for the first one identify what is given information
#help-0
covert brook
lone heartBOT
@wise pasture Has your question been resolved?
fast birch
Ok, so C is the midpoint of AB by hypothesis
unkempt notch
hello! i dont understand why we have to find the second derivative
unkempt notch
why is the second derivative test being done?
stray socket
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thick beacon
how do I do part c of this question ?
lone heartBOT
how do I do part c of this question ?
thick beacon
the marking scheme gives this answer
but i don't understand why my method is wrong
what i did was
<@&286206848099549185>
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thick beacon
<@&286206848099549185>
thick beacon
why is no one here 🥲
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@willow raft Has your question been resolved?
fast birch
What do you mean by coordinate map for $\beta$?
ocean sealBOT
bondalton
fast birch
Think of what $\phi_{\beta}(T_A(v))$ should be for some $v=\sum_{i=1}^n a_ie_i$
ocean sealBOT
bondalton
willow raft
I don't get that
Like I tried
left and right inverse
but then get stuck at TA(v)
oh wait
I'm dumb
ohhhh
aight thank u
i get it now
.close
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willow raft
life saver
fast birch
No problem 🙂
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floral current
Help please.
lone heartBOT
Help please.
sharp gate
What part are you stuck at
floral current
Starting the problem
sharp gate
Like do you know what the big O, omega and theta means
Or how to solve a recurrence relation
floral current
Sorta... I know you have to "unroll" it but even that part is confusing.
sharp gate
So yeah you can use telescoping
Based on the recurrence relation T1(n), you can see it relies on the result of T1(n-8)
So you wanna substitute n-8 into T1(n)
In other words find T1(n-8)
What would that be?
floral current
T1((n-8)-8)+(n-8)
sharp gate
Exactly
floral current
Then?
sharp gate
Now that you know T1(n-8), you can substitute it into the equation for T1(n)
What is T1(n) = to now
floral current
T1(n) now is
T1((n-8)-8)+(n-8) + n
sharp gate
Yeah
Now repeat that process
Next you need to find T1(n-8-8) in other words find T1(n-16)
Then sub it into the equation you just found
Once you do it 2 or 3 times you should see a pattern
floral current
Ok
T1(n-16) = T1(n-24) + (n-16)
Plug back in
T1(n) = T1(n-24) + (n-16) + (n-8) + n?
floral current
T1(n) = T1(n-8k)?
floral current
Okay so this one
T1(n) = T1(n-24) + (n-16) + (n-8) + n?
Simplifies to
T1(n-24) + 3n - 24
So pattern would be
T1(n-8k) + kn - 8k?
floral current
I'm not sure. I'm not good with this series stuff
floral current
Yeah
sharp gate
So expanding, you should get a +8 term on the end
floral current
Ok
sharp gate
also, does it not tell you anywhere what the base cases of the two recurrence relations are?
floral current
Nope
floral current
Just that
sharp gate
Then you can’t really solve the recurrence relation
A recurrence relation must have a base case
Because the next step involves setting what’s in the brackets (n-8k) equal to the base case
Could try just assuming it’s 0 or 1 but I’m not sure if it would be correct
floral current
Okay so the teacher assistant said, "the amount of work done in the base case is always constant"
sharp gate
Ok great
floral current
Also, it is due in 20 minutes
sharp gate
Is it homework
floral current
Yeah
floral current
Procrastination
floral current
Ok
floral current
n=8k
sharp gate
I mean in the generalised form for T1(n) you came up with before
floral current
This one?
T1(n-8k) + kn - 8k?
sharp gate
Yeah and don’t forget the -8 at the end I said about
floral current
T1(n-8k) + kn - 8(k-1)?
floral current
T1(n-n) + n^2/8 - n(n-8)/8
sharp gate
Ok and we can get rid of T1(n-n)
So the highest order in that polynomial is n^2
Therefore it’s O(n^2)
Now you need to solve the next recurrence in the same way and see how it compares to this one
floral current
Alright
And what do these choices mean?
First one: Growth rate of T1 is not asymptotically equal to growth rate of T2?
Possible if you could check ?
Thanks tho
/close
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alpine sable
Hey I need help fast, I need to know if this is wrong
lone heartBOT
Hey I need help fast, I need to know if this is wrong
alpine sable
gray isle
why fast
deep loom
$A=\frac{1}{2}a\times b\times sin(\theta)$
ocean sealBOT
ـDraedon
deep loom
wtf no way i forgot the 1/2 at the start 😭
alpine sable
wtf no way i forgot the 1/2 at the start 😭
I am unsure how that helps this one lol
alpine sable
One second
alpine sable
you have sides a and b, and you have an angle
11 rounded?
deep loom
i think so yes
alpine sable
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proud citrus
how do i do question b?
lone heartBOT
how do i do question b?
shy dove
Plug the values you know, you‘ll get a system of equations for a and b
shy dove
Alright, that‘s your system
shy dove
Looks like it
proud citrus
so then for a i js plug in
shy dove
Yeah
proud citrus
1 = a + 4
alpine sable
Alright, that‘s your system
can you check #help-23 after
shy dove
All seems fine
proud citrus
wait so then how do i find f(x) = 0?
shy dove
What‘s f(x) now that you found a and b?
shy dove
Right. So now you can set this = 0 and solve for x
shy dove
Gotta be careful when you don‘t put parentheses, this is essentially (1/2) * x = 3
shy dove
So what would x actually be?
proud citrus
x = 1/6?
shy dove
Almost. Do you have your work on paper so I can see where you made the mistake?
shy dove
Hm. I think you‘re misunderstanding how the multiplication by 1/2 works. It‘s essentially like dividing by 2. so you could write x/2 = 3
shy dove
You could divide by 1/2 sure, but you have to be careful and flip it yeah. So if you divide by 1/2 on both sides it‘s like multiplying by 2
shy dove
How did you pick up the negative sign?
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hollow lark
can anyone help me with the last part, i used trigonometry to find the modulus of the new roots (acos(pi/5)) and know the angle will be of the form theta = (pi + 2pi(k))/5 but not sure on how to get the equation
hollow warren
(a) they all have the same absolute value
lone heartBOT
@hollow lark Has your question been resolved?
hollow lark
I think i understand why it looks at r
because r is only on the real axis by symmetry so r = -acos(pi/5)
then r^5 = z^5 = -(acos(pi/5))^2
so z^5 + (acos(pi/5))^5 = 0
cool i wouldn’t have spotted that
hard oasis
wait there’s a lot of typos hold on
barren thorn
it's just a notation, we note $V = W_1 \oplus W_2 \oplus \dots \oplus W_k$ (at least that's how we note it in France)
ocean sealBOT
Valsorim
barren thorn
and for each vector $v \in V$ there is a unique set of vectors $w_i \in W_i$ such that $v = w_1 + w_2 + \dots + w_k$
ocean sealBOT
Valsorim
hard oasis
Are the conditions in 2 and the note the same besides notation?
we use oplus after we finish this definition of direction sum
barren thorn
we use oplus after we finish this definition of direction sum
oh ok
to be honest I don't understand why the note says that, in my course it says that "F and G are in direct sum iff $F \cap G = { 0 }$"
ocean sealBOT
Valsorim
barren thorn
maybe the "not" is a mistake and shouldn't be here ?
we even have a proof of why that is true
vale crag
the "not" is not a mistake
barren thorn
oh ok my bad then
vale crag
2 is much stronger than what's in the note
for example take 3 distinct lines in R^2 as your W1, W2, W3
their intersection is 0 yes
but obviously you'll be able to write the vectors in say W3 as a lin combo of vectors in W1 and W2
hard oasis
yes
vale crag
so W1 W2 W3 satisfy what's in the note but not condition 2)
barren thorn
oh ok so we can only replace it by what's in the note if we have 2 vector spaces ?
hard oasis
ohhhhh okay so if we take
(1, 0)
(1, 1)
(0, 1)
Then yes they all intersect at 0, but we may add 1(1, 0) - 1(1, 1) + 1(0, 1) and get zero which isn’t true for 2)
vale crag
oh ok so we can only replace it by what's in the note if we have 2 vector spaces...
yeah your definition only works for a sum of 2 spaces
barren thorn
yeah your definition only works for a sum of 2 spaces
ok thank you
hard oasis
thank you
vale crag
one good way to understand direct sums is as a generalization of bases
basis : "a set of vectors that spans V and is linearly independant"
direct sum : "a set of subspaces of V satisfying 1) and 2)"
- corresponds to spanning
- corresponds to linear independence
hard oasis
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fallen berry
Calc 1: What did I do wrong?
lone heartBOT
Calc 1: What did I do wrong?
fallen berry
I should have gotten $\frac{832pi}{15}$
fallen berry
from 0 - 2 to 0 - 16
Sorry
rough harbor
How do I solve for the equation of BC
lone heartBOT
How do I solve for the equation of BC
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
ocean sealBOT
mason50_50
merry iris
did you plug in a ... 1 here?
why do the bounds change every time theres an equal sign
and then the wrong numbers are plugged in
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granite sandal
A trigonometric series is defined as T_n(x) = A_0/2 + summation from k=1 to n (A_k coskx + B_k sinkx), find its corresponding fourier series and express f(x) = cos^2(x) as a fourier series
granite sandal
Does anyone happen to know how to do this question? any help will be greatly appreciated
(sorry I don't know what the command is for latex)
obsidian nymph
pls help me i know product rule but cant make it with chain rule how does it change with pi inside cos
vast tapir
pls help me i know product rule but cant make it with chain rule how does it cha...
use integration by parts
and to integrate cos(pix) set u = pix
,tex $ u = \pi x$
ocean sealBOT
math X meth ✓
obsidian nymph
is there any chance u write it
vast tapir
,tex $du = \pi dx$
ocean sealBOT
math X meth ✓
vast tapir
$dx = \frac{du}{\pi}$
ocean sealBOT
math X meth ✓
vast tapir
is there any chance u write it
on paper?
vast tapir
vast tapir
@obsidian nymph
if the integration by parts looks unfamiliar, im using the DI or tabular method
you can search DI method on youtube and watch the blackpenredpen video if you want
basically its just integration by parts but easier to look at
obsidian nymph
ive never seen it on khan academy but let me check
i understood the right part you wrote
but didnt get the left part
why it looks so complicated 😭
vast tapir
but didnt get the left part
its just integration by parts, but written in a different way
lone heartBOT
@granite sandal Has your question been resolved?
granite sandal
sadge
obsidian nymph
its just integration by parts, but written in a different way
hi it is actually a quite fun way
thanks a lottt
vast tapir
thanks a lottt
Np
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manic raft
could someone explain to me how this works?
i only know how to get the derivitive to x/x-1, not sure how there can still be a lnx in the final answer
fathom dragon
This would require product rule - that is why the ln(x) is in the answer
merry iris
could someone explain to me how this works?
i only know how to get the derivitiv...
i think you forgot to use product rule
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lime hemlock
how do I find an inverse matrix of A?
lone heartBOT
how do I find an inverse matrix of A?
unreal wedge
A.A^-1 = I
just write it down and place integers in place of A^-1
lime hemlock
A.A^-1 = I
just write it down and place integers in place of A^-1
yeah ok
but idk the method
i just wrote down A and then
1
1
1
1
with the rest being zeros
like multiplied
unreal wedge
this one takes a while to solve as usual from matrix problems
lime hemlock
i switched the 1st and 2nd row with each other
unreal wedge
You gotta do sth like this
bleak vault
how do I find an inverse matrix of A?
do you know how to look for it using gauss-jordan?
you expand that matrix to the right side (make a divisor line) with the same row and columns thats an identity. then you operate your original matrix until it looks like an identity (ALWAYS REMEMBERING TO REPLICATE WHAT YOU OPERATE TO THE OTHER SIDE)
if you do things right and dont miss a step you should have an identity on your left side and the inverse of A on the right
lime hemlock
you expand that matrix to the right side (make a divisor line) with the same row...
ok so if i got 3 in the bottom-right corner then i divide it by 3?
currently i have
1 0 0 2 | 0 1 0 0
0 1 -1 3 | 1 0 0 0
0 0 1 -3 | -1 1 -1 0
0 0 0 3 | 2 -4 2 1
@bleak vault @unreal wedge
bleak vault
currently i have
1 0 0 2 | 0 1 0 0
0 1 -1 3 | 1 0 0 0
0 0 1 -3 | -...
you divide the fourth row by three, yes. remember to apply that divison to the fourth row on the other side too
lime hemlock
ok what should i do after
bleak vault
clear it up so you have an identity o the left side
the usual strategy that i suggest is trying to get only a diagonal on your left side, with the rest being zeroes
and then you can start multiplying the rows to get a proper identity
ocean sealBOT
lime hemlock
is that what the inverse matrix is?
bleak vault
is that what the inverse matrix is?
you can check if it is by multiplying that matrix by your original matrix
if you get an identity back, it is
i reccomend doing that always
lime hemlock
if you get an identity back, it is
you mean I should get
1
1
1
1
with the rest being zeros?
bleak vault
yes thats a matrix identity
lime hemlock
cause you can clearly see that
0 1 -1 3
multiplied by
0 1 0 0
will give
0 1 0 0
and not
1 0 0 0
so i fucked up?
bleak vault
if you do the multiplication process between the first row of your original matrix and the first column of your inverse and you dont get back 1 then yes, something along the process is wrong
remember that the process is
a b c d e
f = a * e + b * f + c * g + d * h
g
h
bleak vault
i'm afraid its a little too messy for me to understand hahah
besides its good practice for you to redo and recheck yourself. these are all the tools that you need, the process is just a little laborious
just little more than sum, substract, multiply and divide with row operations. just keep at it i'm sure you'll get it
wheat pewter
lone heartBOT
wheat pewter
guys i. got 4 answers
what else am i missing
my friend got 6 andwers
i dont ge tot
mortal trellis
what about negative bases
wheat pewter
what about negative bases
ive tried that already
lone heartBOT
@wheat pewter Has your question been resolved?
wheat pewter
<@&286206848099549185> theres 6 answers
drifting maple
friend me if ur good at math
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wheat pewter
.reopen
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alpine sable
<@&286206848099549185> theres 6 answers
2^6 = 4^3 = 8^2 = 64^1 = (-2)^6 = (-8)^2
glad cliff
hi guys im new, i need help with a problem, i must do ruffini with a problem but i got two variables and im kinda lost
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calm kiln
hi
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wraith stratus
would start with the derivative of $\arctan(x) = \frac{1}{1+x^2}$
ocean sealBOT
chebyshev's infinite pee norm
wraith stratus
you can rewrite that as a power series
then integrate to get arctan
evaluate at x^3 and multiply by x^2
lone heartBOT
shadow isle
Rearrange
craggy forge
isolate y
shadow isle
Into linear formula
shadow isle
What’s the formula for a straight line
dense fiber
idk gng
dense fiber
oh
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@dense fiber Has your question been resolved?
soft harness
How do i find the limit of the sequence "An = 1 + 10^n / 9 ^n
jagged cobalt
the 10^n/9^n is a geometric term, but its not convergent
soft harness
what does that mean
jagged cobalt
means the limit isnt going to go to any finite value
(10/9) is greater than 1, so (10/9)^n will tend to infinity
soft harness
okay so then its infinity + 1 which is just infinity which means its divergent?
jagged cobalt
it is divergent, yes
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autumn inlet
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autumn inlet
i dont get it
my friends think the question itself is wrong
cuz standard deviation equals 6.35 not margin of error
pseudo star
The sample mean is the point estimate of the population parameter, and it’s always in the middle of
the CI. Thus, the sample mean in this case is (34.5 + 47.2)/2 = 40.85 years
The margin of error is half of the interval, that is (47.2 – 34.5)/2 = 6.35 years
anyone?
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pseudo star
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brittle mica
quick question, why is a downward/outward normal used here?
lone heartBOT
quick question, why is a downward/outward normal used here?
brittle mica
i understand it has very little bearing on the final magnitude
and that i could conceivably reach a correct answer
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@brittle mica Has your question been resolved?
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round void
how far is O to AB
true crag
Answer is 3
true crag
how far is O to AB
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lone heartBOT
Can help to solve these step by steps
gray isle
question 17?
torpid marlin
your derivative same as function in integral multiply by 8
ocean sealBOT
Dyssrupt
torpid marlin
thanks
ripe river
**Dyssrupt**
How did it get 1/8
gray isle
x/4 = 2x/8
torpid marlin
gray isle
wdym by rationalise here
ripe river
wdym by rationalise here
Ratio
gray isle
identifying the above you'll have
$$\int_{-1}^{1} \frac{x(x-1)}{4(2x-1)^2} \dd{x}= \frac18 \blue{\int_{-1}^1 \frac{2x(x-1)}{(2x-1)^2} \dd{x}}$$
ocean sealBOT
ℝαμΩℕωⅤ
ripe river
The image I circle it in the photo U generated
ripe river
This one
gray isle
yeah but wdym by using or eliminate
ripe river
yeah but wdym by using or eliminate
One after integrated
gray isle
can you please clarify that
i don't understand what you mean
please clearly describe what you mean in full phrases/sentences
lone heartBOT
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wheat rock
hi
wheat rock
uh
hollow timber
how to
wheat rock
whats the ans
steep pike
how can i show that this equals 0
torpid marlin
whats the ans
bruh is this roblox?
torpid marlin
whats the ans
3
lone heartBOT
3
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.
zinc haven
whats the ans
this looks flamboyant but is actually piss easy
zinc haven
whats the ans
can you find the value of the above sigma function?
the above and below argument are the same so its quite literally just subbing them in
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tawdry crystal
calculate the definition set of the function:
$$f(x,y) = \sqrt{(\log(x))^2 - y^2}$$
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alee
tawdry crystal
i have to solve:
$(\log(x))^2 - y^2 >= 0$?
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alee
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sterile sand
PLease help
lone heartBOT
PLease help
wraith stratus
!status
lone heartBOT
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
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
@sterile sand Has your question been resolved?
weary birch
!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 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
@sterile sand Has your question been resolved?
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upbeat olive
L gauthmath
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charred pier
Hi, I'm wondering if anybody would be available to help me with an optimization/gradient descent thing I'm struggling to understand in some sections of the provided training exercises of the math course I'm taking this semester
charred pier
I don't expect you to be fluent in Norwegian, but as I understand it the problem is as such
u(t) is the function describing the temperature variation between the average monthly temperatures of a year cycle reported by a weather station, the cycle repeating every 12 months and seeing an average of -6 with a variation of +- 10 degrees around said average
the overall data showing this graph
From what I understand so far about optimization using gradient descent, the method is used to estimate the position of a minimum assumed to be global in the studied area of a function
Step size is determined by the value of gamma, here 0.00001.
using a simplified example, here I can see the method being applied to this interval
- N is the Y is the top/starting y value at which the gradient descent begins.
- gamma is the step size, here 0.3.
- x is the starting x value of the gradient descent, here 4
- f values describes the entire curve's y values
- x values describes the entire curve's x values
<@&286206848099549185> To summarize, my main hangup seems to be how do I apply the simple example of optimization through gradient descent to the much more complicated dataset I have following the function I've been given
cunning helm
I think we're missing that you have data (y_i,t_i) yes? And the parameter you're optimizing over is t*, right? Then it's the same thing as your example. You just need to pick a starting value t0, say and calc the gradient of U(t) at that value (do calculus), move in that direction prop to learning rate gamma and recompute.
charred pier
I think we're missing that you have data (y_i,t_i) yes? And the parameter you'r...
yes I have a big excel file with temperatures and months
so there you'd say I need to replace f(t) with u(t), then derive it and apply gradient descent?
cunning helm
really the t_i are fixed. So you need to figure out the gradient of U as a function of t*.
but yeah that's the idea. f(t) here is your u(t_fixed, t*).
charred pier
u being the temperature of a given month t right
cunning helm
because f(t.star) is really the sum_i (U(t_i, t.star-y_i)^2...
y_i is observed* temp, t_i is month. u(t_i,t*) is the model's guess about the temp in that month.
charred pier
Hmmm, I think this may help me get unstuck but I'll keep the help channel open just in case I get stuck applying this then I guess
cunning helm
Yeah I'm not giving you the whole answer. That should be enough for you do to the rest. There's some non-neglible getting the gradient. But you could probably python it...
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@charred pier Has your question been resolved?
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@charred pier Has your question been resolved?
charred pier
Yeah I'm not giving you the whole answer. That should be enough for you do to th...
Am I right in assessing that the U(starting_time) function ends up being
-6 + 10 cos((pi/6)*(starting_time - U(starting_time))
or not?
yeah no I'm still slumped my bad
cunning helm
Objective is Sum_i ( -6+10cos(pi/6 * (t_i - start)) -y_i)^2 at start
cunning helm
I don't expect you to be fluent in Norwegian, but as I understand it the problem...
Last line here is f(t*) without the min
charred pier
Yes
cunning helm
So derivative is lik sum_i -2 (u(t_i)-y_i)*du/dt
charred pier
So wait what would the derivative of my optimisation function give me?
cunning helm
The gradient. it tells you how fast and what direction to move for next step
See for example newtons method https://www.geeksforgeeks.org/newton-raphson-method/ and cross ref line 13 in python
charred pier
Wait am I fundamentally misunderstanding the assignment
there's this line: find out the value of f* that makes u(t) fit the data best. Print the result in the console.
am I simply supposed to fiddle with the f* value until I get a graph that fits my original graph
cunning helm
Should be value of t* but yeah that’s the idea
“Fits” means squared error loss sense
This is just a regression with a non linear functional (u) using a learning rate gamma
charred pier
I mean yes t*
cunning helm
You could guess and check it sure. But the exercise is to do it by gradient descent.
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viscid wasp
Stats and prob
lone heartBOT
Stats and prob
viscid wasp
How do I calculate a two tailed test with normalcdf in my ti-84 calculator
This is hypothesis testing
hushed locust
the simpler way would be to use the inbuilt hypothesis test function
on stat-> tests
viscid wasp
on stat-> tests
guessing the 2propztest
hushed locust
for this one, yes
viscid wasp
for this one, yes
aight got it
also one more question
nvm
I'm good
thanks
.close
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quick pike
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quick pike
this is Non-Right Triangles, and I don't get it at all
this is the law of cos
and these are the laws of sin
unborn plover
were you missing the kite area formula?
quick pike
um this doesn't look right but maybe it will work.
idk what my pq is on the problem.
I think the kite area formula is not what I am looking for
unborn plover
we're splitting an angle of 21 into two equal parts
quick pike
ok and then I label the two tragles them a through b and A through B right?
because that's all I know what to do...
unborn plover
uhh not sure if i understand
but what we've done is create two triangles that look like this
do you know how to find the area of this guy?
unborn plover
that's not what i'm getting
quick pike
the formula I used is area= 1/2(ab)sinC
side a is 3.3, and side b is 5.1. And the only degree I got is 10.5
what did I do wrong?
is the foumula not area= 1/2(ab)sinC?
unborn plover
1/2 ab sin C would work
but it seems you did 1/2 bc sin C, which isn't valid
if you wanted to do 1/2 ab sin C you'd have to find side a
quick pike
ah! they are deferent?
unborn plover
1/2 ab sin C would work
but it seems you did 1/2 bc sin C, which isn't valid
in this image you can see your angle has to be in the corner of the two sides
so C is betwen a and b
or, because you have b and c, you could use angle A
unborn plover
do you see how a and b meet at C here
quick pike
yeah
unborn plover
but c and b don't meet at C here?
quick pike
uhh not sure if i understand
but what we've done is create two triangles that lo...
right then I am using area= 1/2(ab)sinC like the pic you sent me.
unborn plover
here's the triangle with sides labeled
quick pike
I was right
unborn plover
what is the length of side a?
unborn plover
try that
unborn plover
hm
actually let's take a step back and find angle A instead
to do that we need angle B
quick pike
um...ok
unborn plover
sorry LOL
to find a we need A anyways
quick pike
Idk how to solve for A sorry...
quick pike
ah that's right I can use that
I think b is 0.28163672?
hang on
sinb/5.1=sin10.5/3.3
I cross mult
yeah I keep getting 0.28163672?. Is that right?
quick pike
yep
unborn plover
this is what i'm getting
unborn plover
this is what i'm getting
maybe try to recreate what i got
but now that we have two angles
and we know a triangle adds to 180
we can find A
quick pike
A is 153.2
unborn plover
yes it is
quick pike
180=10.5+16.3+x
quick pike
yeas
unborn plover
then you're almost done👍
unborn plover
that's it yeah
good job
now if we go back to our original question we have 2 equal triangles
quick pike
is it 14.3954566 all togather?
unborn plover
should just be 3.79*2 = 7.58
unborn plover
umm i'm not sure how you're supposed to round
quick pike
Round to using measurement rules. it said
unborn plover
i would say 7.6 because the given numbers are also 2 digits
quick pike
ok I will answer that.
hey! it's right!
7.6
can you help me once more? Or you gtg now.
unborn plover
umm sure i have time
quick pike
unborn plover
oh this one is much simpler
quick pike
huh?
unborn plover
they're all the same
unborn plover
1/2 ab sin C would work
but it seems you did 1/2 bc sin C, which isn't valid
like technically there are also 3 area* formulas
unborn plover
but in reality these all just take in two sides and an angle the same way
quick pike
so I can use c^2=a^2+b^2-2(ab)cosC
unborn plover
yeah
quick pike
got it 3.30
unborn plover
👍
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unborn plover
you too lol
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solemn wyvern
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solemn wyvern
$$
\begin{aligned}
&y=\sqrt{1+e^x}, 0\leq x\leq9 \
&S=2\pi\int_a^b\sqrt{1+f'(x)^2}:dx \\
&y'=\frac1{2}(1+e^x)^{-1/2}\cdot\frac{d}{dx}(1+e^x) \ \
&y'=\frac1{2}e^x(1+e^x)^{-1/2} \
&y'^2=\frac1{4}e^{2x}(1+e^x)^{-1}\text{ OR }\frac{e^{2x}}{4(1+e^x)} \
&\int_0^9\sqrt{1+\frac1{4}e^{2x}(1+e^x)^{-1}}\text{ OR }\int_0^9\sqrt{1+\frac{e^{2x}}{4(1+e^x)}} \
&\int_0^9\sqrt{1+e^{2x}(4+4e^x)^{-1}}
\end{aligned}
$$
ocean sealBOT
Wolfe
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solemn wyvern
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drifting maple
Help
zinc haven
!1c
lone heartBOT
Please stick to your channel.
zinc haven
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raw bolt
Help
for line 1 to be perpendicular to line 2 with slope 'a', what should be the slope of line 1?
drifting maple
for line 1 to be perpendicular to line 2 with slope 'a', what should be the slop...
Idk, I'M ASKING FOR HELP
raw bolt
cool
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cerulean herald
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swift saddle
solve for x
cerulean herald
without calculator
swift saddle
sin(30deg) = 0.5. Should be memorized
recognize its a 30 60 90 triangle
have that memorized too
swift saddle
yes
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tame nebula
why does looking for asymptotes in tan
is start ( ) - -pi/2
end: ( ) - pi/2
while cot is only
start = ( ) = 0
end = ( ) = pi
swift saddle
rephrase the question?
tame nebula
rephrase the question?
its for graphing tan and cot
see here
solutions for asymptotes
x- pi/2 = 0 and x - pi/2 = 2pi
but if the given was tan
it would be x = -pi/2
and x = pi/2
swift saddle
but whats the question....
tame nebula
its for the start and end of the first 2 grey broken vertical lines you see here
for tangent
sour verge
solutions for asymptotes
x- pi/2 = 0 and x - pi/2 = 2pi
tan(x) has asymptotes whenever cos(x) = 0, since tan(x) = sin(x) / cos(x). This happens when x = -pi/2, pi/2, 3pi/2, ...
cot(x) has asymptotes whenever sin(x) = 0, since cot(x) = cos(x) / sin(x). This happens when x = -pi, 0, pi ...
tame nebula
tan(x) has asymptotes whenever cos(x) = 0, since tan(x) = sin(x) / cos(x). This ...
perfect
thank you
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lofty agate
I'm trying to figure out why we divide by the expected count in the Chi Squared test. This answer was really helpful:
https://math.stackexchange.com/a/2074074/1226290
However, I have the same question as the commenter on the answer "sdd" (see attached image).
Isn't Oi a binomial random variable, not a poisson? I can't see why Oi would be poisson distributed.
lofty agate
Can anyone help me to understand?
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@lofty agate Has your question been resolved?
lofty agate
<@&286206848099549185>
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vapid steppe
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vapid steppe
can someone help me rank the moments of inertia for the 4 objects
they all have the same area
wind cloak
what's the axis
vapid steppe
what's the axis
the dots are the pivots
wind cloak
are the triangles equilateral
limpid turret
The drawings kinda aren't helpful
vapid steppe
i dont think they are triangles either way they didnt give it
limpid turret
Then whoever gave you the problem isn't helpful
wind cloak
The moment of inertia appraoches its minimum value as the axis approaches the center of mass
I'll say that; it'll be helpful on a better diagram
vapid steppe
Then whoever gave you the problem isn't helpful
what would u need to know to solve the problem
oh it said the horizontal lengths are the same
for all of them
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vapid steppe
wait i meant to say the dots are the center of mass
wind cloak
then where're the axes
limpid turret
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vapid shuttle
Consider $$A_G =
\begin{bmatrix}
\begin{matrix}
A_1 & 0 & 0 \
0 & A_2 & 0 \
0 & 0 & A_3 \
\end{matrix} & 0 & \cdots & 0 \
0 & \begin{matrix}
A_4 & 0 & 0 \
0 & A_5 & 0 \
0 & 0 & A_6 \
\end{matrix} & \cdots & 0 \
\vdots & \vdots & \ddots & \vdots \
0 & 0 & \cdots & \begin{matrix}
A_{k-2} & 0 & 0 \
0 & A_{k-1} & 0 \
0 & 0 & A_k \
\end{matrix}
\end{bmatrix}
$$
where each ( A_i ) is a square matrix of size ( (n+1) \times (n+1) ) given by
$$
A_i =
\begin{bmatrix}
0 & 1 & 1 & \cdots & 1 \
1 & 0 & 1 & \cdots & 1 \
1 & 1 & 0 & \cdots & 1 \
\vdots & \vdots & \vdots & \ddots & \vdots \
1 & 1 & 1 & \cdots & 0 \
\end{bmatrix}$$
ocean sealBOT
Austin
vapid shuttle
Okay, I don't know how to type it properly, but imagine the last column is a column of 1's (except the very bottom right entry is a 0) and the same with the last row, it is all 1's except the very bottom right entry is 0.
How can I prove a matrix of this type is diagonalizable no matter its size?
wraith stratus
so every entry is 1 except on the diagonal which is 0?
vapid shuttle
No
The matrix looks like A_G with those diagonal blocks where every entry is 1 except on the diagonal which is 0
wraith stratus
yeah i mean the A_i's
vapid shuttle
except it also has a row all 1's at the bottom
and a column of all 1's on the right
but the very bottom corner entry is still 0
vapid shuttle
yeah i mean the A_i's
yes to this then
keen pasture
yes to this then
And you need to show that A_G with those defined A_i is diagonalizable?
worn fox
if A and B are diagonalisable then
A 0
0 B is diagonalisable
vapid shuttle
if A and B are diagonalisable then
A 0
0 B is diagonalisable
It isn’t block diagonal matrix tho
That’s my issue
The end column and row are 1s
Except a 0 on the diagonal
worn fox
in A_G?
vapid shuttle
And you need to show that A_G with those defined A_i is diagonalizable?
Yes
keen pasture
Isn't A_G symmetric anyways?
vapid shuttle
Do you know symmetric, real matrix => diagonalizable
What about the 0 matrix?
keen pasture
It is already diagonal?
keen pasture
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queen hamlet
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queen hamlet
Not sure how to do this
tribal field
Well, a sector of angle 305° would be what fraction of the full circle?
tribal field
And what's the area of the full circle?
queen hamlet
not sure
tribal field
What's the formula for the area of a circle?
queen hamlet
A=pir^2
tribal field
You have the radius, so what's the area?
queen hamlet
i dont know man i suck at math
waxen shoal
yo yo, does anyone here know graph theory? like euler paths/curcuits, stuff like that?
tribal field
yo yo, does anyone here know graph theory? like euler paths/curcuits, stuff like...
Dude, get your own channel
waxen shoal
oh my bad
tribal field
i dont know man i suck at math
What's your radius?
waxen shoal
fuck
queen hamlet
What's your radius?
7
queen hamlet
OHH
tribal field
U got it? 😃
tribal field
So the area of the sector....
tribal field
Yep
tribal field
Yep
If that's all, you should close the channel now
tribal field
Yeah, that works
queen hamlet
can you check my work for this
tribal field
You need to be a bit more accurate
You're a hundredth of a degree off
tribal field
can you check my work for this
Other than that, you're good
gleaming ivy
hi, how would i go about solving this? the square root and +1 is throwing me off
wet glen
probably need a trig substitution
sour verge
I doubt that would do anything to help, integrals like that just don't have nice solutions. The antiderivatives will end up using error functions/hypergeometric functions.
lone heartBOT
@gleaming ivy Has your question been resolved?
livid urchin
you would need to numerically calculate
gleaming ivy
@livid urchin @wet glen @sour verge this is the whole question, i thought the first step was finding the integral but maybe im going about this incorrectly?
sour verge
Ah
wet glen
ohh thats way easier
gleaming ivy
is it? yeah my approach was probably wrong
sour verge
n=5 means we will split the interval we integrate over i.e. [0,1] into 5 intervals.
gleaming ivy
n=5 means we will split the interval we integrate over i.e. [0,1] into 5 interva...
so like .2 .4 .6 .8?
sour verge
Yeah like [0, .2], [.2, .4] ...
Now we consider those as rectangles, and their height is given by the value in the middle of the interval.
So for instance, the first rectangle has width .2 (they all do), and then the height will be f(0.1).\
f is the integrand here
So, for a given rectangle, we get its area by multiplying f(middle point) * 0.2
And add all of them up.
Can you write that in sigma sum notation?
gleaming ivy
So, for a given rectangle, we get its area by multiplying f(middle point) * 0.2
do i have the idea down?
sigma notation is still new to me so im tryna figure out how to write something in it myself
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gleaming ivy
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gleaming ivy
do i have the idea down?
<@&286206848099549185>
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@gleaming ivy Has your question been resolved?
edgy drum
How would you test for convergence or divergence. Alternating and ratio test won't work?
naive valley
do the terms go to zero?
edgy drum
do the terms go to zero?
Wdym?
vapid steppe
nth term test
edgy drum
nth term test
Nth term for the terms goes to 3/2
merry iris
Nth term for the terms goes to 3/2
so it diverges?
edgy drum
Oh isn't it different for alternating series?
merry iris
no
you can effectively ignore the alternating part
(-1)^n
well think about it like this
is 1-1+1-1+1... convergent
a series which can be represented by 1 * (-1)^n
nth term test gives us the limit = 1 ignoring the alternating part
so it diverges
and it should be obvious that that series doesnt converge to anything just by looking at it
if the limit ≠ 0 then the series diverges even if it is alternating
edgy drum
Ok thank you for the explanation
crimson field
It’s pretty simple to prove too if you know all the definitions
I’m just learning about cauchy sequences
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wanton holly
