Can y’all help with getting the coordinates for these
#help-42
mellow pier
calm coralBOT
Can y’all help with getting the coordinates for these
leaden bramble
ahhh I knew it was that I just circled the wrong one accidentally
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mellow pier
Nope but I’m already gone from my home so sure
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tranquil wasp
just put the numbers into the calculator bro💀
cunning reef
Parallelogram ABCD has AB= 456, BC = 246. If the line that bisects angle BAD and ADC meet at point M, and angle BAD = MBC, find the length of BM
west horizon
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west horizon
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glacial steeple
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Answer is not negative
west horizon
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west horizon
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glacial steeple
Yes
west horizon
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glacial steeple
What is the denominator
west horizon
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glacial steeple
Which is what
west horizon
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cunning reef
find the area of ABCD
calm coralBOT
find the area of ABCD
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lapis thunder
Dk what happened, I was in help-25. I was working on finding the 400th derivative of cos(3x)
lapis thunder
I got 3^400cos(3x) and they wanted 3^100cos(3x)
dull wagon
are you sure you're looking at the correct answer section
dusky verge
hey! i dont know if im calculating this incorrectly
can you pls check what number you received for thi s
i got 9.63e-26 as an answer but the answer is supposed to be
0.0580
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sonic python
For a finite Taylor series calculating result of f(t)=square root(sum of each dimension change squared), I could solve an integral 1 to 0 of f(t) dt if only I could figure how to do Taylor series for a square root with any number may be t, anyone here understand more? All but for t values may be considered constant and I think I can do an antiderivative of a Taylor series part if I can find how to do it in a computer. https://math.stackexchange.com/questions/1106344/taylor-series-for-sqrtx, https://byjus.com/maths/taylor-series/, I just can't find square roots, how do I do that? X E.
sonic python
If it helps, result is always real and I can filter out 0. X E.
Also, it will always be for positive numbers. X E.
Like we have sqrt(x(t)^2+y(t)^2+z(t)^2) in an integral from 1 to 0, 0 cancels, 1 is left, how to find this square root?
If there is no Taylor series for this you can tell me maybe or maybe not, maybe.
<@&286206848099549185> Okay, 15 minutes, too complex?
I can basically calculate what I will be doing numbers, t, or t^2 with in total before doing this. X E.
Is there even a way to find antiderivative of that with or without Taylor series?
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sonic python
https://m.youtube.com/watch?v=flfaaZGaFzk, does chain rule help?
sonic python
https://m.youtube.com/watch?v=_2p_svlzBB8, This helps right?
sonic python
If I understand correct, f(g(x)) anti-derivative is f'(g(x)) times g(x) so f(x)=x to power of 1/2, f'(x)=-(2/(x to power of 1/2)) and then g(x) is innerds of square root, is this correct?
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quiet urchin
this is a intro to probs and stats class and for question #2 i don't understand what comes after finding the p-value and how to write my conclusion after.
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this is a intro to probs and stats class and for question #2 i don't understand ...
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amber bay
what does the level of significance mean
snow folio
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heady jungle
when performing u-subs and integration by parts in the same question, is it improper to define u multiple times? or would it still work since we redefine u each time
modern peak
try not to do that
drifting seal
when performing u-subs and integration by parts in the same question, is it impr...
just use different variables
t, w, v
whatever
modern peak
mhm?
heady jungle
and the integral it gives me requires u sub
if I solve that on the side
is it fine to neglect +C
in the u-sub integral
which isn't part of the final answer
drifting seal
you mean like $\int v du$?
potent lotusBOT
knief
drifting seal
$\int u \dd v = uv - \int v \dd u$
heady jungle
yeah
drifting seal
lol
drifting seal
you add a space though
heady jungle
as in
if I were to solve that integral off to the side of the page
because if it for example required a u-sub
or if I just showed it in a different section
then substituted the value back into the original integral
is it fine to neglect the +C when solving this one
apologies if I'm explaining it unclearly
<@&286206848099549185>
drifting seal
is it fine to neglect the +C when solving this one
yea it’s fine
just make sure you use one at the end
this happens a lot
i guess you’re not familiar with differential equations yet
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marble pendant
Sorry didn't come online for a few days lol
guess copter helped you lol
hasty flame
Why am I getting wrong answer in this way
calm coralBOT
Why am I getting wrong answer in this way
hasty flame
Rather than this way
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hallow wharf
Wait
hallow wharf
Why am I getting wrong answer in this way
Here the problem is that in differentiation d/dx(log 10 x ) is not 1/x
hallow wharf
1/x is possible only when base is e
hallow wharf
Mmm this is main problem
hallow wharf
Are u separating log x/log 10 with base 10?
hasty flame
Yes
hallow wharf
Then again it becomes log x base 10 right
hasty flame
Base should be e na
hallow wharf
So separate with base e
hallow wharf
Base should be e na
If base is e then log 10 will not 1 na
hallow wharf
In initial step separate with base e not 10
If u separate with base 10 then again u come back to previous log
hasty flame
hasty flame
If u separate with base 10 then again u come back to previous log
What's the difference
hallow wharf
Log 10 base e isn't 1
hasty flame
Ohhhk
hasty flame
Which is log e base 10
So I have to put the value before differentiating
hallow wharf
Yes
hallow wharf
Hmmm try now
hasty flame
Ig my basic is weak
hallow wharf
Ig my basic is weak
It's ok , just practice more
hasty flame
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odd egret
Hi
odd egret
I got 138, is tat right?
pseudo wedge
I got 138, is tat right?
well 138>137 so you can reduce this further
odd egret
I mean if I use binomial theorem on (1233+1)^4321, only the last ought to b not divisible by 137, so it b 1?
Ye just realised
So 1?
pseudo wedge
,w 1234^4321 mod 137
potent lotusBOT
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mossy wigeon
is this true or false
calm coralBOT
is this true or false
mellow cape
true
On rearranging v = -(a/b)u
since v = ku, they are parellel
ornate meadow
Maybe you defined parallel so that the vectors have to face the same direction
mellow cape
but its not even given that a and b are positive
ornate meadow
Maybe you defined parallel so that the vectors have to face the same direction
Have you defined parallel that way?
remote mural
i dont think it holds when a = b = 0
mellow cape
yea you are right
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eternal shard
i dont think it holds when a = b = 0
exactly, that would then make u and v linearly independent, and by that they cannot be parallel
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mossy wigeon
i know its u-v here
calm coralBOT
i know its u-v here
ocean cypress
yeah
mossy wigeon
opkty
swift laurel
d(u,v) = ||u - v|| = ||v - u||, this is basically how we define distance in vector spaces
ocean cypress
opkty
(a-b)^2 = (b-a)^2
in fact you could swap any component of u with the corresponding component of v and have the same distance between u and v
mossy wigeon
okokoktytyt
mossy wigeon
in fact you could swap any component of u with the corresponding component of v ...
wait
if its like
u v and z
can i
put any in any
swift laurel
like 3 different vectors u,v,z?
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mossy wigeon
like 3 different vectors u,v,z?
yes, sorry i was away
calm coralBOT
yes, sorry i was away
swift laurel
what would it mean to find the distance between 3 vectors?
mossy wigeon
what would it mean to find the distance between 3 vectors?
find the distance between point final and point initial
?
swift laurel
what is the final point and initial point, then?
swift laurel
you can certainly find
||u - v - w|| for given vectors u, v, and w but i'm not sure what geometric meaning it would have in relation to u, v, and w
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dark relic
the best choice for u here would be x^2 if you follow the LIATE method right?
swift laurel
i would not necessarily try integration by parts first
dark relic
what would be the better choice
I know I need to set infinity to a variable as it approaches infinity
swift laurel
substitution is always preferable if it can be managed
dark relic
so just doing u=x would be preferable then?
swift laurel
u = x would not change anything so it would not be very useful
dark relic
im not sure which would be preferable here because none of their derivatives are present in this one
swift laurel
are really no functions whose derivative is present?
dark relic
well thers no lnx so 1/x would be out, there isn't an x on its own so x^2 would be out as well
and the derrivative of e is just itself so I don't think that would be too useful either
slate field
what happens when you make u = 1/x?
dark relic
if u is x^-1 then du is -x^-2 right
meaning that whgat im left wiith after substitution is -Integral of e^u du
dry magnet
what happens when you make u = 1/x?
could you do that even if the upper bound becomes 1/0?
slate field
could you do that even if the upper bound becomes 1/0?
you have to use a limit.
dark relic
this problem is divergent correct
after doing the math I believe the final form is that -e^1/x evaluated from 0 to T
and 1/0 makes it undefined so its divergent
wait no it cant be divergent because of the P test right
dry magnet
you have to use a limit.
ohhh a left hand side limit so as x aproaches 0 from the left 1/x approaches negative infinity
pretty cool :p
dark relic
or does the P test not apply here?
spark stratus
or does the P test not apply here?
?
spark stratus
and 1/0 makes it undefined so its divergent
thats not exactly whats happening here
dark relic
sorry that may not be a official thing but what my instructor had taught us was that when it is in the form of /x^p if p is less than or equal to 1 then the function is divergent
dark relic
yeah
spark stratus
this integral converges
dark relic
and then i evaluate that from 0 to T
spark stratus
T?
dark relic
the limit i used to replace infinity
dark relic
im not sure on what your saying
dark relic
yea
spark stratus
so whats $\lim_{x\to0^-}\frac1x$
potent lotusBOT
mtt
dark relic
infinity
spark stratus
positive infinity?
dark relic
no negative
spark stratus
you need to say "negative" next time, infinity by default is positive
,,\int_{-\infty}^0\frac{e^{1/x}}{x^2}dx=-\int_0^{-\infty}e^udu
potent lotusBOT
mtt
dark relic
wait why do the bounds change places?
spark stratus
lets try this again
dark relic
when i was doing it I didn't know that they changed places
spark stratus
stop looking at it
lets try this again
you are getting the wrong idea
when you u-sub, you also change the bounds along with the integrand
the bounds were from x=-∞ to x=0
and you are integrating between them
dark relic
I thought that you only do that if you dont want to change U back to x
dark relic
but if you back substitute x after your done then you don't need to do that
spark stratus
the work youd have to do is not worth considering that
unless youre doing an indefinite integral and youre using a variable for one of the bounds, which doesnt really apply here
spark stratus
I thought that you only do that if you dont want to change U back to x
as a definite integral, you should always do this
dark relic
If i remember correctly to find the new bounds I have to set the function equal to zero and plug the new bounds in to the U function right?
dark relic
youi mean I take whatever my value of U is and plug in the old bounds to iot
and whatever I get is that new respective bound?
so whatever u=0 would be my new top bound and u=-infinity would be my lower bound?
spark stratus
so whatever u=0 would be my new top bound and u=-infinity would be my lower boun...
I listed the bounds from beginning to end
,,\int_{-\infty}^0\frac{e^{1/x}}{x^2}dx=-\int_{u(-\infty)}^{u(0^-)}e^udu=-\int_0^{-\infty}e^udu
potent lotusBOT
mtt
dark relic
yea but im asking to make sure I understand the process of how you got there
spark stratus
you know that 1/-∞ is 0 right
spark stratus
so whatever u=0 would be my new top bound and u=-infinity would be my lower boun...
so whats makign you say this
here the integral's new bounds has 0 as the lower bound and -∞ as the upper bound
dark relic
im saying that to find the new upper bound when doing this U sub the process would be to take U(which is 1/x) and replace the X with whatever was previously in the upper bound and if that is the process to find the upper bound with respect to U
I can see what the answer is since you gave it to me but im trying to put this in my notes so that later on if im asked to do a similar problem I understand the process
spark stratus
thats understandable, but then you go on to say something concerning and youre not answering that right now
spark stratus
so whatever u=0 would be my new top bound and u=-infinity would be my lower boun...
after that, what happened here
are you saying that you already simplified it to $=\int_{-\infty}^0e^udu$
potent lotusBOT
mtt
dark relic
thats what is currently on my paper but those are the old bounds
I need to find the bounds with respect to U so for the upper bound I would get that (1/0) which is where I'm unsure on what that would translate to as a bound and for the lower bound I get that (1/-infinity) which is 0
spark stratus
originally x is between -∞ and 0
that means x is negative, right
dark relic
yes
spark stratus
now consider values of x close to 0
in this case, youre only considering negative numbers
now what would 1/x approach
dark relic
okay I think i get it now
spark stratus
in general, youre approaching the bounds instead of using them
that applies for improper integrals, so when youre switching over to new improper bounds, you have to do the same
dark relic
so then with new bounds and after using U sub my equation should be -e^u from 0 to -infinity
dark relic
and then to evaluate where the integral converges I have to replace the -inf bound with a variable as it approaches -inf and then substitute that variable in
and whatever number I'm left with is where it converges
so then im with -e^1/variable -(-e^1/0)
wait no
I get that -e^t -(-e^0)
or that -e^t +1
and t is as it approches -inf so its 1/infinity +1 or that it converges at 1
this would be correct right?
mossy wigeon
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marsh valley
The dot product of a vector with itself is the same as its magnitude squared
$u \cdot u = ||u||^2$
mossy wigeon
The dot product of a vector with itself is the same as its magnitude squared
btw deosnt this only yhappen if
potent lotusBOT
Azyrashacorki
mossy wigeon
v=u?
swift laurel
(vector) * (vector) = ||vector||^2
u + v is a vector
tulip herald
Just had a test today, the question was let $(x^2-1)(x^2-2^2)....(x^2-18^2)=x^{36}+a_1x^{34}+...+a_{17}x+a_{18}.$
Show that $a_i \equiv 0 \pmod {37}$ for $1\le i\le 17$
tulip herald
Any clues for how this is supposed to be done?
I notice that 1,...,36 modulo 37 are solutions and got stuck there
potent lotusBOT
somethingwrong
tribal bane
I think vietas relation might help but you'll have to do each one.
Which is tedious and not recommended for test
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normal spindle
I've never been taught this method, but I also believe it is just a modified quadratic formula where a=1. So how new is this method? And is it taught anywhere? I'm curious about it.
frozen rampart
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sacred elm
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sacred elm
what did i do wrong
torn gorge
the function $f(x)=x^3$ is injectiv
potent lotusBOT
everg
sacred elm
the function $f(x)=x^3$ is injectiv
what's that
glad parrot
sry I'm dumb
Nah you not
glad parrot
what's that
The words for what i said
sacred elm
Nah you not
thanks vro
torn gorge
what's that
if you don't know the definition of being injective then it is not important to understand what I wrote
sacred elm
The words for what i said
what does injective mean
sacred elm
if you don't know the definition of being injective then it is not important to ...
does that mean an odd function
glad parrot
what does injective mean
f(x) = f(y) ==> x = y
sacred elm
where did the sin come from
torn gorge
where did the sin come from
my remark would have been useful if you knew the definition of being injective ,,, in that case don't worry about it ...it is just making the things more complicated than they are
sacred elm
my remark would have been useful if you knew the definition of being injective ...
what grade do u take injectives in
let me google that
torn gorge
what grade do u take injectives in
I am not use to your grade system
sacred elm
I am not use to your grade system
what
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slender stratus
Y
unkempt drift
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unkempt drift
I need help
!da2a
slender stratus
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I need help
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
unkempt drift
oh okay
slender stratus
Can anyone help
first the 3rd q in the first paper says to Find the solution set of the inequality and round the results to the nearest ten-thousandth and the 2nd pic q1 a b c d f and q 3 c says to solve the equation and then check if my soulution is correct
the first pic q 3 and second pic q 1 a b c d f , I want to understand these
tulip herald
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slender stratus
<@1073314133996486778> Has your question been resolved?
No
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rotund granite
I've a question
calm coralBOT
I've a question
rotund granite
whats the result of X'BX supposed to be again
where x is a vector and B is a matrix
It's been on the tip of my tongue but I can't remember the significance
zealous mulch
whats the result of X'BX supposed to be again
What's X'?
rotund granite
X' is just
the vector inverted so
I guess like
the wald test here
takes a similar form
zealous mulch
the vector inverted so
What do you mean by “inverted“?
rotund granite
[x1 times some matrix of which parameters I forget, and then times it by [x1 x2]
x2]
rotund granite
[x1 times some matrix of which parameters I forget, and then times it by [x1 ...
but this is math
I just don't remember what it's supposed to equal
not what it somes to
X'MX = ???
zealous mulch
I may be totally wrong
But it seems to have something to do with eigenvectors, assuming B is the matrix associated to a linear transform
tidal scarab
[1,3] times [3,3] gives you [1,3]; [1,3] times [3,1] gives you [1,1] for example.
so the result is a number
rotund granite
okay whatever
I just don't get the point in
uh
The prime of a vector times the main argument times the original vector
I suppose there's no generality
I just saw it in my notes so
whatever
thanks
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delicate moon
Hi, got two questions. Where does this 1/2 come from?
calm coralBOT
Hi, got two questions. Where does this 1/2 come from?
delicate moon
And if I start with this formula, substitute for a, where does the rho go?
old falcon
hmm is v(z)
swift laurel
,, \pdv*{v^2} z = 2v \pdv vz
by the chain rule
then we are just taking that in reverse
potent lotusBOT
cloud
old falcon
yea
delicate moon
Ah yeah the chain rule, ofcourse that stuff again. 😅
Totally didn't see that here. How was I supposed to notice to apply that here?
Thank you guys
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wintry echo
Calculate the limit, if it exists, of the second derivative of the definite integral of ( f(x) ) between (\ln\left(\sqrt{\infty}\right)) and (\sin^{-1}(x^3)) as ( x \to \infty ), considering that the function is only defined for complex values.
potent lotusBOT
crazytime
wintry echo
Pls help!
pallid halo
wdym by $\ln(\sqrt{\infty})$?
potent lotusBOT
Bungo
fleet verge
Can you show the original picture?
wintry echo
it's this one
fleet verge
I don’t see any picture
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mossy wigeon
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fierce gate
Maybe they meant draw
Drop a perpendicular doesnt mean anything
Also bgl the wording of that text is garbo
fierce gate
Vectors
leaden thunder
the red dotted line is the result of the "drop a perpendicular from the tip of u to the line through a"
dotted line for when the perp extends past a
fierce gate
the red dotted line is the result of the "drop a perpendicular from the tip of u...
Oh lmao, that wording is complete garbo
leaden thunder
and the dotted line for when the component points in the "opposite" direction of a
the component being w1
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spark stratus
you can shorten the configuration by allowing O1, O2, O3, E1, E2 to be empty
other than that, looks good to me
dense coral
you can shorten the configuration by allowing O1, O2, O3, E1, E2 to be empty
oth...
im not sure what you mean by that but if its fine as is thats great too 🙏 ty for your confirmation
spark stratus
np
Im meaning that you can | epsilon for E1, O1, and O2 in addition to E2 and O3
(you are allowing O1, O2, O3, E1, E2 to be empty)
spark stratus
yea, then you can reduce the number of |s you have to use since theyre allowed to be empty
for example, O -> 1O1 | 3O2 | 5O3
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echo vault
can someone help with this question
calm coralBOT
can someone help with this question
potent lotusBOT
glad parrot
You on 1a or 1b ?
echo vault
one a
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echo vault
Have you tried finding the roots ?
can u help me
wiry that
like finding everyone and knowing how to graph it
that's my problem
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echo vault
how do u find the roots
echo vault
<@&286206848099549185>
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glad parrot
can u help me
You can factor it and set it equal to zero
glad parrot
like finding everyone and knowing how to graph it
And after you can find the top point of the parabola by calculating -b/2a where a and b are the coefficient of ax² + bx + c of your parabola
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native dragon
If 4 whole numbers taken at random are multiplied together, find the chance that the last digit in the product is 1,3,7 or 9
its clear till number 7 that its 4/10
but for 9 im confused cuz theres supposedly 2 cases here
9 x 1 x 1 x 1
and
3 x 3 x 1 x 1
so why is the probability of it the same (4/10)?
dull wagon
there are more than two cases for 9
native dragon
which ones
modern peak
3 x 3 x 9 x 9 for instance
distant thunder
basically its always gonna be 4/10 then?
Yeah
Since the last digits range from 0-9 and (I hope) we can assume that the probability for a single digit is 1/10
We have four digits in your example
So yes, I think the answer to your question is 4/10
native dragon
yeah i mean thats the case of 9
including the others its
(4/10)^4
cool cool thank you
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echo snow
I'm confused on what it means by scalar notation and isn't this involving something like A(x_1+x_2) = Ax_1 +Ax_2
brisk yarrow
can we get more context?
echo snow
That's the only context given
brisk yarrow
so there is no question a) ?
brisk yarrow
and what is A?
echo snow
A matrix
brisk yarrow
ok great
echo snow
Though I preferably use a 2 by 2
brisk yarrow
what do you mean?
echo snow
Something like A=(a b ; c d)
brisk yarrow
Do you have a given matrix or is it just a random matrix?
echo snow
No matrix is given so I guess it can be assumed to be random
brisk yarrow
ok then you really just need to show that A(x1 + x2) = Ax1 + Ax2 ig
i suppose you have some given axioms
echo snow
So is that linearity principle or not
brisk yarrow
afaik yes
echo snow
Is this sufficient enough
brisk yarrow
ig but is only true for 2 x 2 matrices
echo snow
Well this isn't a linear algebra class so for differential equations we restrict ourselves to a 2 by 2 matrix for a first order system
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tidal garden
calm coralBOT
tidal garden
Could someone please help me with the question on the right?
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shy nova
In triangle ABC, BE is the bisector of angle B, CD is perpendicular to BE at D. A = 68º , B = 2C and CD = 24 m
tawdry tendon
i have a question about polynomials
calm coralBOT
i have a question about polynomials
tawdry tendon
The polynomial p(z) = z^3 -3^2 + 2iz + 4 + 2i has a zero at z = -1 Determine all zeros of the polynomial, i have some trouble with the long division on this task, could someone explain for me pls
mortal orbit
The polynomial p(z) = z^3 -3^2 + 2iz + 4 + 2i has a zero at z = -1 Determine all...
what have you tried? maybe showing your work would help
tawdry tendon
tawdry tendon
what have you tried? maybe showing your work would help
i got the remainder to be: z^2 - 4z + 4 + 2i but im not sure if its correct
mortal orbit
I think it is correct
tawdry tendon
ok but how do i continue, do i need to calculate z from the remainder? could you explain for me pls
calm coralBOT
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mortal orbit
ok but how do i continue, do i need to calculate z from the remainder? could you...
you're left to factor a quadratic
quadratic formula
-> finding a root of the discriminant
eternal shard
oh i figured he already had one?? #help-25 message
tawdry tendon
i understand now, thanks for help!
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latent gulch
guys, how to differentiate (dy/ dx) an equation that has x on both its numerator and denominator?
limpid pilot
guys, how to differentiate (dy/ dx) an equation that has x on both its numerator...
differentiate y = x/x with respect to x?
latent gulch
wait how to do that
visual fern
denominator is to the power of -1, use product rule
limpid pilot
you dont really need to do anything
thats just y=1
derivative of that (wrt x) is zero
limpid pilot
quotient rule
visual fern
sorry yes ignore what i said ☠️☠️☠️
latent gulch
guys is there another way
in my book's curriculum, we still haven't learnt that
but i know how to do it
visual fern
which rules have you learnt?
visual fern
Like product, chain?
latent gulch
yes chain rule
not yet product
just addition substraction rule, scalar multiple rule, and differentiation of power functions
tacit moat
you can split the fraction
latent gulch
ohhh
latent gulch
you can split the fraction
okayy thankss
latent gulch
Like product, chain?
btw thankuu
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remote mural
i’m stuck ym😞😞😞
calm coralBOT
i’m stuck ym😞😞😞
remote mural
<@&286206848099549185>
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ripe spade
can u say what uve tried
hollow wren
This
hollow wren
Starting date 1/11/24 btw
But the first divisor date would be 2/12/24
I have no clue how to even start
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@hollow wren Has your question been resolved?
hollow wren
<@&286206848099549185>
hollow wren
<@&286206848099549185>
primal ferry
We want dates in the format D/MM/YY that satisfy:
- 1<D<MM<YY1 < D < MM < YY1<D<MM<YY.
- DDD must be a divisor of YYYYYY, specifically the last two digits of the year (let's call it yy=YYmod 100yy = YY \mod 100yy=YYmod100).
Thus, for a date D/MM/YY to be valid:
• DDD must divide yyyyyy without a remainder, meaning yymod D=0yy \mod D = 0yymodD=0.
Step 2: Identify Divisor Dates
To check if a date D/MM/YY meets the conditions, we:
• Ensure 1<D<MM<yy1 < D < MM < yy1<D<MM<yy.
• Verify that DDD divides yyyyyy (i.e., yymod D=0yy \mod D = 0yymodD=0).
For example, the date 04/08/24 is valid because:
• 1<4<8<241 < 4 < 8 < 241<4<8<24.
• 444 divides 242424 (since 24mod 4=024 \mod 4 = 024mod4=0).
Step 3: Find the Longest Gap Between Divisor Dates
After identifying all divisor dates between now and the end of 2099: - Calculate gaps between consecutive divisor dates.
- Identify the longest gap and find the first and last dates in this gap.
Step 4: Format the Result
For the longest gap:
• The answer format is d mm yy D MM YYd , mm , yy , D , MM , YYdmmyyDMMYY, where:
o d mm yyd , mm , yydmmyy: the starting date of the gap (first non-divisor date).
o D MM YYD , MM , YYDMMYY: the ending date of the gap (last non-divisor date).
0312460103 TEN DIG
hollow wren
how can there be a 31 in the months bit bro
and how can there be 03 in the years
also d have to be bigger than 1 so how do u have 0 in the d part
hollow wren
<@&286206848099549185>
remote mural
What's your question, I'll help you
hollow wren
remote mural
@hollow wren
hollow wren
Ye
remote mural
Ok wait 5 mins, please I need to read, and solve
hollow wren
Cool thx
remote mural
This is related to programming? @hollow wren
hollow wren
nope
remote mural
How, not? Read it, omg
hollow wren
I mean u can use programming to figure it out
hollow wren
thats just how u have to format ur answer
a string is a just a collect of characters written out in a row
remote mural
The longest gap between a successive divisor dates between now (2024), and the end of 2099 would be 2099 - 2024 ( - is a minus sign)
So your answer for the years would be 75
hollow wren
no because they have to be successive dates
remote mural
This is the longest year gap between a successive divisor dates
hollow wren
so there cant be any divisor dates between them
40824 and 21224 are successive divisor dates because there arent any divisor dates between them
but that isnt the biggest gap you can get
remote mural
d:mm mm:yy divisor dates. Take 4.08.24 with the next 2/12/24. The longest gap between successive divisor dates between 2024, as of now ( the year that we're in), and end of 2099, 75 is successive, because it comes divided from 2024, and 2099, so it is successive divisor, because it is divided from a successive collection of numbers.
remote mural
so there cant be any divisor dates between them
There aren't any, they are successively divided each by each date, by eachother, so they are successive, because they are successively divided by each other, giving you a successive number 75.
Between the years.
remote mural
40824 and 21224 are successive divisor dates because there arent any divisor dat...
How?
Can you prove it?
remote mural
but that isnt the biggest gap you can get
The gap is infinite, because the numbers are stated to be.
hollow wren
successive means they have to be one after another
you cant have the years 2024 and 2099 because there will be a divisor date in the year 2036 for example
hollow wren
Can you prove it?
bro thats the example they gave in the question
<@&286206848099549185>
hollow wren
<@&286206848099549185>
mystic phoenix
<@&286206848099549185>
what is this related to?
mystic phoenix
okay, i would start defining the criteria for 'divisor date' where d, mm, and yy, must satisfy 1 < d < mm < yy.
hollow wren
okay, i would start defining the criteria for 'divisor date' where d, mm, and yy...
Wdym
hollow wren
<@&286206848099549185>
primal ferry
how can there be a 31 in the months bit bro
This means the longest gap of non-divisor dates starts on 03/12/46 and ends on 01/03/48.
hollow wren
This means the longest gap of non-divisor dates starts on 03/12/46 and ends on 0...
u cant have 1 as d it needs to be bigger than 1
primal ferry
0312460103 TEN DIG
THIS 10 DIG NUMBER
primal ferry
U NEED n div number
hollow wren
what?
3/12/46 isnt a divisor date because 12 isnt a factor of 46 and 1/03/48 isnt a divisor date because d>1
primal ferry
from datetime import datetime, timedelta
Define the time range from today until the end of 2099
start_date = datetime(2024, 11, 3)
end_date = datetime(2099, 12, 31)
Helper function to check if D is a divisor of YY
def is_divisor_date(day, month, year):
if 1 < day < month < year % 100:
return year % 100 % day == 0
return False
Generate a list of all valid divisor dates
divisor_dates = []
current_date = start_date
while current_date <= end_date:
day = current_date.day
month = current_date.month
year = current_date.year
# Check if the current date is a divisor date
if is_divisor_date(day, month, year):
divisor_dates.append(current_date)
# Increment the date by one day
current_date += timedelta(days=1)
Identify the longest gap between divisor dates
max_gap = timedelta(days=0)
gap_start = None
gap_end = None
for i in range(1, len(divisor_dates)):
gap = divisor_dates[i] - divisor_dates[i - 1]
if gap > max_gap:
max_gap = gap
gap_start = divisor_dates[i - 1] + timedelta(days=1)
gap_end = divisor_dates[i] - timedelta(days=1)
Format the result as a 10-digit string "d mm yy D MM YY"
result = (
f"{gap_start.day:02}{gap_start.month:02}{gap_start.year % 100:02}"
f"{gap_end.day:02}{gap_end.month:02}{gap_end.year % 100:02}"
)
result
Résultat
'031246010348'
i cant help you more then this
The correct answer in the 10-digit format is:
0312460103
hollow wren
The correct answer in the 10-digit format is:
0312460103
it isnt the correct answer because I have put that in and its wring
it literally came up as incorrect so it isnt right
hollow wren
also the format for the answer is dmmyyDMMYY so why does your day have a 0 and also why is the year for the second date 03
primal ferry
max_gap = timedelta(days=0)
gap_start = None
gap_end = None
for i in range(1, len(divisor_dates)):
gap = divisor_dates[i] - divisor_dates[i - 1]
if gap > max_gap:
max_gap = gap
gap_start = divisor_dates[i - 1] + timedelta(days=1)
gap_end = divisor_dates[i] - timedelta(days=1)
answer here
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clear kernel
I am having trouble with the definite integral. For the problem I need to express this as a limit of sums (Riemann sum) then afterwards evaluate the limit. The book says it’s 2/3 but no matter what I try I only get things like -16/6.
clear kernel
It is 2/3 the book isn’t wrong, I verified that it was correct using FTOC
But I just cant get 2/3 by expressing the integral as a Riemanns sum
eternal shard
I am having trouble with the definite integral. For the problem I need to expres...
You are showing a fraction of your work
nimble harbor
lplz show full work
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blazing coyote
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potent lotusBOT
A dense set
blazing coyote
Let $x=a_0$
potent lotusBOT
A dense set
blazing coyote
Then we have $a_0(1+a_0)$
potent lotusBOT
A dense set
blazing coyote
So the factor would be $a_0,1+a_0, (a_0)(1+a+0),1$
potent lotusBOT
A dense set
blazing coyote
$f(a_0)= a_0+a_0a_1+a_1a_0^2+ \dots a_na_0^n = a_0(1+a_0+\dots + a_0^{n-1})$
potent lotusBOT
A dense set
calm coralBOT
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upbeat venture
not exactly true since a_0 could be 1
blazing coyote
hmm, yeah
found an answer on MSE, I think I'll look at that
been stuck on this for far too long
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blazing coyote
thanks
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cunning reef
<@&286206848099549185>
lethal vault
Yes
modern peak
"yes" isn't really a response
cunning reef
real
lethal vault
Ok sorry
cunning reef
can you guys help?
lethal vault
Yes sir
cunning reef
dont really know what to do next
^
lethal vault
Show Question
tacit moat
think about the sum of all the roots
and that 23 is prime
cunning reef
z^22 + z^21 + z^20 + ... + z = -1 right
but theres a 21,18,15,... multiplied in the exponents wouldnt this sum change
tacit moat
that's why the fact that 23 is prime is important
if you do 3k mod 23, it'll hit all numbers from 0 to 22
and it's true for every other number except multiples of 23
tacit moat
yea
tacit moat
if you do 3k mod 23, it'll hit all numbers from 0 to 22
not sure how to prove this though
got it from like integer ring mod p or something
ah Fermat's little theorem I think
nvm it's not that
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wintry kernel
calm coralBOT
wintry kernel
here's what I've done
my logic feels wrong, but i just wanted to make sure i'm right
a) $$ 5^8 +21^8 $$
potent lotusBOT
adam
wintry kernel
b) $$ 26^8 $$
potent lotusBOT
adam
wintry kernel
c) $$ 26^8 - 26^6 $$
potent lotusBOT
adam
wintry kernel
d) $$ 26^8 - 23^8$$
potent lotusBOT
adam
versed galleon
a) $$ 5^8 +21^8 $$
this one is right
versed galleon
b) $$ 26^8 $$
u sure this is b? in your paper you wrote 5x26^7
on c and d I'm not pretty sure, can you explain you logic?
autumn nebula
I already got the suremum which is 5 by using 1/n <=1 but I dont know how to do it on infimum T_T
dense fog
I already got the suremum which is 5 by using 1/n <=1 but I dont know how to do ...
Your supremum is wrong.
Sup (=max here) is found when n is as small as possible (since then 3/n as large as possible) while n+1 and n(n+1)/2 is even
Similar logic needed for inf
autumn nebula
Sup (=max here) is found when n is as small as possible (since then 3/n as large...
ohh i see, thank youu for this!! i'll try it out
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north gulch
can someone explain the 2nd step to me?
calm coralBOT
can someone explain the 2nd step to me?
@north gulch Has your question been resolved?
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@north gulch Has your question been resolved?
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@north gulch Has your question been resolved?
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shy wadi
im so lost....
calm coralBOT
im so lost....
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hollow relic
According to my math class, this is the answer
calm coralBOT
According to my math class, this is the answer
zealous mulch
What they're giving ya is the epsilon delta definition of a limit
hollow relic
Yeah I know
zealous mulch
Is this right? Shouldn't it be |f(x) - f(a)| = epsilon
Not really
L isn't always equal to the value of f(a)
hollow relic
L isn't always equal to the value of f(a)
Well yeah but if it's not then in this case it's not continuous
zealous mulch
Hm, well, I see why you could say that
zealous mulch
Is this right? Shouldn't it be |f(x) - f(a)| = epsilon
But remember epsilon is something you choose
It's arbitrary
hollow relic
Yeah
zealous mulch
If they were equal regardless of the value you chose, either L or f(x) would be constantly shifting
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neat veldt
hello , i wanna ask if someone can help me with these (those are in french but i can translate)
neat veldt
i havent got anything in the whole chapter...
magic imp
hello , i wanna ask if someone can help me with these (those are in french but i...
t'as besoin d'aide pour quels exos
j'ai un peu de temps stv
magic imp
okok alors
Exo 1;
on étudie un polynôme du second degré
c'est quoi un polynôme du second degré <=> un truc en x^2 <=> une parabole (en U ou en n)
neat veldt
ok... mais encore ?
magic imp
souvent ce qu'on fait dessus c'est qu'on regarde quand il est égal a 0
et pour ça on a un outil : le discriminant
aka delta(le discriminant) = b²-4ac
c'est quoi ces lettres?
c'est les coefficients devant tes "monômes"
en gros on étudie les : ax² + bx +c
ici b=-4, a= -1/3 et c=-12
donc le discriminant c'est 16-4x(-12)x(-1/3)
=0 (je te fais la correction en vif)
donc rep 1 : ▲=b² -4ac = 16-4x(-12)x(-1/3)= 0
Q2 : cette formule te donne les deux racines
mais bon quand ▲=0 bah tu vois bien en remplaçant dans la racine que tes deux racines sont (-b + 0)/2a et (-b-0)/2a donc la même chose
rep 2: c'est f(x=0) si x= -2/3
(en remplaçant)
j'espère que tu captes je vais un peu vite mais j'essaie d'expliquer vite et bien
neat veldt
j'espère que tu captes je vais un peu vite mais j'essaie d'expliquer vite et bie...
après y'a des trucs avec des fractions aussi
neat veldt
oki j'attends mais merci tu sauves 😭
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neat veldt
@magic imp le bot s'excite tout les combien ?
magic imp
15 mins je crois
au pire tu m'envoies un dm et je te résouds ça demain
c'est pour quand to dm?@neat veldt
neat veldt
c'est pour quand to dm?<@597054388359397376>
demain a 8h05
très exactement
(l'heure ou j'ai maths)
neat veldt
c'est pour quand to dm?<@597054388359397376>
y'a aussi une partie en python mais ez
magic imp
aie mais la ça va etre chaud j'ai cours a 8h uasis mdrr et j'ai pas fini mon bordel
neat veldt
aie mais la ça va etre chaud j'ai cours a 8h uasis mdrr et j'ai pas fini mon bor...
tu peux rester genre jusqu'a 2h du matin ?
magic imp
je vais te faire une correction speed
tableau de signe :
de -infini a +infini c'est négatif
donc tu mets un -
et sinon c'est f(x)=0 en x= -2/3 d'après Q2
l'alure : une parabole en forme de n qui a pour point max la valeur 0 en x = -2/3
le tableau de variation :
fleche vers le haut jusqu'en -2/3 ou tu mets en haut de la flèche 0
puis flèche vers le bas
Ex2:
1.aire totale :20 * x+ x² (* ça veut dire multiplication)
- 20x + x² = 525
donc x² +20x -525 =0
b² -4ac ça fait 2500
donc ça fait x= 15 ou x= 35
(bizarre)
mets juste x=15 au îre
pire
le reste prends en photo et colle dans chatgpt il arrive très bien a faire tout ça dsl je peux pas sacrifier plius ma nuit
j'ai testé ça marche nickel et il explique toiut
neat veldt
(copying)
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neat veldt
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blazing coyote
I would like my proof verified
calm coralBOT
I would like my proof verified
blazing coyote
We wish to proceed by induction
\
Base case : $1 \leq 1$
\
Inductive hypothesis $\sum_{i=1}^{n} \frac{1}{i^2} \leq 2 -\frac{1}{n}$
\
We wish to proved that it follows that $\sum_{i=1}^{n+1} \frac{1}{i^2} \leq 2 -\frac{1}{n+1}$
\
It follows that$\sum_{i=1}^{n+1} \frac{1}{i^2} = \sum_{i=1}^{n} \frac{1}{i^2} + \frac{1}{(n+1)^2}$
\
So $\sum_{i=1}^{n} \frac{1}{i^2} + \frac{1}{(n+1)^2} \leq 2 - \frac{1}{n+1} + \frac{1}{(1+n)^2}$
\
From this it follows that
\
\
$$\sum_{i=1}^{n} \frac{1}{i^2} + \frac{1}{(n+1)^2} \leq 2 - \frac{1}{n+1}(1 - \frac{1}{n+1}) = 2 -\frac{1}{n+1} ( \frac{n}{n+1})$$
\
We can also establish that $\frac{1}{n+1} ( \frac{n}{n+1}) \leq \frac{1}{n+1}$.
\
it thus follows that
\
$\sum_{i=1}^{n+1} \frac{1}{i^2} \leq \sum_{i=1}^{n} \frac{1}{i^2} + \frac{1}{(n+1)^2} \leq 2 - \frac{1}{n+1}(1 - \frac{1}{n+1}) = 2 -\frac{1}{n+1} ( \frac{n}{n+1}) \leq 2 -\frac{1}{n+1}$
\
As desired