(cx + r) cos(1.25pi) is what I was using as a calc
#help-23
cobalt estuary
ah, the () are wrong then
i guess that would make sense
flat frigateBOT
cobalt estuary
,w 50cos(1.25pi)+55
flat frigateBOT
cobalt estuary
,w 50sin(1.25pi)+55
flat frigateBOT
cobalt estuary
i forgot that the y axis on SVG are reversed as well
cunning patio
Like the y-axis goes from top to bottom instead of the other way around?
cobalt estuary
yes
cunning patio
What about flipping the sin then. So (50cos(t) + 55, -50sin(t) + 55)
cobalt estuary
,w -50sin(t) + 55
flat frigateBOT
flat frigateBOT
cobalt estuary
that works
cunning patio
Nice
cunning patio
Good, and np
cobalt estuary
.close
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hushed anchor
Why does PIE not work for this question:
In a 13 card deck 2 through A, how many 5 card hands can you select that don’t have any adjacent cards
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Why does PIE not work for this question:
In a 13 card deck 2 through A, how many...
buoyant shadow
when looking for an intersection of "hands with 23" and "hands with 34" it has a different size from intersection of "23" and "45"
that would be one way to make it not work, i don't know if that's how you did it
hushed anchor
what do you mean
the way i was thinking was
(13 choose 5)-12*(11 choose 3) + 11 (10 choose 2) - 10(9 choose 1 ) +9
because like first is just part of complimentary
second is because of i choose a pair(12 ways) then the rest three chosen from rest 11
similarly
well thats the way i was approaching it
buoyant shadow
11 (10 choose 2) is supposed to be hands with 2 pairs of adjacent cards
instead it only counts the ones that have "234"
and misses "2356"
buoyant shadow
i'll get back in 3 minutes
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buoyant shadow
i don't know how to solve it
hushed anchor
nw ty i got my mistake atleast
buoyant shadow
60% there's an easy trick i forgot
so like there's 13 parking spots and 5 cars
yeah, defintiely forgot the easy trick
there's 8 cards that aren't picked
so it's 9 choose 5
hushed anchor
i also tried thinking of
like
a< b <c< d <e from 1 through 13
and b-a>=2 c-b>=2 d-c>=2 e-d>=2
buoyant shadow
you can think of it as stars and bars
buoyant shadow
there are 6 buckets where the extra 8 cards go
but 4 of them definitely go in between, there's 4 cards left to distribute
buoyant shadow
i gave 2 similar solutions
hushed anchor
Gave 126 in end
hushed anchor
Well atleast now I know the answer just gotta think of how to formally say it
merry fog
derivative = 0 at the minimums and maximums
the uhm, relative minimums and maximums? i think thats the english term
the tip of the U shapes basically sorry for the bad english lol
its positive when the functions y value is increasing and negative when the functions y value is decreasing
merry fog
derivative = 0 at the minimums and maximums
i think the first two might be zero, because of this
but i cant see the x = 6 point
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jolly stirrup
hello i do not understand the last step
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hello i do not understand the last step
lapis stump
first
they multiply 4 with the second parenthesis
so that goes into 48x
now
that 48x gets passed to the front
and now its just (x²+3)⁻³ · (x² +3)⁻²
using exponents properties
lapis stump
how did they multiply it?
u get it?
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jolly stirrup
and now its just (x²+3)⁻³ · (x² +3)⁻²
i dont get this
lapis stump
i dont get this
x² · x⁴ = x⁶
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lean otter
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lean otter
Hey could someone help me with this, I understand that reflections occur when the multipliers are negative but I’m struggling still
lean otter
Okay so that’s the original graph
magic junco
No it’s not
lean otter
Then what’s that
lean otter
Uhhh..
magic junco
Do you know you can set restrictions to a function?
lean otter
Yes
magic junco
lean otter
I just want to write an equation for the function y= x^2 + x reflected in the given axis
magic junco
That’s what I intended to notify
magic junco
I just want to write an equation for the function y= x^2 + x reflected in the gi...
Ik
magic junco
Just move the negative symbol to the right side
-f(x)=x^2+x
f(x)=-x^2-x
lean otter
I think i figured it out
When reflecting on the x axis, the - multiplier goes on the outside of the original function given
When reflecting on the x axis you put the negative multiplier IN the brackets ex : (-x)?
Please confirm or deny
@magic junco
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spiral sun
What are the number of ways that 4 runners can finish including the combinations where at least 2 runners tie?
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What are the number of ways that 4 runners can finish including the combinations...
brazen ravine
first the one where they finish at different times
spiral sun
I did 4! First for if nobody ties.
2nd scenario:
If 2 people tie there can be 4C2 ways times 2! For the other two who do not tie (the ways they are arranged?) . However they can tie either 1st 2nd or 3rd so
4C2 x 2 x3
3rd scenario is where 3 tie right so it can be 31 or 13 so it's 4C3 x 2
and last scenario is they all tie which = +1
Is this right?
Or am I missing something?
So total = 4! + 4C2 X 2 X 3 + 4C3 X 2 +1
Can someone please check
hushed anchor
What are the number of ways that 4 runners can finish including the combinations...
case work?
spiral sun
Wdym?
hushed anchor
did you try case work
spiral sun
What's that
hushed anchor
well seperating into the 6 scenarios
hushed anchor
wait just wodnering for teh question
when you say tie
do you mean only for first or for any position
hushed anchor
case 1 : no ties
case 2 :2 tied for first/second
case 3:2 tied for second/third
case 4: 3 tied for first/second/third
case 5: 3 tied for second/third/fourth
case 6: 4 tied for first
would that be correct to say
spiral sun
case 1 : no ties
case 2 :2 tied for first/second
case 3:2 tied for second/third
...
Wdym second twice for case 2 and 3
hushed anchor
case 2 example:
First Place: 1 and 2
Second Place 3
Third Place 4
case 3 Example:
First Place: 1
Second Place: 2 and 3
Third Place: 4
hushed anchor
so number of ways per case:
case 1: 4!
case 2: (4c2) *2!
case 3: (4c2) *2!
case 4: (4c3)
case 5: (4c3)
case 6: 1
sum that up
that should idealy work lmk if i am missing something
Got it?
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tame zephyr
does a convergent subsequence mean monotoned subsequence?
safe radishBOT
does a convergent subsequence mean monotoned subsequence?
devout shale
does a convergent subsequence mean monotoned subsequence?
No
You can be convergent without being monotone
tame zephyr
right
but thats for the whole sequence..
what if just the subsequence is convergent
devout shale
Your question needs to be more specific, it isn’t clear what you are asking
devout shale
what if just the subsequence is convergent
The subsequence can be convergent without being monotone
For example take a subsequence of (-1)^n / n where you take every 5th and 6th term
It alternates in sign, so it’s not monotone
But it converges to 0
tame zephyr
if the whole sequence converges to 0, then every subsequence also converge to 0 too
so basically the convergence and divergence of subsequences will be the same as the whole sequence?
devout shale
No
Consider the sequence (-1)^n
This does not converge
We can take a subsequence -1, 1, -1, 1, 1, 1, …. 1, … 1
Not monotone
But still convergent
tame zephyr
ahh okok
so to be clear, if the whole sequence converges to some value, then every subsequence converges to the same value, BUT this is not true for divergence
devout shale
so to be clear, if the whole sequence converges to some value, then every subseq...
Yes
tame zephyr
thank you!
devout shale
No problem
tame zephyr
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tame zephyr
question abut a section of the proof
so we suppose that Xnk -> b.
but it says for this eps >0, there exists n_0 s.t |xn-b| <eps for all n> n_0
but that would only be the case if EVERY subsequence converges to b
right?
rustic goblet
i believe so
well, if X_n_k converges to b, then every subsequence of X_n_k has to converge to b too
tame zephyr
yea
but in the proof somehow they assumed its every subsequence of x_n_k that converges to b
wouldnt you have to explicitly state that
tame zephyr
but in the proof somehow they assumed its every subsequence of x_n_k that conver...
like they didnt state that its every subsequence
they said there exists such susequence where it converges to b
junior smelt
The assumption that there's an even n 
tame zephyr
lol yea
junior smelt
They should really justify why there should be one 
Think they messed their proof up quite a bit 
junior smelt
tame zephyr
is my "concern" correct tho?
junior smelt
They very most likely wanted to talk about the subsequence rather than the whole sequence here
junior smelt
is my "concern" correct tho?
And the previous comment was more that every "sub"subsequence (
) of that x_n_k converges to b, because it's a subsequence of the sequence x_n_k (if you take it as a sequence in its own right)
It doesn't need to be that all subsequences of x_n converge to b, but if you have one subsequence that does, then any sub-subsequence of that also converges to b too (if that makes sense? Probably a bit confusingly worded 
)
tame zephyr
ok yea I agree, if X_n_k -> b then all its subsequences also converges to b
thats why I was confused cause they are saying x_n converges to b, but only stating there exists x_n_k->b
junior smelt
Yep, that's their error
Anyways, if you replace that with the subsequence, you won't have the indices being "eventually" odd or "eventually" even (why not?)
Then you can make the statement that you can take an even n_k then do what they did and all 
tame zephyr
Anyways, if you replace that with the subsequence, you won't have the indices be...
what do you mean
junior smelt
As in, you know how the subsequence is basically x_n_k
You won't get to a point where all of the n_k's are purely odd, or purely even, after some point
tame zephyr
huh? im not following..
cause you can have say n_k = 2k and so they are all purely even
junior smelt
cause you can have say n_k = 2k and so they are all purely even
You can't, not in this case 
You can't have anything either that's, say, some random integers for a while, then purely even, like 1, 5, 17, 18, 20, 22, 24, ... or anything like that either
If you did, something goes wrong... 
tame zephyr
You can't, not in this case <:catGiggle:668948717772079128>
how do you know not in this case
junior smelt
how do you know not in this case
You tell me, I'm asking you
tame zephyr
hm waittt
well if Xnk converges to b, and b != 1, then n_k=2k wont work, same goes for n_k=purely odd indices....but I dont think this is the case
I was gonna say the sequence xn is itself a subsequence
tame zephyr
You won't get to a point where all of the n\_k's are purely odd, or purely even,...
this is true, but its is also true for any n_k thats not only purely odd or even?
junior smelt
I was gonna say the sequence xn is itself a subsequence
(as above, it is, but we're talking about one specific subsequence of x_n, not all possible subsequences)
junior smelt
this is true, but its is also true for any n_k thats not only purely odd or even...
And you could potentially have a choice of n_k's to form your subsequence such that you can always find some odd and some even as you go along - you're going to contradict that separately...
junior smelt
well if Xnk converges to b, and b != 1, then n_k=2k wont work, same goes for n_k...
And I'll take that 
if you were eventually even, then the subsequence becomes eventually constantly 1, and so must converge to 1 - but then we assumed b wasn't 1 (ditto with eventually odd and -1)
After all, limits need to be unique (including when considering subsequences as sequences in their own right!)
tame zephyr
ahh ok
yes because you only have to prove there exists one subsequence st it goes to b
and easiest to just say, take an even n
wait
take an even n_k
not n
yea so easier than to use the whole sequence, where even though it is still a subsequence, you gotta then prove contradiction for both odd and even
thank you!
junior smelt
yes because you only have to prove there exists one subsequence st it goes to b
Well more that you're trying to show that there's no such subsequence that can converge to anything that's not 1 or -1 (which is stronger than proving the whole sequence doesn't converge) - you're doing this by contradiction, so assume just the one subsequence exists, and get something impossible 
tame zephyr
ok
junior smelt
if the subsequence was such that you only had even indices from some point on, then you'd contradict the assumption that b wasn't 1, but if it weren't, it's basically what they did 
tame zephyr
how they defined eps>0
thats something i'll never think of
how would you even know to set eps = (b-1)/2
ahh wow
junior smelt
It's one of those things I guess that come with experience and seeing how to break things 
tame zephyr
ahhh its so clever
junior smelt
Yep 
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@tame zephyr Has your question been resolved?
tame zephyr
currently working on smth else
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@tame zephyr Has your question been resolved?
tame zephyr
oh my goodness
so update i guess
im currently working on this questio
tryna gather some pieces together and just write down some notes
I like some portions of this proof
Im thinking I have to do something similar
but yea, im still sort of looking around
tame zephyr
this is just one section of the proof to the proposition
yea so i definitely dont have a natural gift for proofs and stuff
likely I'll have to continure this tmr or smth
but im getting some stuff i guess?
random jot notes which I dont think is getting me anywhere but atleast its something
but also Im like getting sidetracked and going on my phone lol😂
yea I'll take like a short break heheh
and um idk if i'll continue this
maybe i will maybe not
tame zephyr
yea lolol so what I ended up doing was explaining the proof we just did to a friend
tomorrow I'll do more
thanks @junior smelt !!
.close
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junior smelt
thanks <@788085606483361802> !!
A pleasure! I’m just getting some sleep now
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pine fjord
help 14
sonic spruce
!status
safe radishBOT
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 is $(0.008)^\frac{-1}{3}$
flat frigateBOT
Adrien-Marie Legendre
pine fjord
3ssqrt0.008(-1)?
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@pine fjord Has your question been resolved?
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@pine fjord Has your question been resolved?
pine fjord
oh my good
lool
eager torrent
$2\int{1-\frac{b^{2}}{2}}^{1}\sqrt{1-x^{2}}dx+2\int{\frac{b^{2}}{2}}^{b}\sqrt{b^{2}-x^{2}}dx = pi/2$
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$2\int{1-\frac{b^{2}}{2}}^{1}\sqrt{1-x^{2}}dx+2\int{\frac{b^{2}}{2}}^{b}\sqrt{b^...
flat frigateBOT
Pablo
eager torrent
i need help solving this, its from the goat problem search it up on wiki for more info
Second question (There are 2 in the wiki)
<@&286206848099549185>
sweet thorn
<@&286206848099549185>
i can integrate it idk if thats exactly what u want
tall bough
U need to find the value of b?
eager torrent
i can integrate it idk if thats exactly what u want
solve for b
sweet thorn
solve for b
Let's see
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jade oriole
Guys can someone tell me whats the formula to answer this ❓
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Guys can someone tell me whats the formula to answer this ❓
jade oriole
In a shop,
380
people buy socks,
150
people buy shoes, and
200
people buy belts. If there are a total of
580
people who bought either socks or shoes or belts and only
30
people bought all the three things? So, how many people bought exactly two things?
The answer is 90 but idk how the answer is 90
jade oriole
Look my friend send me this
jade oriole
Are you familiar with inclusion/exclusion?
I dont
strange ginkgo
No worries
jade oriole
Please Tell me how it become 90
strange ginkgo
So let's start by seeing how many of each item were sold
jade oriole
Ok
strange ginkgo
Please Tell me how it become 90
We'll get there, no worries
So we have 380 socks, 150 shoes and 200 belts, so in total 380 + 150 + 200 = 730 items were sold
jade oriole
Yes
strange ginkgo
We also know that 580 people bought only one item
meaning that 730 - 580 = 150 items were bought by people who bought more than 1 item
jade oriole
Why you minus it 🤔
strange ginkgo
Because there were 730 items sold, of which 580 were sold to people who bought only one item, so the number of items that were sold to people who bought more than one item, must be the difference
Does that make sense?
strange ginkgo
Give me just a moment, I mght have misinterpreted part of the question haha, I'll get back to you within a couple of minutes
jade oriole
Okay
strange ginkgo
Okay I see I made a mistake and interpreted the question wrong, so forget what we did so far ^^'
jade oriole
Ok
strange ginkgo
New approach: we have 380 people who buy socks, of which some buy just socks and some may buy other items as well.
The same holds for the shoes and belts
strange ginkgo
If we draw a diagram just like your friend did:
we can make a whole bunch of equations using these letters
If each circle represents one of the items
jade oriole
A venn diagrams ok
strange ginkgo
for example the top left circle represents the socks, then we have that regions a,b,d and e together must be 380, since 380 people bought socks
similarly for the other two circles we get:
b+e+c+f = 150
d+e+f+g = 200
The question asks of us the total number of people who bought precisely two items, which is the number of people in the regions b, d and f combined
We have 2 more clues in the question, namely that e = 30, since that is the number of people who bought all 3 items
and a + c + g = 580, since that is the number of people who bought only one item
Does this all make sense?
jade oriole
Yes it starts to make sense when u drew a venn diagram
strange ginkgo
That's good to hear! in general for a lot of these questions with categories and overlaps it is very useful to draw a venn diagram
At this point we have all the equations we require to solve the problem, we just need to add and subtract them in a clever way
jade oriole
But can u tell where is the 730 items?
strange ginkgo
That's actually pretty hard to do
jade oriole
What hard
strange ginkgo
since we don't know at this point how many of the people who bought items, bought multiple items
jade oriole
At this point we have all the equations we require to solve the problem, we just...
What next here
strange ginkgo
So we have these equations:
a+b+d+e = 380
b+e+c+f = 150
d+e+f+g = 200
e = 30
a+c+g = 580
And we want to know the value of b+d+f = ?
jade oriole
Yes
strange ginkgo
So to start out we would like to add some equations to obtain a large equation with b,d and f in it.
For example we could add the first 3 equations
jade oriole
It equals to 730
strange ginkgo
We then get
a+c+g+2b+2d+2f+3e = 730
At this point we can use the 4th and 5th equations to get rid of everything that is not b,d or f, to obtain our answer
jade oriole
How?
strange ginkgo
we know e =30, so we can substitute that in the equation
so we get a+c+g+2b+2d+2f+90 = 730
same for a+c+g = 580
strange ginkgo
e = 30, so 3e = 3 * 30 = 90
jade oriole
Yeah but why its times 3
strange ginkgo
So we have these equations:
a+b+d+e = 380
b+e+c+f = 150
d+e+f+g = 200
e = 30
a+c...
We added the first 3 equations here, adding up the RHS got us to 730, and adding the LHS you have to add all the variables, and since each of those equations had an e in it, we end up with 3e
jade oriole
Ah ok
strange ginkgo
Now the interesting thing is that after performing the final calculations we don't get to b+d+f = 90, but to b+d+f = 30.
That's also why I thought I messed up before when using a different method haha, but I think your solutions manual might have an error in it
If it suggested the answer should be 90
Or I must've messed up something along the way, but I'm fairly certain we did do it the right way just now
strange ginkgo
so we get a+c+g+2b+2d+2f+90 = 730
We had this right?
after filling in a+c+g = 580 we get
580 + 2b+2d+2f + 90 = 730
2b+2d+2f = 60
b+d+f = 30
and that is the number of people that bought exactly 2 things
But at the start you mentioned that the answer should be 90, so I'm curious how you knew, since we just got to a different answer
strange ginkgo
Okay, so his solution is actually incorrect
strange ginkgo
The question tells us that the number of people who bought only 1 item, is equal to 580 right?
jade oriole
Yes
strange ginkgo
In his diagram the sum of the numbers that are in only one circle is:
290 + 110 + 40 = 440
strange ginkgo
ah whoops my bad, but still, we then get 290 + 110 + 60 = 460
strange ginkgo
I'm not entirely sure where he got it from either, but the method we just went through together is definitely the way to do it here.
jade oriole
The real answer is 60?
strange ginkgo
30
jade oriole
Same as the people who bought 3 items?
strange ginkgo
correct
A quick way to double check in this case (which we could've also used to solve the problem) is that we have 580 people buying 1 item, 30 buying 2 items and 30 buying 3 items, so the total number of items bought would be 580x1 + 30x2 + 30x3 = 730 items,
jade oriole
Thanks
strange ginkgo
You're welcome
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@jade oriole Has your question been resolved?
jade oriole
@strange ginkgo hey frosty another question how do i pit the values in the venn?
Put*
Are u still there frosty? @strange ginkgo
strange ginkgo
Hey
In this case you don't actually know the values of each individual area
We just found that the sum of some values was equal to something\
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unique abyss
How many solutions does x² + 1/x² = 1/1998² + 1998² have?
safe radishBOT
How many solutions does x² + 1/x² = 1/1998² + 1998² have?
lean otter
Put x² = u
1/x² = 1/u
Roots of the new equation are solution for u
Later deduce those for solving for x
unique abyss
isn't that gonna be longer than when I multiply both sides by x²
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desert pasture
Find the maximum value of $\frac{1}{5\sec^2\left(x\right)-\tan^2\left(x\right)+4\operatorname{cosec}^2\left(x\right)}$
safe radishBOT
Find the maximum value of $\frac{1}{5\sec^2\left(x\right)-\tan^2\left(x\right)+4...
flat frigateBOT
Why am. I here
desert pasture
so where do I even start here
what identity do I use?
I thought of expressing everything in terms of sin(x) and cos(x)
but that doesn't seem to help
hmm, maybe I express sec^2(x) in terms of tan^2(x)
ok, that gives
\frac{1}{5+4\left(\tan^2\left(x\right)+\operatorname{cosec}^2\left(x\right)\right)}$
why isn't TeX working?
$\frac{1}{\left(5+4\left(\tan^2\left(x\right)+(cosec}^2\left(x\right)\right)\right)}$
flat frigateBOT
Why am. I here
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
desert pasture
now what?
lean otter
uh probably am gm
desert pasture
I have to minimse the denom I guess
desert pasture
uh probably am gm
how would I apply that here?
lean otter
change csc to cot and sec to tan
vapid anvil
**Why am. I here**
Compile Error! Click the <:errors:504266556054962196> reactio...
I feel like it's right till here
I have a strong feeling
desert pasture
hmm, maybe it's at x=0
vapid anvil
You are going the right way
desert pasture
change csc to cot and sec to tan
hmm, ok, let me try that
wait, how would that work?
vapid lantern
Why can't you just use geogebra or something and type max(f(x)? haha
soz for interrupting
desert pasture
because I won't be allowed to use geogebra in my exam
desert pasture
, Trying to figure out how to do that,
obtuse jackal
Find the maximum value of $\frac{1}{5\sec^2\left(x\right)-\tan^2\left(x\right)+4...
have you tried just taking it as a calculus problem and finding when the derivative of the denominator is 0 ?
desert pasture
I was hoping to learn to do this without calc, but I;ll try that, thanks
obtuse jackal
it works very well
desert pasture
**Why am. I here**
Compile Error! Click the <:errors:504266556054962196> reactio...
hmm, differentiating the denom here gives, $8(tan(x)sec^2(x)-cosec^2(x)cot(x))$
equating that to zero, that gives
$4tan^4(x)=1$
flat frigateBOT
Why am. I here
desert pasture
or $tan(x)=\frac{1}{\sqrt2}$
flat frigateBOT
Why am. I here
flat frigateBOT
Why am. I here
safe radishBOT
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lean otter
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thin bridge
whether you differentiated correctly depends on the full equation
lean otter
.close
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alpine palm
Is this correct?
safe radishBOT
Is this correct?
junior smelt
Why'd you react w a cryingcatno emoji...😭 <@788085606483361802>
Explain your 7?
alpine palm
Explain your 7?
The axis is vertical and it's standing upright so if I rotate it, I'll get the side part which isn't identical and then I rotate it again, I'll get the identical part (1), and then I rotate it again and I get the sode part, then I rotate it again and get the original (2)
junior smelt
Wait are you supposed to have drawn in the axis, or was the axis given to you?
alpine palm
Wait are you supposed to have drawn in the axis, or was the axis given to you?
We had to draw the axis
It can either be vertical, horizontal, or diagonal I think
I prefer vertical and horizontal
)
alpine palm
<:catThink:1073406415575728200> why did you choose vertical over a horizontal on...
For q5 or 7?
If 7, won't the answer still be 2 orders
Or am I mixing this all up 😭
junior smelt
For q5 or 7?
For q7: I’m saying to compare what you did there with what you did in q5
hybrid wedge
Isn't q 7 is same as qstn 2
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@alpine palm Has your question been resolved?
alpine palm
For q7: I’m saying to compare what you did there with what you did in q5
I'm confused as it's standing upright
Wait nvm I get it
But I'm mainly confused on the axis
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native robin
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native robin
How can I do part d?
last spruce
does anyone know how to do an arima model in excel
safe radishBOT
does anyone know how to do an arima model in excel
last spruce
i need helpp
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@last spruce Has your question been resolved?
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@last spruce Has your question been resolved?
dry pecan
can some explain how this diverges - i get -1/2 as the answer
safe radishBOT
can some explain how this diverges - i get -1/2 as the answer
delicate sphinx
What about when you plug in 3?
safe radishBOT
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lean otter
The solution set of the system
1/2 x - 2y +8z =0
2x - 8y -32z =0
Is a 2 dimensional subspace of R^3
lean otter
It is a true or false question
So I know how to find basis
what have you tried
Since the two eq are parallel
z= s
y= t
So we get x= -16s + 4t
And we can write this in vector form
Um
It will be in R^3
Cause in the vector I'll get 3 rows
But I don't understand if it will be 2D subspace of R^3
-16
0
1
Times s
And
4
1
0
Times t
How so I know if this goes through origin?
If it goes through origin then yes the statement is true
lean otter
The solution set of the system
1/2 x - 2y +8z =0
2x - 8y -32z =0
Is a 2 dimen...
<@&286206848099549185>
The solution set of the system
1/2 x - 2y +8z =0
2x - 8y -32z =0
Is a 2 dimensional subspace of R^3
True or false
.lcose
.close
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loud grove
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slender pendant
Well you know x + y = 42
Using trig you can get x/y
Then you can just solve the eq
loud grove
What
slender pendant
Use tan
loud grove
Yes but how
slender pendant
So you know $\tan(41) = \frac{|BD|}{|AD|}$ and $\tan(35) = \frac{|BD|}{|DC|}$
flat frigateBOT
casework
loud grove
Yes
slender pendant
Divide those 2 to get x/y
slender pendant
The equations
loud grove
Yes
slender pendant
I mean ig you can just get $|BD|$ and make those 2 equal
flat frigateBOT
casework
slender pendant
Same thing
loud grove
How do you get BD
slender pendant
I meant like $|BD| = |AD| \tan(41)$ and $|BD| = |DC| \tan(35) $
flat frigateBOT
casework
loud grove
hm
slender pendant
**casework**
So x + y = 42
And you get x/y from here
Since both those things are $|BD|$ they are equal so $|AD| \tan(41) = |DC| \tan(35)$
flat frigateBOT
casework
slender pendant
That gives $\frac{|AD|}{|DC|} = \frac{\tan(35)}{\tan(41)}$
flat frigateBOT
casework
slender pendant
And you also have $|AD| + |DC| = 42$
flat frigateBOT
casework
slender pendant
So you just solve those 2 eqs
loud grove
hm
Before you go
Could you also explain what my teacher did
I don’t get what he did
safe radishBOT
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lean otter
Given a cube ABCDEFGH with edge 6 cm. If a is the angle between line AG and plane BDG, the value of sin a = .
safe radishBOT
Given a cube ABCDEFGH with edge 6 cm. If a is the angle between line AG and plan...
lean otter
,rotate
flat frigateBOT
lean otter
<@&286206848099549185>
glossy dew
ig root 6
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@lean otter Has your question been resolved?
quartz wasp
In a geometric sequence the a1,a2,…..a60 the first member is 3 and the difference is 1/4 out of this 4 what intervals do all the members sum equal
A)(3,4). B(4,5). C(5,6). D(6,+infinity)
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In a geometric sequence the a1,a2,…..a60 the first member is 3 and the differenc...
halcyon carbon
In a geometric sequence the a1,a2,…..a60 the first member is 3 and the differenc...
!status
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In a geometric sequence the a1,a2,…..a60 the first member is 3 and the differenc...
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
@quartz wasp Has your question been resolved?
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@quartz wasp Has your question been resolved?
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devout shale
what are the marks for?
arctic vapor
its uni stuff
devout shale
is it a test?
arctic vapor
nah, just a coursework
devout shale
Okay, show your graph
hot thistle
oh is this like a homework or something @arctic vapor
arctic vapor
this is the graph and my work for a(n), b(n) and the series itself
ignore the fact that one of the pages is red pen X'd, it is correct
didnt mean to
devout shale
@arctic vapor your graph loooks fine
honestly just start plotting your fourier series term by term
see if it matches uo
up*
or integral calculator where you have doubts
I'm not sure if anyone will look over 6 pages of integration
for fourier coefficients
arctic vapor
ye, i think the rest is fully correct too but its just so messy that its crazy. When i say messy im talking about the a(n) and b(n) values, do u see what i mean when u look at them?
arctic vapor
I'm not sure if anyone will look over 6 pages of integration
HAHAHA ye i agree
ive been doing it for hours and quadruple checking everything
devout shale
it's the worst
fourier coefficients are the worst
I feel like no matter how slow I go
arctic vapor
i believe its legit impossible to not be correct, but ye, it is messy
devout shale
I mess up somewhere along the way
devout shale
just graph it
arctic vapor
just graph it
im kinda struggling with this, not sure how to plot it in Mathematica properly. Its actually next subpoint of my coursework. They want me to plot the truncated series at n=5, 4 and 3
devout shale
use desmos
arctic vapor
does the fourier series converge pointwise to f?
well it has a lot of jump discontinuities periodically
i tried x=12 as a value out of curiosity
with n truncated at 5
and it kinda converges to 0.4 but it should be 0.5 i think
which begs my next question
i might be dumb but im really "struggling" with d) i think?
or is it really that simple that i think im struggling when im not
cause if you use the convergence theorem of the limits thing you get that it converges to 1/2
devout shale
Do you know what it means for f to be standardized?
arctic vapor
hmmm not sure
devout shale
At the points of jump discontinuity
if f is standardized
it takes on the average value at the jumps
and
if the fourier series is piece-wise C0
arctic vapor
which it is in this case
devout shale
we expect it to converge pointwise to the standardized f
which is f at all points of continuity
and ^ what I said above at points of discontinuity
arctic vapor
but doesnt that mean if x=12 it should converge to 12-12^2=-132
or am i dumb
obviously converging to such value is impossible in our case
arctic vapor
ye
devout shale
that's the value of standardized f at 12 then
which is what we expect our series to converge to pointwise
arctic vapor
the thing is
in the drawing u made
they want me to use the fact that
well, the theorem of convergence with the limits from left and right
the average of them 2 i mean
and for some reason thats where i struggle
devout shale
well, the theorem of convergence with the limits from left and right
I don't know what theorem you are referencing
arctic vapor
2 sec
devout shale
yeah
that is what I am referencing
that is the standardized f
notice at points of continuity
f(x0+)=f(x0-)
so that is just f(x0)
when f is continuous
and when it isn't it takes the average value of the jum
jump*
if f is piece-wise C0, its fourier series converges pointwise to f at all points of continuity, and at points of discontinuity it converges pointwise to the standardized f (which is what you have in your theorem there)
arctic vapor
ye, but for some reason i dont understand what the average value is from my graph
like
u drew it
for example
arctic vapor
the jump discontinuity at 2
arctic vapor
but then
ok, so that means
that the series converges to 1/2 in general? Like all of it? Because if you sub values in for the Fourier series (say x=12, n truncated at 5) it will go to around 0.4, not 0.5
any idea why that is?
devout shale
the fourier series at x=12 will converge pointwise to 1/2
at all points of discontinuity
it will converge pointwise to 1/2
devout shale
any idea why that is?
if this is happening, either you're not doing enough terms and it's just an innaccurate estimate, or you have made a mistake in your fourier series
arctic vapor
so does that have anything to do with the fact that i put the values of n=5 and x=12 in the series and the result for the series that i got was 0.4
ye
i figured
i should try
with more terms
i feel like 5 isnt enough
devout shale
likely not
arctic vapor
maybe ill give 10 a try, altho im not sure if it can go from 0.4 to 0.5
devout shale
I'd just graph your series
if your series is right, your sum estimate is right
it does converge pointwise to 1/2
arctic vapor
trying to see how the fuck i can plot this fourier series on desmos
btw
wouldnt also 1 be a point of jump discontinuity from the graph?
and so on, every integer
devout shale
yes
safe radishBOT
@arctic vapor Has your question been resolved?
arctic vapor
@devout shale
i fucked an integral up
;d
u know how u have -integral of vdu at the end
when u do integration by parts
i basically integrated the..integral of v
instead of integrating the v
🙂
hence why i have terms that are to the power of 4 rather than to the power of 2
kill me please
safe radishBOT
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Available help channel!
prisma condor
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prisma condor
This is what I have so far:
Which determinant properties can I use to solve this one?
eternal carbon
Which determinant properties can I use to solve this one?
det(A)det(B) = det(AB)
prisma condor
det(A)det(B) = det(AB)
So in this case:
$|AA^{T}| = (a^2+b^2+c^2+d^2)^4 = |A||A^{T}|$
flat frigateBOT
hamr
eternal carbon
more or less
prisma condor
more or less
If I don't know |A| or |A^T| then what do I do?
prisma condor
is this a linear algebra class
yes
eternal carbon
they did not tell you det(A) = det(A^T) ?
eternal carbon
quite indeed
prisma condor
so the answer is |A| = (a^2+b^2+c^2+d^2)^2
eternal carbon
yep 👍
prisma condor
Ty
eternal carbon
welc
prisma condor
.close
lean otter
safe radishBOT
pine spoke
!status
safe radishBOT
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
Hmm let me try and phrase it
I made a quick drawing here
As 19= 3x+7
3x=12
x=4
lean otter
thank you
btw, whenever the question is "show that x=4" ʻ its indicating to show a calculation right? --> an equation? or does it not necessarily have to be an equation?
median yacht
Assuming a 3x3 matrix, yk how when you compute the determinant of such a matrix, you split it up into 3 scaled 2x2 matrices and compute those determinants first. Basically, what do you call the product of the values not used in the first matrix computed (according to the picture, the first scaled 2x2 would be the number in position 1i * det(2,3;j,k), so does 1j * 2i have a special name or is it solely 1j * 2i? Alternatively, if not for just 1j * 2i, is there a name for 1i * 2j + 1k * 3i? I hope this makes sense
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median yacht
Question: #help-23 message
safe radishBOT
Question: https://discord.com/channels/268882317391429632/903481106819612714/121...
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lean otter
Question: https://discord.com/channels/268882317391429632/903481106819612714/121...
ping helpers
safe radishBOT
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sleek saffron
hi im following a book and idk how does this work
safe radishBOT
hi im following a book and idk how does this work
sleek saffron
severe pond
true
sleek saffron
any help pls? :D
safe radishBOT
@sleek saffron Has your question been resolved?
median yacht
<@1089061676080443412> Has your question been resolved?
No lmao
median yacht
ping helpers
I was doing something else
sleek saffron
open up another channel
median yacht
😐
sleek saffron
dont take mines
sleek saffron
no
u left
and thats that
theres 4 free rn just open a new one its not that hard
sleek saffron
uhh hold up lemme check again
median yacht
C = 27 + π²/2
sleek saffron
ty
sleek saffron
Assuming a 3x3 matrix, yk how when you compute the determinant of such a matrix,...
its called the minor
median yacht
Thanks to you as well
sleek saffron
Assuming a 3x3 matrix, yk how when you compute the determinant of such a matrix,...
basically the small 2x2 thing is called minor
after applying the (+/-) sign it is the cofactor
after transposing the cofactor thing u get adjoint
i assume ur finding the inverse of a 3x3 matrix
median yacht
Yeah eigenvalues or smth
sleek saffron
yeah thats basically it ig
median yacht
Thanks
safe radishBOT
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novel lintel
Can someone help me how to eliminate the m and n
safe radishBOT
Can someone help me how to eliminate the m and n
safe radishBOT
@novel lintel Has your question been resolved?
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@novel lintel Has your question been resolved?
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@novel lintel Has your question been resolved?
plain herald
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plain herald
$sqrt (x^2)(x^2 + 2x + 1)$
flat frigateBOT
cricketislife
plain herald
pls help on this question
plain herald
**cricketislife**
this is what i have so far
frigid locust
think of it like this
$$\sqrt{x^4 + 2x^3 + x^2} = \sqrt{(x^2)^2 + 2x^2x + (x)^2}$$
flat frigateBOT
JustToPro
plain herald
but aren't i supposed to factorise it
frigid locust
$\sqrt{(x^2)(x^2 + 2x + 1)} = \sqrt{(x^2)((x)^2 + 2(x)(1) + (1)^2)}$
flat frigateBOT
JustToPro
frigid locust
the solution says this but i dont understand the second part
familiar with
$$(a+b)^2$$?
flat frigateBOT
JustToPro
frigid locust
whats the answer
frigid locust
but how do you just look at it and know that its (a+b)^2
practice ig
frigid locust
!done
safe radishBOT
If you are done with this channel, please mark your problem as solved by typing .close
plain herald
.close
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worldly sinew
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worldly sinew
how come it isnt 0.62 if it asks for the mean of the sample proportion
oh wait is it because Mean: μpˆ = p
.close
safe radishBOT
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lean otter
Hi there, I was studying different graphical relationships in economics and I need a little help understanding some pointers in mathematical terms
safe radishBOT
Hi there, I was studying different graphical relationships in economics and I ne...
lean otter
AR is average revenue and MR is marginal revenue
I need to compare the slopes
Ik that MR = change in total revenue/ change in quantity
AR/Q graph is same as demand curve
How do I proceed
<@&286206848099549185>
spice furnace
I need to compare the slopes
So that what text does. Are you familar with gradients?
lean otter
So that what text does. Are you familar with gradients?
Yes
Okay I think I can do this one now
But I have another doubt about this same graph
Why are they intersecting on the y axis?
lean otter
When clearly AR = MR = 5 when Q = 1
lean otter
So that what text does. Are you familar with gradients?
I was able to write algebraic equations and differentiate to find slopes
spice furnace
I was able to write algebraic equations and differentiate to find slopes
So what is your question?
lean otter
So what is your question?
So is the graph incorrect?
spice furnace
Ah I miss that, your understanding is correct
lean otter
Ah I miss that, your understanding is correct
Wdym? So the graph is incorrect?
But everywhere I checked, it’s this same graph
spice furnace
It going to intersect at the y-axis, atually letting quantity equal 0 will mean MR and AR = 0
lean otter
No but see units sold = 1, AR= 5 = MR
lean otter
It going to intersect at the y-axis, atually letting quantity equal 0 will mean ...
I don’t get it
safe radishBOT
@lean otter Has your question been resolved?
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tulip wraith
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tulip wraith
can someone help me out with this
vagrant ice
can someone help me out with this
Sure, have you tried differentiating to find M?
tulip wraith
oh alright just give me a sec
do we need to differentiate tho?
cus when i do i get 2x-5
tulip wraith
so how exactly would it go
vagrant ice
Right so the axis of symmetry is x = -b/(2a) = 5/2
If you set 2x - 5 = 0 you get x = 5/2 as well; that's the coordinates of the vertex
And then find the y-coordinate
tulip wraith
okay so lemme find y rq
rocky isle
Heya! May I ask why its not the same?
safe radishBOT
Heya! May I ask why its not the same?
rare thistle
of course it's not the same
rocky isle
of course it's not the same
can i get an explanation :p since i followed the exponential rule tho
thin bridge
which rules
rare thistle
there's no rule here
rocky isle
which rules
this thing lol
rare thistle
two lines are just not equal
thin bridge
which rules were you applying to what exactly
rare thistle
the converted is wrong
rocky isle
and it seems like its not equal