oh i just used them because i couldn't figure out how to add subscripts
#help-10
royal basin
underscores work just fine
rugged kite
@summer stone For the record, my earlier question about factoring was leading to this.
Every polynomial such that P(2)=0 is divisible by X-2, so every polynomial in H is of the form (X-2)Q with Q some polynomial. Since we are restricted to degree 2 or less, Q must be of degree at most 1.
Since a basis for such polynomials is {1,X}, a basis for H is {X-2, X(X-2)}
royal basin
despite discord treating them as italics, the tex bot does them just fine
$c_0 + c_1t + c_2t^2$
warm shaleBOT
Ann
rugged kite
But it was good to yake your time with it
summer stone
$c_(0) + c_(1)t + c_(2)t^2$
rugged kite
As my teacher says, "the correct method will be whichever one you wind up using"
summer stone
oh it works without brackets
summer stone
<@380989650615140362> For the record, my earlier question about factoring was le...
oh okay okay
alright, thanks a lot!
and sorry for taking up so much of ur time
.close
finite flame
How?
finite flame
How it forces it to be one-one?
royal basin
isn't that exactly what is explained in the next lines
rugged kite
The fact that it is injective is explained right after
Surjectivity isn't too hard to see, because for instance f(f(n)+f(0))=n so every natural number is reached
finite flame
Yo lol my math’s weak i dont get it
finite flame
Surjectivity isn't too hard to see, because for instance f(f(n)+f(0))=n so every...
How do you see it?
royal basin
Yo lol my math’s weak i dont get it
have you read the lines immediately after the "In fact, we see that"?
rugged kite
How do you see it?
The definition of surjectivity is that for any number n, you can find an input k such that f(k)=n
i.e every output is reached
In this case, we have f(f(n)+f(0)) = n
So for any output, we can find a corresponding input, namely f(n)+f(0)
By definition, it is surjective
finite flame
The definition of surjectivity is that for any number n, you can find an input k...
But in here k is independent of n right?
.close
fallen crane
Hi, can anyone help me? I don't know how to start 😄
obtuse pebbleBOT
Hi, can anyone help me? I don't know how to start 😄
@fallen crane Has your question been resolved?
real orchid
Without working it out myself, I would start with working out the probability of getting two 6's in a row in 2 rolls. Then getting two 6's in a row on the third roll without getting it on the 2nd roll. I'd then either expect to see some telescoping sum or to realise that I have to work out the probability of not getting two sizes in a row on the 2nd, then third...
fallen crane
Without working it out myself, I would start with working out the probability of...
Let's say I have 3 throws, then there are two possible solutions, 6X6 and XX6. What are the chances of me throwing one of them?
(1/6)(5/6)(1/6) + (5/6)(5/6)(1/6) = 5/36
that's good?
Or I have to do all the possible combinations
real orchid
If X is a result that is not 6, your calculations are correct. Don't you want to find when there are two 6s in a row?
So for two rolls, you're looking for exactly (6,6), which is (1/6)(1/6).
For 3 rolls, we have (X,6,6) which is (5/6)(1/6)(1/6).
For 4 rolls, (6/6)(5/6)(1/6)(1/6).
fallen crane
I have to calculate the probability of "ai" first.
(does not fall twice 6 in a row and six fall in the last roll)
Then the probability of "bi."
(does not fall twice 6 in a row and six not fall in last roll)
So then I can calculate it now as described.
Then I have to find the generating function for a (x) and b (x) with a system of recurrent relationships
real orchid
Your calculations look correct for ai for 3 rolls.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
void helm
What do you do when two directional vectors aren't parallel and they intersect, how do you calculate that?
obtuse pebbleBOT
What do you do when two directional vectors aren't parallel and they intersect, ...
real orchid
Break them up into components.
void helm
What do you mean?
strong sinew
What do you do when two directional vectors aren't parallel and they intersect, ...
Do u want to calculate the point where they interesect?
void helm
Do u want to calculate the point where they interesect?
I'm unsure, to be honest.
My teacher gave us this sort of map, what they are if they're parallel and if they're not. But we aren't at that point of just what to do if they intersect.
stable oak
What do you do when two directional vectors aren't parallel and they intersect, ...
are you aware of vector equations?
if 2 vectors intersect you can equate the vector equations
and then find a common scalar product value
then plug them back into the equation to get the position vector for the point of intersection
void helm
Yes!
stable oak
ok so imagine you have 2 vectors
and the question says they intersect
You just have to equate the vectors
(r=r)
and then split them into components
them solve them simulatenously
to find t
it's hard to explain without a question
void helm
You mean like in this example mutliply (-4) by 7 and 4 by (-2) ?
stable oak
Okay so I found this question, now they have given the 2 vector equations
Now we know that these 2 equations aren't parallel as the direction vectors aren't equal/aren't a multiple(the direction vector is the one after μ or λ
Now r gives a position vector on any point of the line of the vector
The μ or λ is known as the scalar parameter so I would be refering to it as that from hereon. The scalar parameter varies to give a position vector on the line relative to an origin O.
Now if these 2 intersect the position vectors should be same. So let's equate the 2 terms as they have done here
r=r
and then you can split the that into i, j and k as they have shown
Now you can use simulataneous equations to solve it to find a value for either μ or λ
And then after you find a value for either one, you can substitute that into the relevant equation (r) to get the position vector
void helm
what's μ and λ ?
void helm
So it's like a variable but for a specific point?
stable oak
This is the vector equation format btw
a vector equation is defined in this form
Where (-4 7) is any point on the line and (7 -2) is the direction vector(the vector which gives that direction)
think of it like in the y=mx+c form
stable oak
So it's like a variable but for a specific point?
yes
it changes on where you put the point
void helm
Hmm
stable oak
a vector equation is defined in this form
Where (-4 7) is any point on the line ...
Ok so for example
Try calculating the vector equation for AB
where OA=(5 6 7) and OB=(1 2 3)
now the direction vector would be any vector parallel to AB or the vector of AB itself
in this case finding AB is easier
AB=OB-OA
=(1 2 3)-(5 6 7)
=(-4 -4 -4)
So now that vector equation would be r=(5 6 7) + λ(-4 -4 -4)
or r=(1 2 3) + λ(-4 -4 -4)
as (1 2 3) and (5 6 7) both lie on the vector line
void helm
But those two are different numbers, so how are they the same?
stable oak
the vector equation is defined like that
those 2 points can be any point on the line
but depending on the point which you choose to put, the value of λ changes at a different rate
stable oak
alright
void helm
The two directional vectors are the same, so it doesn't matter just where the locational vector lies, since the directional vector dictates that they're both on the same line and are thus overlapping or the same
Right?
stable oak
Uhh the 2 directional vectors of 2 vector lines will be the same only if they are parallel
Directional vector
is the one after λ
void helm
Yeah I get that
stable oak
I think what you are talking about is the one before that
void helm
Wait so what was this
stable oak
?
void helm
I mean, there's two things to do if a directional vector is parallel or not
Yes: they're identical or parallel or No: They intersect and are "warped"
stable oak
Are you asking how to prove if 2 vectors are parallel?
what I did above was to prove that 2 vectors intersect and if so find the position vector of the point of intersection
void helm
I was looking for what do to if they're unparallel
stable oak
ok so you want to find the position vector if they aren't parallel right?
and if they intersect
void helm
Yea!
stable oak
coz if they are parallel they would never intersect in the first place
stable oak
np, if you don't understand you can ask again
void helm
Thank youuu
stable oak
although I might be offline
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rose bolt
Just curious, how is laguerre eq'ns related to associated laguerre eq'ns? The same with the legendre eq'ns and its associated counterpart.
obtuse pebbleBOT
Just curious, how is laguerre eq'ns related to associated laguerre eq'ns? The sa...
@rose bolt Has your question been resolved?
obtuse pebbleBOT
@rose bolt Has your question been resolved?
opal musk
obtuse pebbleBOT
robust sleet
so it's just derivative?
opal musk
so it's just derivative?
yh think so
robust sleet
,w derivative of e^(-2x)*tanx
warm shaleBOT
robust sleet
it's correct
opal musk
👀 huh
robust sleet
?
timid silo
Factor the e term
opal musk
how do i get it inot the given format then?
timid silo
Out
timid silo
The e^-2x
opal musk
$$ e^-2x (-2tanx+1+tan^2x) $$
warm shaleBOT
Snickerdoodle
timid silo
Isnt that -1 + tanx squared?
opal musk
oh right i see
$$ e^-2x (-1+tanx)^2 $$
warm shaleBOT
Snickerdoodle
opal musk
thankyou!
timid silo
:)
opal musk
.close
dim ocean
i was wondering how i could find the height i dont know the formula
obtuse pebbleBOT
i was wondering how i could find the height i dont know the formula
slate cosmos
I assume they both say 10 for each side so
Take the isosceles triangle on the end and split it down the middle to give a right angle triangle
Use Pythagoras to work out the height
dim ocean
yes, theyre both ten
thank you ill do that
i got 9.53 as my answer
im assuming thats correct?
oak pond
help
dim ocean
@slate cosmos
slate cosmos
Yes
Tho I would leave rounding it until the final answer
dim ocean
thank you so much
dim ocean
alrighty
slate cosmos
Np
obtuse pebbleBOT
@dim ocean Has your question been resolved?
covert pine
There is a pet with 8 skill slots , now it has 8 skills ABCDEFXY and the target is to change the skills to ABCDEFGH. If you use a skill book , it will randomly replace one skill slot with the new skill like I use skill book G and it replace B it becomes AGCDEFXY. What is the expected value of skill books in order to get ABCDEFGH. I think I need to use markov chain to deal with this question but I don't know how to actually compute this. Futhermore, the skill book is A 100,B200,...,H 800 gold. what is the strategy of minimum gold
obtuse pebbleBOT
There is a pet with 8 skill slots , now it has 8 skills ABCDEFXY and the target ...
@covert pine Has your question been resolved?
obtuse pebbleBOT
@covert pine Has your question been resolved?
rocky cosmos
How do I determine the shortest possible distance between these two functions?
brave bramble
Shortest possible vertical distance?
Then you want to minimize:
h(x) = e^x - 2x
warm shaleBOT
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
rocky cosmos
Shortest possible *vertical* distance?
Then you want to minimize:
h(x) = e^x - 2...
How do I minimize that? h'(x) = 0?
scarlet gale
h'(x) = 0 will give you all the extreme points except perhaps the endpoints.
So, it can give you minima or maxima.
rocky cosmos
And we're interested in the minimum?
scarlet gale
Right.
rocky cosmos
Is this right?
scarlet gale
So, h''(x) > 0 will happen at the minima since the slope (first derivative) is increasing at a minimum.
Yes, that looks good. Check h''(ln(2)) > 0 to ensure it's a minimum.
Unless you're allowed to just look at the graph.
hollow sun
so ln(2) is the minimum distance between these two graphs?
scarlet gale
No, that's the x value it happens at.
You need to fill that x into the two functions to see how far apart they are there.
hollow sun
e^ln(2)-2*ln(2) is the distance?
scarlet gale
Yes, that's right.
brave bramble
Minimum vertical distance. A neat challenge to find the minimum actual distance
obtuse pebbleBOT
@rocky cosmos Has your question been resolved?
rocky cosmos
@scarlet gale Is it possible to set up a function using the distance formula, then get the derivative for it to find the shortest distance or?
scarlet gale
Yes, if you want the shortest distance, not the shortest vertical distance.
@rocky cosmos
rocky cosmos
I tried to find on Google, but why can't we find the shortest vertical distance using the distance formula?
fierce lagoon
You want to minimize vertical distance right
fierce lagoon
I tried to find on Google, but why can't we find the shortest vertical distance ...
Distance formula is not vertical distance
rocky cosmos
@fierce lagoon ”2D distance formula gives the shortest distance between two points in a two-dimensional plane.”
what we have in our q is also two points.
so why doesn't it work more specifically?
fierce lagoon
Hm
Atcually
It should work if x is the same throughout
But that's so redundant
rocky cosmos
But that's so redundant
what's redundant?
so the distance formula can be used?
,w √((ln(2)-ln(2))^2+(2-2ln(2))^2
warm shaleBOT
rocky cosmos
@fierce lagoon@scarlet gale
isn't this the same answer?
this is the distance formula
,w e^ln(2) - 2ln(2)
warm shaleBOT
scarlet gale
@rocky cosmos Yes, that works, but it's not the easiest way.
rocky cosmos
@scarlet galeWhy, in your opinion?
scarlet gale
Because the first term is always 0.
Then the second term is just sqrt(something²).
Which is essentially |something|.
Which, since it's nonnegative is just something.
fierce lagoon
You'll find out that it'll be f(x)-g(x) in the long run
And you might as well maximize f(x)-g(x) from the get go
what happens is this
$\sqrt{(x-x)^2 + (f(x)-g(x))^2}$
What the
scarlet gale
\sqrt
warm shaleBOT
Umbraleviathan
fierce lagoon
You know I'm smart
fierce lagoon
**Umbraleviathan**
This is just f(x) - g(x)
rocky cosmos
This is just f(x) - g(x)
√(f(x)-g(x))² = f(x) - g(x), yeh
but don't we get our answer faster this way
what do you think
scarlet gale
No, because you have to calculate f(x) - g(x) for both.
And the distance formula has you doing extra work besides that to get the same thing.
Just f(x) - g(x) is the simplest.
rocky cosmos
Okay thanks
scarlet gale
No problem.
rocky cosmos
.close
obtuse pebbleBOT
fierce lagoon
but don't we get our answer faster this way
No because knowing you want to minimize vertical distance, that just follows the suit f(x) - g(x)
obtuse pebbleBOT
Available help channel!
vernal gyro
B here is a banach space and (1) is any series.
I understand why absolutely implies unconditionally, but how can I show the other direction?
(This is from ABSOLUTE AND UNCONDITIONAL CONVERGENCE IN NORMED LINEAR SPACES By A. DVORETZKY AND C. A. ROGERS)
obtuse pebbleBOT
B here is a banach space and (1) is any series.
I understand why absolutely impl...
@vernal gyro Has your question been resolved?
haughty coyote
B here is a banach space and (1) is any series.
I understand why absolutely impl...
So this is a bit above my level regarding series (I just looked up the definition of unconditionally convergent), but maybe this can be a starting point (I'm using a the idea of positive/negative so I guess it doesn't work for not totally ordered fields unless you can generalize it) ?
By contraposition: let's take a series that doesn't converge absolutely and show it doesn't converge unconditionally. Since we're in finite dimension, let's use a basis and limit ourselves to a dimension/coordinate (there is a least one) for which the projected series (i.e. its values in that coordinate) does not converge absolutely. Then it is known (?) (in the reals at least) that you can rearrange the sum to converge anywhere, by changing the order of the positives and negatives. This would mean that different permutations converge to different values, hence it is not unconditionally convergent in this dimension, thus not at all.
obtuse pebbleBOT
@vernal gyro Has your question been resolved?
vernal gyro
I'm assuming by way of contradiction, that although the series converges unconditionally, it does not converges absolutely?
And now I'm rearranging the elements... In what way... ? Something to do with the positive and negative factors of a chosen basis ?
I think I lost you. Can you be a bit more rigorous?
haughty coyote
"I'm assuming by way of contradiction" I said by contraposition: not ACV => not UCV so UCV => ACV
vernal gyro
sorry, I misread
haughty coyote
as I'm trying to detail this I realized that even just talking about coordinates is weird because ACV is done looking at a series in R+, so that already is problematic
but by triangular inequality it works
vernal gyro
we can use the max norm, according to some basis, since all norms are equivalent
if it helps?
haughty coyote
my idea was to go to a single coordinate so that the things we sum are in a field and not a vector space, thus simpler to work with
so then since the series doesn't ACV it implies that for one dimension the series of the vector's coordinates in that dimension doesn't ACV
then if (for now with loss of generality) we were in a R vector space, we know that we could rearrange the sum (as it converges, because we easily restrict ourselves to the study of convergent series) to converge to different values with different permuations
and that's what you wanted me to detail ?
The fact that different permutations can converge to different values ?
vernal gyro
Let me think for a minute, see if I understand
If we are in one dimension R, we can split the series to its positive and negative values, sum of two series, assuming that it doesn't converge absolutely, one of them must not converge. Therefore by rearranging the terms we get a series that does not converge. Thus the 1 dimensional case (I think) is solved, right?
haughty coyote
if the series converges but not absoutely, both the sum of the negatives and of the positives go to their respective infinity. So if you want a sum that converges to L, (wlog L >= 0) you just add positive terms until you're above L, then add negative terms until you're below L, and repeat. There's a permutation that does that so it shows that the series doesn't UCV
but I don't know how to generalize this to non-ordered fields
do you have any idea if/how we might generalize this ?
vernal gyro
no, but it's getting late where I'm at, so I think I'm done with math for the day, and hopefully I will get back to it tomorrow
should I close even though it is not resolved?
haughty coyote
if you're going to bed the bot will probably close it during the night anyways
vernal gyro
I will let it close when the time comes if so, just in case someone will have an idea I could check in the morning
haughty coyote
I'd recommend pinging helpers to people are more likely to have a look at it
vernal gyro
<@&286206848099549185>
tardy epoch
I almost never see helpers be able to answer questions on Banach Spaces. Maybe the question is better suited for #advanced-analysis
obtuse pebbleBOT
@vernal gyro Has your question been resolved?
obtuse pebbleBOT
@vernal gyro Has your question been resolved?
wintry remnant
obtuse pebbleBOT
wintry remnant
is C correct?
short spruce
seems so, though i don't like how close that graph is to 2 at x=0 
long sinew
seems so, though i don't like how close that graph is to 2 at x=0 <:bleak:877093...
Lol
Not sure why they would do something like that...
wintry remnant
long sinew
More room for confusion rather than understanding the idea of limits
wintry remnant
I think C is also correct here
cuz there is a discontinuity at 0
and lim as x approaches infinity is -1
short spruce
are you sure about that last one?
wintry remnant
half sure
with l'hopital's rule it comes out to be 0
I'm just worried I got something wrong because I've selected C in the last three problems...
thanks
.close
obtuse pebbleBOT
short spruce
C isn't right on this one 
short spruce
you just told me lhopitals tells you the limit is 0
short spruce
yeah
gilded needle
if (I) is true then how can only (III) be true?
wintry remnant
.reopen
obtuse pebbleBOT
✅
wintry remnant
if (I) is true then how can only (III) be true?
I thought 1 wasn't true
there is a discontinuity at 0
short spruce
the function is defined at x=0
gilded needle
the value assigned at x=0 matches the limit as x -> 0
wintry remnant
Ohh shit I just noticed
gilded needle
hence continuous
wintry remnant
Yeah idk bro brain fart
gilded needle
no worries, it happens 😀
wintry remnant
So it is A
wintry remnant
It is D
gilded needle
in particular, III is implied by I (do you see why?)
gilded needle
and II is true because |1 - cos(x)| <= 1 + |cos(x)| <= 1 + 1 = 2
wintry remnant
.close
timid silo
obtuse pebbleBOT
timid silo
from the step in blue to the step in red
im rather confused
they factor out a $(-1)^k(k+1)$
warm shaleBOT
Joseph Fourier
timid silo
and it becomes: $(-1)^k(k+1)[\frac{-k}{2} + (k+1)]$
civic zealot
So which part confuses you
timid silo
how does $(-1)^k(k+1) * \frac{-k}{2} = \frac{(-1)^{k-1} k(k+1}{2}$
warm shaleBOT
Joseph Fourier
timid silo
tell me its an error please
warm shaleBOT
Joseph Fourier
civic zealot
$(-1)^k(-1) = (-1)^{k+1} = (-1)^{k-1}$
warm shaleBOT
Zybikron
civic zealot
$(-1)^{k+1} = (-1)^{k-1} (-1)^2 = (-1)^{k-1}$
warm shaleBOT
Zybikron
timid silo
they breaking the rules here chief
ay bro this should be illegal
im calling the police
civic zealot
why? they're just using the fact that it's -1 to a power. This wouldn't work for anything else
except 1, i guess
timid silo
they're using some sorcery
thanks man
why do u do it
like just spend so much time helping people
@civic zealot
civic zealot
I like teaching, here I get to choose who to help (I can skip over the a-holes)
and I usually do this when I'm not doing something else lol
plus it keeps me up to date on my fundamentals, which is nice
I've relearned a bunch of stuff I forgot since I showed up here
obtuse pebbleBOT
@timid silo Has your question been resolved?
wild forge
2/ 4-5x is equal to 2(4-5x)^-1 right?
obtuse pebbleBOT
2/ 4-5x is equal to 2(4-5x)^-1 right?
sacred root
2/ 4-5x is equal to 2(4-5x)^-1 right?
Ye it is
west pagoda
obtuse pebbleBOT
crimson berry
limber quartz
crimson berry
,rotate
obtuse pebbleBOT
@west pagoda Has your question been resolved?
crisp wren
I am not sure how to find out if f"(2) is positive or negative. I know that f(2) = 0 and that because its decreasing f'(2) is some negative number.
obtuse pebbleBOT
I am not sure how to find out if f"(2) is positive or negative. I know that f(2)...
obtuse pebbleBOT
@crisp wren Has your question been resolved?
crisp wren
Is it not 0?
The answer key says it has to be C
I watched a khan academy video about it and looking at f(x) around f(2) its decreasing more from the left than the right, so shouldnt there be a concavity change at f'(2) making f''(2) = 0?
f(x) decreases by 1 on [1, 2] and decreases less than 1 at [2,3]
I think f(2) is an inflection point
I might be 100% wrong though, just laying out my thought process
alpine raven
f(2) = 0, look at the graph
but im not sure about f'(2)
f is decreasing so f'(2) should be negative
But i dont know how to compare f'(2) and f''(2)
obtuse pebbleBOT
@crisp wren Has your question been resolved?
echo heron
I am not sure how to find out if f"(2) is positive or negative. I know that f(2)...
The slope is going from a more negative number to a less negative number
So f’’(2) is actually positive
obtuse pebbleBOT
@crisp wren Has your question been resolved?
storm crescent
hello
rugged kite
storm crescent
oh sorry
im having trouble with this
I solved the first 2 but this one is different and I have no clue how to do it
rugged kite
What are the quantities denoting? Lengths? If so, of what?
storm crescent
What are the quantities denoting? Lengths? If so, of what?
imma be honest its for a test and idk how to so it just trying not to fail you dont have to help tho if u dont want to waste time
rugged kite
Wait, homework or...?
storm crescent
no its a test
rugged kite
• Cheating on tests and exams, as well as other forms of academic dishonesty, will result in an immediate ban.
from #❓how-to-get-help
storm crescent
oh
rugged kite
I'd advise you to close this
rugged kite
imma be honest its for a test and idk how to so it just trying not to fail you d...
i have a hard time trusting you on this
storm crescent
what if i cashapp you
rugged kite
don't make me call mods
storm crescent
: (
tardy epoch
imma be honest its for a test and idk how to so it just trying not to fail you d...
Don't cheat. Kthxbai
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fathom lion
obtuse pebbleBOT
fathom lion
What does the unlined statement mean?
I've always thought dividing in trig equations was a no go because you lose solutions
rugged kite
Well, perhaps cosθ+sinθ ≠ 0 does get rid of solutions, but you can check those later
Right now, you can exclude that and find the other solutions
rugged kite
Who knows
Dividing and making hypotheses can and often does lose solutions, but it's not a big deal as long as you go back and check if you missed anything by making these hypotheses
rugged kite
$\cos\theta+\sin\theta = 0$ means $\cos\theta = -\sin\theta = cos(\frac\pi{2}+\theta)$, which is a nice formula to have in mind
warm shaleBOT
Syst3ms
rugged kite
The equality of cosines means either $\theta = \theta+\frac\pi{2} [2\pi]$ or $\theta = -\theta-\frac{\pi}2 [2\pi]$
warm shaleBOT
Syst3ms
rugged kite
The first equation has no solutions
The second one means 2t = -π/2 [2π] ie t = -π/4 [π] (notice the modulus change)
Hence t = 3π/4 or t = -π/4
You just have to check if those are solutions that you didn't account for yet
high shell
hey
cedar flicker
Where did 4+sqrt12+sqrt 8 come from
high shell
Where did 4+sqrt12+sqrt 8 come from
thats where i got stuck
high shell
whats the next step after 2√3 -2√2 / 4
cedar flicker
yea
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Okay, so i have a task to do with basic maths and im paying 10€ if someone can solve it.
If you know Coding (Javascript) it will be perfect.
https://i.xpyth.dev/paclOR9l.png
Default rate:
a: 10
b: 60
c: 40 (ME)
If i put custom rate (Line 89)
a: ? (something like 8% ??)
b: ?? (something like 50% ??)
c: 60 (ME)
If i set my rate for c to 60, how can i get the rate of a & b using their default rate and considering they will be shrinked because C is taking from their part.
If im not clear just tell me i will give mor details
obtuse pebbleBOT
Okay, so i have a task to do with basic maths and im paying 10€ if someone can s...
timid silo
10€ On the line rn, willing to pay a lil bit more if someone can even bring the code with it
(This is not homework assignment btw)
nocturne minnow
Okay, so i have a task to do with basic maths and im paying 10€ if someone can s...
Please read #❓how-to-get-help and #rules
timid silo
I don't think im violating the rules considering thoses are not homework assignment, am i wrong ? @nocturne minnow :/
nocturne minnow
Bullet 5 in rules
timid silo
Oh, do you know where this type of request could be placed ?
nocturne minnow
I'm not sure sorry but definitely not this server
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
soft elm
Need help with b
obtuse pebbleBOT
Need help with b
mighty geyser
hmm what are the two equations you found?
soft elm
soft elm
hmm what are the two equations you found?
a) x = r - 4
mighty geyser
and?
mighty geyser
you have two equations right?
soft elm
one was the answer for a, which was what one side of the triangle was and the other one i was tryna use pythagorus to find the hypotenuse (radius)
mighty geyser
Yeah, did you manage to use the Pythagorean theorem?
soft elm
yeah but i got stuck at
c^2 = 7^2 + (r-4)^2
c^2 = 47 + (r-4)^2
soft elm
Yeah, did you manage to use the Pythagorean theorem?
so is this correct
c^2 = 7^2 + (r-4)^2
c^2 = 49 + (r-4)^2
c^2 = 49 + x^2 - 8x + 16
c^2 = 65 + x^2 - 8x
c = sqrt(65 + x^2 - 8x)
therefor r = sqrt(65 + x^2 - 8x)
mighty geyser
yeah but i got stuck at
``c^2 = 7^2 + (r-4)^2``
`c^2 = 47 + (r-4)^2`
can you express c in terms of x and r?
mighty geyser
so is this correct
`c^2 = 7^2 + (r-4)^2`
`c^2 = 49 + (r-4)^2`
`c^2 = 49 + x^2 -...
ouch 7^2 is 49
soft elm
soft elm
can you express c in terms of x and r?
c^2 = a^2 + b^2
c is the hypotenuse but also equivilent to the radius so
c, r and (if sub x for c in the eq), c are all equal so ill just use r for the term to describe em all
so in the end
r = sqrt(67 + r^2 - 8r)
mighty geyser
it's not very useful to have r stuck inside and outside
we want all the variables r to be put on one side
$c^2 = 7^2 + (r-4)^2$ is okay, which can substitute to get $r^2 = 7^2 + (r-4)^2$
warm shaleBOT
Element118
soft elm
okay so solving a bit we can deduct r^2 and change 8r to be on the other side to get
8r = 65
hmm that dosent seem right
soft elm
$c^2 = 7^2 + (r-4)^2$ is okay, which can substitute to get $r^2 = 7^2 + (r-4)^2$
oh so i should of just left it
mighty geyser
you have r=65/8 yeah?
we can also check our answers by substituting them back into the equations we found
x=r-4, so we can calculate x from there
and see if x^2+7^2=r^2
soft elm
r^2 = 7^2 + (r-4)^2
r = sqrt(49 + (r-4)^2)
mighty geyser
don't repeat the simplifications when you check it
mighty geyser
x=r-4, so we can calculate x from there
and see if x^2+7^2=r^2
here we should get x=33/8 so x^2+7^2=1089/64+49=(1089+3136)/64=(4225)/64=(65/8)^2
soft elm
here we should get x=33/8 so x^2+7^2=1089/64+49=(1089+3136)/64=(4225)/64=(65/8)^...
yeah but this is non calculator work
for us
so liek 33/8 shouldnt need to be done as that is a horrible number to do in your head
especially at our level
mighty geyser
yeah but r=65/8 seems to be it
timid silo
so
mighty geyser
what is the question you are asking?
mighty geyser
maximise x^2y given that x+y=2022?
timid silo
yes
mighty geyser
there's no maximum
timid silo
wait u sure?
timid silo
mighty geyser
yeah, there's no maximum
mighty geyser
there's no maximum, i.e. you can get as large as you want
timid silo
Aaaaa
thx
but
Can I solve also dis one
4^x+6^x=9^x
Wait
nvm
I found it
We divide everything by 9^x
then
we have a quadratic
and then
as a final answer we get
Phi
(1+sqr(5))/2
thx
obtuse pebbleBOT
@timid silo Has your question been resolved?
formal echo
how would you expand 9(x + 1)(x - 1)
obtuse pebbleBOT
how would you expand 9(x + 1)(x - 1)
mighty geyser
like, multiply it out? FOIL?
formal echo
9x + 9 + x - 1, like this?
formal echo
9x + 9 + 9x - 9?
mighty geyser
how did you get 9x+9+x-1?
if you can't multiply all 3 at once, maybe multiply two at a time
formal echo
9x^2 - 9
earnest elk
thats correct
plain grove
lets say i have x number of things to form combinations with. of those x number of things i can form combinations with, theres a constraint of the range u can have per thing, say 4-6. how do i find all the configurations given the range and number of things to form a certain total
obtuse pebbleBOT
lets say i have x number of things to form combinations with. of those x number ...
plain grove
hopefully that made sense 🥴
tardy epoch
pretty vague. can you just pick a sufficiently complicated example to solve?
Your answer should be expressed in this language
https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/7%3A_Combinatorics/7.5%3A_Combinations_WITH_Repetitions
obtuse pebbleBOT
@plain grove Has your question been resolved?
wintry stream
can someone please explain how to solve this step by step
obtuse pebbleBOT
can someone please explain how to solve this step by step
short spruce
what is "second part"
obtuse pebbleBOT
@wintry stream Has your question been resolved?
wintry stream
what is "second part"
oh i meant i need help on the second part
first one has been solved (look at second image)
tardy epoch
Plug this into the series
In math, whenever there are multiple parts to a problem, you should use the earlier solutions to solve the later problems
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Hi
timid silo
Is there a common “way” to find the general form of a succession by having its values?
Or is it just about luck and some logic? 🤔
For the recursive way its way simpler…
For example, by having: {-2; 6; -18; 54; -162; …}
How can I find out that one general form might be: An = (-3)^(n-1) * (-2)
?
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
rugged kite
Honestly, pattern recognition is just trying out things and hope they get you somewhere
There isn't any set method, otherwise many problems would be solved by now
In this case, perhaps you could have tried factoring everything by 2 since every term is divisible by it
You'd have gotten -1,3,-9,27,-81,... which are clearly powers of -3 in some capacity
mossy hull
obtuse pebbleBOT
mossy hull
so
∫tan^3(x)sec^3(x)
∫secxtanx * sec^2 * tan^2
∫secxtanx * sec^2 * (sec^2(x)-1)
u=secx
du=secxtanx
∫u^2(u^2-1)
∫u^4-u^2
1/5(u^5) - 1/3(u^3)
1/5(sec^5) - 1/3(sec^3)
this makes a lot of sense to me
but thats not what the book has
idk what I did wrong
slim lake
What does the book have?
mossy hull
slim lake
Differentiating your answer is always a good check
Anyways your answer is the same as there no?
mossy hull
oh duh
slim lake
Integrating, putting in u=cosx and changing to secx you get the same
Good way to check if your unsure is differentiating
neon crypt
$$\left(x^2\right)^{log_2x^2}=16$$ $$log_2\left(x^{4\log _2\left(x\right)}\right)=log_216$$ $$4\log _2\left(x\right)^2=4$$ $$\log _2\left(x^2\right)=1$$ $$x^2=2$$ $$x=\sqrt{2},:x=-\sqrt{2}$$
obtuse pebbleBOT
$$\left(x^2\right)^{log_2x^2}=16$$ $$log_2\left(x^{4\log _2\left(x\right)}\right...
warm shaleBOT
ElegantSort
neon crypt
what am I doing wrong here?
mild ocean
@neon crypt why did log_2(x)^2 turn into log_2(x^2)
hybrid gull
^^
neon crypt
right my bad
but still, the results I get are x=2 or x=0.5
in the book its x=+-2 or x=+-0.5
rich holly
wait what's happening here?
mild ocean
i think you lose solutions since you did log_2(x^2) = 2log_2(x)?
neon crypt
wait what's happening here?
mistake, but even after doing it correctly its wrong
neon crypt
i think you lose solutions since you did log_2(x^2) = 2log_2(x)?
maybe, what would be the correct way to do it?
short spruce
<@326752663679008770> why did log_2(x)^2 turn into log_2(x^2)
you just need to fix this mistake
and solve like normal
go from $4\log_2^2(x)=4$
warm shaleBOT
a disappointing son
short spruce
if it helps, let u = log_2(x)
neon crypt
if it helps, let u = log_2(x)
I already did that.. the problem is that my solution is different from the right one
short spruce
what are you getting as your solutions
mild ocean
a^(log_2(a)) = 16
(a^log_2(a))^(1/log_2(a)) = a = 16^(1/log_2(a)) = 16^log_a(2) = 16^(0.25log_a(16)) = 2^(log_a(16))
a^log_a(16) = 16 = 2^(log_a(16)^2)
short spruce
mild ocean
what?
short spruce
what're you doing lol
neon crypt
when you take the sqrt, consider the +-
I get log_2(x) = -1 and log_2(x) = 1
mild ocean
i eventually got log_a(16) = 2 and log_a(16) = -2 with a = x^2
i edited my above message
neon crypt
can you send the full way you got to the point? just to write it on paper or something
rich holly
yeah it's hard to read
mild ocean
a^(log_2(a)) = 16
(a^log_2(a))^(1/log_2(a)) = a = 16^(1/log_2(a)) = 16^log_a(2)...
this is literally all my work
i can put it in latex i guess
neon crypt
$$a^{\left(log_2\left(a\right)\right)}:=:16\left(a^log_2\left(a\right)\right)^{\left(1/log_2\left(a\right)\right)}:=:a:=:16^{\left(1/log_2\left(a\right)\right)}:=:16^log_a\left(2\right):=:16^{\left(0.25log_a\left(16\right)\right)}:=:2^{\left(log_a\left(16\right)\right)}a^log_a\left(16\right):=:16:=:2^{\left(log_a\left(16\right)^2\right)}$$
warm shaleBOT
ElegantSort
neon crypt
mild ocean
god
neon crypt
$$a^(log_2(a)) = 16$$ $$(a^log_2(a))^(1/log_2(a)) = a = 16^(1/log_2(a)) = 16^log_a(2) = 16^(0.25log_a(16)) = 2^(log_a(16))$$ $$a^log_a(16) = 16 = 2^(log_a(16)^2)$$
warm shaleBOT
ElegantSort
quantum
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
mild ocean
i am not typing that again
tardy epoch
rich holly
I found 2 as the only answer lol
short spruce
your mistake is on the 2nd line, multiplying the exponents instead of bringing the log down
as quantum said earlier, you lose solutions by doing that
mild ocean
$a^{\log_2(a)} = 16\implies a^{\log_2(a)\cdot 1/\log_2(a)} = a = 16^{1/\log_2(a)} = 16^{\log_a(2)} = 16^{0.25\log_a(16)} = 2^{log_a(16)}\implies a^{\log_a(16)} = 16 = 2^{\log_a(16)^2}$
you might just have to suffer and read my original message
neon crypt
I think I will do my own translation to paper
short spruce
your way works just fine if you bring the log down immediately
neon crypt
anyway, thanks for the help, although I think this question is pretty absurd
short spruce
neon crypt
your way works just fine if you bring the log down immediately <:bleakcat:913340...
which way?
short spruce
your og way
neon crypt
at what point?
short spruce
the first pic you posted
instead of multiplying the exponents, bring the log down first
like quantum said, you lose solutions when getting rid of the x^2
that's why you only have the positive solutions
rich holly
I went the easy way
$$\left(x\right)^{4 log_2x}=16$$ $$\left(x\right)^{4 log_2x}=2^4$$
mild ocean
there
warm shaleBOT
Hyperlix
rich holly
plug 2 into x and boom
neon crypt
like quantum said, you lose solutions when getting rid of the x^2
oh my god
mild ocean
note that 1/log_a(b) = log_b(a)
neon crypt
ok its solved
a question that should have taken 5 minutes, finally solved after an hour
regardless, thanks guys! you helped me a lot
.close
obtuse pebbleBOT
rich holly
how'd you do it?
neon crypt
didn't get rid of x^2 in the start
obtuse pebbleBOT
Available help channel!
dire glade
I need some help with LinearModelFit on mathematica and sinusoidal functions
dire glade
this is my work thus far. just trying to fit the data to basis functions 1, sinpix, cospix
the issue is
sorry i meant to add 1 to the basis function after data, {
actually you know what i just saw the actual channel i need, sorry
.close
mint rampart
How do you factor
14a2 +a-3
obtuse pebbleBOT
How do you factor
14a2 +a-3
mint rampart
<@&286206848099549185>
primal lark
How do you factor
14a2 +a-3
$14a^2+a-3$
warm shaleBOT
Sus
primal lark
<@&286206848099549185>
Ping after 15 minutes see #❓how-to-get-help
Ok got it not sure how convenient it is
But use vanishing factor
And try to find the zeros of the quadratic
It will be a decimal btw
Like 0.5
mint rampart
Mm
primal lark
What about 16x^4 -y^4
$16x^4-y^4$
warm shaleBOT
Sus
primal lark
What about 16x^4 -y^4
Here you don't need it
Because you can use a^2-b^2 formula
But i don't think there is any other way in the earlier one
mint rampart
Because you can use a^2-b^2 formula
What would it b then
primal lark
What would it b then
$a^2-b^2=(a+b)(a-b)$
warm shaleBOT
Sus
mint rampart
oh right
primal lark
$16x^4-y^4= (4x^2)^2 - (y^2)^2$
warm shaleBOT
Sus
mint rampart
.close
obtuse pebbleBOT
mint rampart
Thanks @primal lark
obtuse pebbleBOT
Available help channel!
timid silo
Hey
timid silo
I am trying to confirm if I am solving this question correctly
Number 13
Is it 0 ?
I make it
X + 4/ X + 4
But they cancel eachother
But it is 0
Is it that simple ?
crystal moss
if they cancel each other it's 1, right?
crystal moss
yeah they cancels so ur right
obtuse pebbleBOT
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Available help channel!
proven veldt
Can someone help me please! it’s inverse functions
obtuse pebbleBOT
Can someone help me please! it’s inverse functions
fickle shell
composing two inverse functions gives you the identity function
proven veldt
composing two inverse functions gives you the identity function
Can you elaborate please?? i’m sorry i don’t know how to do this at all..
proven veldt
I get that but i’m more so asking on how to solve question 1..
proven veldt
i’m saying this as a visual learner lol.. i’m not asking you to solve the whole question ..
fickle shell
wdym
proven veldt
For question one how would I solve that equation..
Uh okay nvm is there someone else that can like explain step by step…?
obtuse pebbleBOT
@proven veldt Has your question been resolved?
obsidian isle
To find the inverse you swap x and y then solve for x
prime anvil
Hi, I'm doing vector calculus and I am having a bit of trouble computing the supremum and infimum of a function over some closed region
obtuse pebbleBOT
Hi, I'm doing vector calculus and I am having a bit of trouble computing the sup...
prime anvil
this is the problem
so I have showed that there exists a critical point at (0,2) and that it's actually a local minimum
now I want to search for the supremum, which can only occur at the boundary because the region is closed and boudned
so I tried using Lagrange multiplier
astral ivy
Why does closed and bounded imply supremum is on boundary
prime anvil
wait it doesn't?
but if you think about something like a 1 var function
and you restrict the domain
fickle shell
now I want to search for the supremum, which can only occur at the boundary beca...
the minima might also be at the boundary?
prime anvil
min and max either occur at a cirtiical point or the boundary
prime anvil
the minima might also be at the boundary?
oh yea I know, so I'm trying to search for that at the boundary
and to do that I use lagrange multiplier
but uh, when I solved it, I get some nonsensical answer, so I don't know if my approach is wrong or my calculations are wrong
fickle shell
show your work
prime anvil
wait why would x=0 give you the max or the min?
fickle shell
why not?
prime anvil
yea but how would you even prove that?
fickle shell
prove what?
prime anvil
that max/min occurs when x=0
prime anvil
oh
wait oh I just realised
in that lagrange multiplier working out, I did exclude x = 0 huh
right ok
give me a sec
oh my god that makes a lot of sense
@fickle shell tysm
fickle shell
np
prime anvil
alright how do I mark that my question has been solved?
fickle shell
.close
prime anvil
.close
radiant gale
how do i verify the identity of this?
obtuse pebbleBOT
how do i verify the identity of this?
@radiant gale Has your question been resolved?
Available help channel!
hybrid kraken
whats an easy way to calculate from 1+2+3... +23 here?
obtuse pebbleBOT
whats an easy way to calculate from 1+2+3... +23 here?
hybrid kraken
is the best way to just plug into summation calc?
hybrid kraken
I hope you know what is that
just read it on wiki, is it : 23(1+23)/2?
actually no slightly off.. shld be 253
fallen mantle
wrong
but formula is correct
try to think again what should be first term, last term and n
hybrid kraken
i get the ans if i do 23(22)/2
n is the num of thigns to add up right?
first term is 0, last is 22?
fallen mantle
n is the num of thigns to add up right?
yes
fallen mantle
first term is 0, last is 22?
this one wrong
hybrid kraken
whats an easy way to calculate from 1+2+3... +23 here?
isnt that what they do here?
fallen mantle
first term is 0, last is 22?
read the question again carefully
hybrid kraken
frst is 22, last is 0?
fallen mantle
why last is 0?
hybrid kraken
sorry its 1
fallen mantle
yes
hybrid kraken
but if I do 23*23/2 its not right
fallen mantle
so now you have first and last term ady
for n, you can count from first term to last term. see how many numbers are there in between
fallen mantle
yes
fallen mantle
welcome
hybrid kraken
.close
sturdy zealot
obtuse pebbleBOT
obtuse pebbleBOT
@sturdy zealot Has your question been resolved?
mental mortar
how would you go about this
obtuse pebbleBOT
how would you go about this
fallen mantle
List out and count how many numbers is a multiple of 2 or 3
mental mortar
there are 10 numbers
wait nah
thats for both mb
4 for 3 and 6 for multiples of 2
is the answer
10/12?
fallen mantle
no
not 10
you need to take into account of the repetition of numbers between multiple of 2 and 3
mental mortar
8/12
fallen mantle
yes
mental mortar
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
violet token
How do I find Cos,sin, and tan
obtuse pebbleBOT
How do I find Cos,sin, and tan
primal lark
How do I find Cos,sin, and tan
How u compute it?
There are 2 main methods for some special angles like 45 60 and 30
U can use trig table
earnest elk
sin=opposite/hypotenuse
SOH
cos=adjacent/hypotenuse
CAH
tan=opposite/adjacent
TOA
primal lark
For others machlaurian series of sin
primal lark
sin=opposite/hypotenuse
*SOH*
cos=adjacent/hypotenuse
*CAH*
tan=opposite/adjace...
I think we ment how we compute them without actually having to draw a unit circle
primal lark
Exactly what he said
Who is "he"?
earnest elk
the longest side of the right angled triangle
violet token
What if it's not a traingle and they are all equal
earnest elk
opposite to the right angle
earnest elk
What if it's not a traingle and they are all equal
??
primal lark
primal lark
What if it's not a traingle and they are all equal
Trigonometry is only about triangles and angles!
earnest elk
equilateral triangle then
violet token
You just break it into a triangle
primal lark
What if all sides are equal is what I mean
But u said all sides equal
And
Not a triangle
earnest elk
which question?
violet token
It's says to
Find the area of each regular polygon. Round your answer to the nearest tenth if necessary
earnest elk
the area
echo heron
Area=1/2(ap)
Were you taught this formula?
echo heron
If not then it’s best not to abuse it idk
violet token
I forgot to bring them for Easter break