2.99 or 2.999
indigo zinc
got it