Hello, I have been searching on the internet but couldn't find anything relevant, is there any formula for sum of n square roots?
#help-0
scarlet shore
karmic rapids
-ζ(-1/2, n + 1) - ζ(3/2)/(4 π)
scarlet shore
That's Riemann's function rigth?
karmic rapids
Im in grade 10 lol
and?
karmic rapids
just cuz you're in 10th grade doesn't mean you shouldn't know advanced stuff
scarlet shore
I know, just wanted to note I don't
lean depot
There's no easy way to do this that I'm aware of, I'm afraid
normal bridge
lone heartBOT
alpine sable
anything u tried?
normal bridge
anything u tried?
xy^3 = ky^2 but I'm not sure whether this approach is correct or what to do next lol
alpine sable
xy^3 = ky^2 but I'm not sure whether this approach is correct or what to do next...
yes it correct why do u think that's wrong?
u need to be a biit careful and use the fact that $ky \neq 0$
ocean sealBOT
∆y/∆x=sin(x) + cos(y)
alpine sable
indeed yes
normal jasper
any hints or pointers on how i could approach this question?
hollow shale
What is 94^2?
alpine sable
hint: the square root of 8881 is <95
normal jasper
hmm
keen bear
what do you know regarding the properties of primes? There are ways to determine this by just checking all primes for divisibility by brute force, but that doesn't seem very elegant
normal jasper
im still a bit stuck, so there being a bound on the square root of the number would mean that if u list out pairs of factors it would be less than 95?
i honestly dont know much about primes except the standard definition
keen bear
a particular fact about the prime factorization of a composite number is that it is guaranteed to have at least one factor less than its square root
prime badge
it's a bit simpler i think
normal jasper
yea id have never gotten that
keen bear
it probably is, since that's the brute force method
prime badge
it says prove by contradiction, the alternative would mean that all factors are 97+
is it one 97+? no it's not prime!
is it two 97+? no that's already more
proved it
normal jasper
i assume the solution is a bit simpler since this was a problem given after the first 10 pages or so of an "intro" to pure mathematics
keen bear
yea id have never gotten that
it's the multiplicative equivalent to the fact that every number can be written as the sum of two numbers of the form A+-x where A is the average and x is some distance away, and they always come in these pairs
keen bear
it says prove by contradiction, the alternative would mean that all factors are ...
you also have to check if it's prime itself, as it would then have a prime factorization above 89
prime badge
what do you mean
keen bear
oh, given that it's composite
nvm
the text of the question contains the scope of the question
normal jasper
hmm i think maybe it is enough to say that the next greatest prime is 97 and if there are no prime factors less than 89, then the least number u can get with primes above 97 is 97*97.
hollow shale
the factors "revolve" around the sqrt of the number
any factor > sqrt has the other factor be < sqrt
any factor = sqrt has the other factor be = sqrt
in either case, there must exist a factor that is <= sqrt
prime badge
that's too hard
hollow shale
and since you're looking for primes, that factor is at most 89
vale wigeon
d < sqrt(n) => n/d > sqrt(n)
north perch
8881 =
vale wigeon
easier expressed symbolically
north perch
we can try to find some squares whose difference is 8881
real gazelle
why?
north perch
to find the factors
lean depot
we can try to find some squares whose difference is 8881
Great idea. I think this works
real gazelle
the question doesn't ask to find the factors
hollow shale
you're not supposed to find the factors
vale wigeon
got a feeling it might be a little overkill
lean depot
Ah wait in fact it doesn't, nvm
vale wigeon
the idea is you're not supposed to compute much, if anything
hollow shale
just argue the existence
north perch
the question doesn't ask to find the factors
oh sorry
vale wigeon
every number has a factor not above its own square root
real gazelle
every composite number has a prime factor not above its own square root
alpine sable
lone heartBOT
alpine sable
can anyone help me prove this?
mystic dew
This involves binomial theorem
alpine sable
hmm the start point is the binomial theorem?
mortal trellis
the left side tells us how many options there are how to select p elements from n+m elements
can you tell me what (n choose k)*(m choose p-k) tells me?
lone heartBOT
@wild hare Has your question been resolved?
keen python
can I do this ?
lone heartBOT
can I do this ?
keen python
i calculated the possible limits of a_n+1 = a_n
and came out there is only one, for a = 2
so now I need to show that its really the limit right ?
noble sinew
If you have done a and b
You have a theorem that says limit exist
So no need to do anything else
real gazelle
kennen Sie der Satz von der monotonen Konvergenz?
real gazelle
haben Sie schon (a) gelöst?
lone heartBOT
@keen python Has your question been resolved?
timber sparrow
lone heartBOT
timber sparrow
feeling kind of braindead today, can't seem to visualise the bottom angle being 2theta
clear stump
Im braindead too
timber sparrow
any quick explanation is appreciated
lone heartBOT
@timber sparrow Has your question been resolved?
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solemn basin
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rose blade
im ngl im very confused idek what im doing i was just doing random math
last ether
Do you know derivatives?
Otherwise you just gotta find the vertex if it ends up being a quadratic
$$2L + W = 68$$
$$A = LW$$
ocean sealBOT
Umbraleviathan
vale junco
How would he find A then tho
lone heartBOT
@rose blade Has your question been resolved?
lone heartBOT
rose blade
ohh woops i did 2 w by accident
so 2l + 4
w
= 68
aight
But the stuff I did, was it right?
Like the way i solved for area
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Available help channel!
rose blade
bruh
keen socket
2L+W=68
68-2L=W
A=LW
A=L(68-2L)
A=68L-2L^2
dA/dL=68-4L
dA/dL=0
4L=68
L=68/4
2(68/4)+W=68
@rose blade
last ether
would u be able to explain
Not necessarily
Not without using limits which you probably don't know
rose blade
to get the max i think my teacher wants me to find the vertex by converting the equatioon into vertex form
rose blade
Not without using limits which you probably don't know
alr
rose blade
I learned what differentiation is
keen socket
lol
rose blade
i get where the 4 came from now
last ether
Damn okay then
last ether
I mean I was gonna write like
rose blade
u can still write it
cus im still confused
just curious if any of u guys actually solved it is the area 578?
last ether
First, construct a set of equations based off given information:
$$2L + W = 68$$
$$A = LW$$
We can rearrange the first equation so that $W = 68-2L$. Then we get:
$$
\begin{align*}
\begin{split}
A &=L(68-2L) \
& = -2L^2 + 68L
\end{split}
\end{align*}
$$
You need to find the vertex. If $(h, k)$ is the vertex of quadratic polynomial ${\color{lime}{a}}x^2 + {\color{cyan}{b}}x+{\color{orange}{c}}$, then $h = -\frac{{\color{cyan}{b}}}{2{\color{lime}{a}}}$. We can rewrite A:
$$A = {\color{lime}{-2}}L^2 + {\color{cyan}{68}}L + {\color{orange}{0}}$$
You can now find the vertex which will give you maximum area and the dimensions.
Bruh
rose blade
what are the dollar signs
rose blade
oh ok
ocean sealBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
last ether
There
rose blade
yeah thats what i thought
but u guys had me confused
everyone is so high level in this server
last ether
Yeah
keen socket
completing the square is boring
keen socket
oh gl
rose blade
thanks
is the vertex (5.83,17) and if not can someone please check to see where i went wrong
sorry
keen socket
is it not (17,578)
rose blade
i thoight the area was 578
keen socket
but our equation was A=-2L^2+68L
so if we were graphing we would plot L on the x axis and A on the y axis
rose blade
im so confused now because the ewquation i used previously worked to find the area but the vertex is wrong
yeah
ok nvm imma jus re do this
keen socket
**Umbraleviathan**
Compile Error! Click the <:errors:504266556054962196> reactio...
use this
rose blade
use this
right
but
ok so i get 17 for x or the length, then if u pluf that back into 2l-68 u get -34 which doesnt make sense
oh no
no
keen socket
-2L^2+68L
rose blade
tes tyes
vague cedar
isn't it (68-34)/2 which gives the width which is 17?
tired osprey
Julia launched a rocket vertically upward from the top of a cliff. The height of the rocket above the base of the cliff is approximated by the model h=-5t^2+30t+20, where "h" is the height in meters, and "t" is the time in seconds
A) how high is the cliff?
B) After how many seconds does the rocket hit the ground?
C) When does the maximum height occur?
D) What is the maximum height?
E) When is the rocket at 45m from the ground I'm not sure how to do this i've tried for like 30 mins and i can't figure it out and its due in 45 mins
tired osprey
i tried to solve the quadratic and figure out the height of the cliff.
alpine sable
ok, but u don't need to solve it
just try to think
at what time the object is on top of the cliff?
tired osprey
30 seconds
alpine sable
well the answer is 20
but I mean, u just need to substitute the values of t in the equation
at t=0 the rocket is on top, and then is starts going down
so if u substitute t=0 into the equation, u'll get h=20
for the second point, if the rockets hits the ground, what's its height?
oh sorry, upwards. so it goes up and then down
well but the answer is the same
at t=0 the rocket is on the cliff, so h=20
are u following?
tired osprey
yeah
tired osprey
ok
alpine sable
if the rocket hits the ground it means that h=0
so if h=0 it means that the equation is equal to 0
so then u just solve the equation 0=-5t^2+30t+20
u can devide by so 0-t^2+6t+4
and then u just solve it
it should give u two solutions, one must be negative and the other is positive
the answer should be around 6.6
seconds
tired osprey
wait so for this you just make h = 0 and solve the rest?
tired osprey
yes
tired osprey
yeah
tired osprey
yes
alpine sable
u can think that t=x and h=y
so the highest point
is actually the turning point
bc the parabole is like a sad face, so it reaches a maximum and then it goes down again
are u able to follow this?
tired osprey
yes
alpine sable
so do u wanna how to calculate the turning point of a parabola?
tired osprey
yes please
alpine sable
so u can calculate in a lot of different ways
the easiest one is t=-b/2a
where a is the coefficient of t^2 and b of t
so the t of the maximum high is t=-30/(-5)
so t=6
now that u have the time u can calculate the height
u just need to put t back into the equation
tired osprey
i see
tired osprey
yes
alpine sable
so for the last question
u know that h=45
so just substitute into the equation and solve for t
45=-5t^2+30t+20
devide by 5
9=-t^2+6t+4
rearrange and sum
t^2-6t+5=0
and it has twho solutions
t=5 or t=1
tired osprey
thank you
tired osprey
ok will do
thanks for the help tho u really helped me understand this better
.close
sullen vapor
lone heartBOT
pearl pagoda
∠DHF= ∠DHE+ ∠EHF
∠EHG= ∠EHF+ ∠FHG
but ∠DHF=∠EHG, then…
∠DHE+∠EHF=∠EHF+∠FHG
then ∠DHE= ∠FHG
∠DHE= ∠2
∠FHG= ∠3
=> ∠2=∠3
“m” can be reduce.
lone heartBOT
@sullen vapor Has your question been resolved?
sullen vapor
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dusk thorn
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keen socket
,rotate
ocean sealBOT
fresh parcel
How do i get to (a+b)(a²+3ab+b²) from here?
you factor out the (a+b)????
desert moon
I was able to do it this way
so you did it, what do you want to know?
that looks like the right method
dusk thorn
I wanna know if its possible in this method...if so...how?
lone heartBOT
@dusk thorn Has your question been resolved?
azure trout
lone heartBOT
azure trout
how would I even do this 😭
echo socket
Law of cosines could help
Although the problem does not mention which sides b and c are but I'd assume c is the one opposite to the angle C and b is the one opposite to the angle B
echo socket
Well applying the law of cosines here yields that c^2 = a^2 + b^2 - 2abcos(C)
Assuming what I said about the position of b and c is correct*
So from here you can solve for a
azure trout
would I have to do 2 triangles? for all "possible solutions"
echo socket
Eh yeah, pretty much
azure trout
but how?
echo socket
You mean what cases to consider?
azure trout
yes
echo socket
I think those are when a is opposite to C, b is opposite to C and when none of them are opposite of C (meaning they're both adjacent to it)
azure trout
so theres only one possible solution?
echo socket
There are 3 cases as I mentioned those
azure trout
im so confused
echo socket
Just consider each case separately and those will lead you to the possible answers
azure trout
how do i even consider those lol
echo socket
But again I think the author meant that c is the side opposite to angle C
azure trout
But again I think the author meant that c is the side opposite to angle C
yes they did
echo socket
Oh
azure trout
so its only one triangle?
lone heartBOT
echo socket
Well applying the law of cosines here yields that c^2 = a^2 + b^2 - 2abcos(C)
Just start with this then
Good luck
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Available help channel!
sharp moth
When do I know how to do the product rule?
lone heartBOT
When do I know how to do the product rule?
sharp moth
In this equation, I just multiply the two values together
But how do I know the difference between doing that and applying the product rule
Is it going to specifically say to use the product rule?
Or is it indicated by putting the prime symbol, with yprimex?
crisp grail
Is it going to specifically say to use the product rule?
the answers will be the same no matter which method you use
but its good to use the product rule to practice it i guess
stable gazelle
Hello
dry ridge
stable gazelle
I tried to apply the coulomb formula between a helium core and an electron, but I come to a confusion:
The strange thing about the coulomb force is that the force exerted by the electron on the nucleus is the same force exerted by the nucleus on the electron. Yet we could say that the force of generated by the electron is 2 times smaller than that generated by the 2 protons of the helium nucleus
lone heartBOT
@stable gazelle Has your question been resolved?
stable gazelle
No but it doesn’t matter no problem
reef field
Small question
lone heartBOT
Small question
reef field
r^2 = (s/pi/r)^2 - (h^2)
rv^2 = (2s/pi/rv)^2 - (hv^2)
(2 * pi *r) + (2 * pi * rv) = 100
Solve for r, rv, h, and hv
My brain is dead
Pi is pi
iron mulch
Schizo this chat is taken
zealous ruin
reef field
I just don’t know where to approach this
.
<@&286206848099549185>
If anyone is available
reef field
Doesn’t look like it unless I messed up
tacit arch
Show the original question and all your work
lone heartBOT
reef field
I’m an idiot
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Available help channel!
fresh parcel
im having trouble with this matrix multiplication\
lone heartBOT
im having trouble with this matrix multiplication\
fresh parcel
im getting the exact same thing except with a 2 instead of a 10 on the bottom left corner
tacit arch
2 is correct
tacit arch
Assuming E32 is the first matrix, E31 is the second matrix, and E21 is the third matrix
tacit arch
The first column in E31 is only nonzero in the first entry
So you just need to dot the last row of the first matrix with the first column of the second matrix
lone heartBOT
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Available help channel!
shell urchin
lone heartBOT
shell urchin
I don’t know what to do
tacit arch
Use a z score
lone heartBOT
@shell urchin Has your question been resolved?
shell urchin
Use a z score
-0.50?
alpine sable
Well, you know he's below average so his percentile rank is below 50%, so we throw out option 3. But it can't be something absurd like 0.19 or 0.5 given his value is within 1 standard deviation of the mean, so we throw out option 2 and option 4. What are you left with?
That's a "multiple choice thinking" way of solving it.
shell urchin
Thank you
tacit arch
I was only guessing
Using a formula is not guessing. Use the z score formula
shell urchin
It’s a practice problem because I’m studying so it doesn’t actually count. So I was hoping to learn the process of it since I forgot, but I learn really slow
shell urchin
Using a formula is not guessing. Use the z score formula
Okay
shell urchin
Using a formula is not guessing. Use the z score formula
I got -0.5
When using the z score formula
tacit arch
Show your work
shell urchin
Show your work
tacit arch
Looks good. Just plug it into a table for percentile
shell urchin
Okay
shell urchin
Looks good. Just plug it into a table for percentile
Um:/ idk what else I’m supposed to look for on the z table. I know -0.5 but idk the other one
tacit arch
Show your z table
shell urchin
It doesn’t give me one
shell urchin
Show your z table
It just gave the question
I tried looking for one
But not a good one
tacit arch
shell urchin
http://www.z-table.com/
Ty
shell urchin
http://www.z-table.com/
What number am I looking for at the top and why?
I know the left is -0.5
tacit arch
I don’t really understand that but okay 😭
say you have a positive z value of a.bcd then you look for the row under the z column with a.b
then you scan right until you get 0.cd
shell urchin
I’m trying to understand 😐 I don’t learn fast
tacit arch
oh sorry i was wrong
you add 0.cd to a.b
0.cd is 0.05 in this case. i guess it's always 0.0d
and a.b is 0.2
so for the z score of 0.25, you look in the first column for 0.2, then scan that row until you get 0.05 because 0.2 + 0.05 = 0.25
another SAT example
https://towardsdatascience.com/how-to-use-and-create-a-z-table-standard-normal-table-240e21f36e53
shell urchin
you add `0.cd` to `a.b`
Because it has 0.25
You look for the two and then the 5?
tacit arch
lucid apex
https://cdn.discordapp.com/attachments/326138757474680852/1000168308559061113/IMG_0040.jpg
So basically I have been trying to understand this question but I dont know how to find triangle angle sums in spherical geometry. Can someone explain triangle angle sums in spherical geometry to me?
chrome plank
,rotate
ocean sealBOT
chrome plank
f
lone heartBOT
@lucid apex Has your question been resolved?
chrome plank
I made a nice sketch
If you zoom in at the sphere's surface and make a very small triangular shape (Something like going outside and drawing a triangle on the ground), the sum of the interior angles will be super close to 180°, and can be approximated very well by a 2D plane
But if you make such a big triangle on a sphere, do you expect it's interior angles to be bigger or smaller than 180°?
lucid apex
Bigger I think
lucid apex
Is it 185?
chrome plank
Yes, I think so
lucid apex
Alr
Thanks for explaining this to me I’ve been struggling with this for a while lol. Have a great day!
.close
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chrome plank
You too!
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forest orchid
does anyone know if for the final form of this equation is it possible for n to equal 4
ocean sealBOT
Nonna
forest orchid
yes
chrome plank
Yes of course
forest orchid
oh I didnt know for sure because I knew 3 meant it was cubed and 2 it was squared so i wasnt 100% sure if you could use 4 in it
forest orchid
0 is pretty much undefined right?
chrome plank
0 is defined, the division by 0 is undefined
vernal thunder
not 0 I think
I did say positive integer
chrome plank
I did say positive integer
you mentioned rationals too, it's to not bring confusion
vernal thunder
you mentioned rationals too, it's to not bring confusion
I forgot to say positive in front
My mistake
chrome plank
m and n can be negative
vernal thunder
<:thonk:406575732563902485> m and n can be negative
Is it possible to have a negative root
ocean sealBOT
Nonna
ocean sealBOT
Nonna
chrome plank
and it becomes\
$\sqrt[n]{x^{-m}}$
vernal thunder
Ok so a negative root works
ocean sealBOT
Nonna
chrome plank
Yes, but because of the definition as x^(m/n)
$\sqrt[n]{x^{-m}} = \sqrt[-n]{x^{m}}$
ocean sealBOT
Nonna
chrome plank
because
$x^{\frac {-m} {n}} = x^{\frac{m}{-n}}$
ocean sealBOT
Nonna
chrome plank
Does it make sense?
chrome plank
Nice
@forest orchid If you have more questions feel free to ask, otherwise .close the channel
forest orchid
<@423476992319422485> If you have more questions feel free to ask, otherwise .cl...
Im good now, thank you for the help
.close
lone heartBOT
chrome plank
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fluid raven
help
fluid raven
abstract fractal
What have you tried
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quasi rover
Working on a larger problem, I got this as a part of an equation. Wasn't sure how to approach, so plugged numbers in. Got the Bernoulli Triangle sums [(1), 1, 3, 8, 20, 48].
I worked out that the sum permutation on the left -- if isolated -- form the fibonacci numbers, and the isolated sum of the permutation on the right give triangular/tetrahedral/etc. numbers.
Anyways, would like to prove whether or not the summation will give the n-1th Bernoulli number.
quasi rover
<@&286206848099549185> I will pay 3 boiled eggs
I have tried marking values in Pascal's triangle, but I don't think it works.
For reference: http://oeis.org/wiki/Bernoulli's_triangle
I have plugged it into desmos too, though different variable names. https://www.desmos.com/calculator/akc1qbgvye
lone heartBOT
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quasi rover
<@&286206848099549185>
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@quasi rover Has your question been resolved?
fluid raven
help
reef lantern
are these false?
lone heartBOT
are these false?
reef lantern
hello?
abstract fractal
Can you explain why for each?
reef lantern
for 1 f'(x) = 0 could just be the graph platueing but it can still carry on in any direction, it doesnt necessarily mean there WILL be a local minimum and max
I think
fallen verge
could you perhaps draw out what you mean
reef lantern
some thing like this
fallen verge
yup
reef lantern
so 1 is false then
fallen verge
good example
reef lantern
f''(x) is 12x^2
fallen verge
that would work yup
reef lantern
but 3 i have no idea
fallen verge
consider the graph of f'
fallen verge
#3 is true
its a little hard to prove in what i would assume is calc 1?
i could be wrong
reef lantern
yes this is calc 1
alpine sable
Oh yes it can be an inflection
fallen verge
no it would still be a minimum
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ocean sealBOT
dawn ridge
what does this question mean and how do i check?
lone heartBOT
@dawn ridge Has your question been resolved?
tacit arch
Plug in the formula for a_n and a_{n-1} into the recurrence relation
dawn ridge
yes. it comes from o-th term to 3th term
tacit arch
There is no 0 index
dawn ridge
a1,a2 like that
tacit arch
What's a2
dawn ridge
3
tacit arch
Nope
dawn ridge
2
tacit arch
Use the given formula and stop guessing
dawn ridge
what is mean by one expression is olution recurence of another
i just started yesterday so i know some basic term only
tacit arch
Did you have a lecture on it?
dawn ridge
little bit videos
tacit arch
Just means you plug in your given formula into the recurrence relation
But you need to understand the formula a_n
dawn ridge
an=dan -1
tacit arch
You know what $2^n + 1$ means?
dawn ridge
so i should each expression by n-1
ocean sealBOT
riemann
dawn ridge
its a rec reln?
tacit arch
Do you know how to evaluate a_n for 1,2,3,4?
Do this
tacit arch
its a rec reln?
Also, no
dawn ridge
just replace n in 2n + 1 by 1,2,3,&4?
tacit arch
yes
dawn ridge
so how do i check one reln is recursive reln of another,,..I have solved basic number related problem yet
tacit arch
just replace n in 2n + 1 by 1,2,3,&4?
What's your answer for this
tacit arch
so how do i check one reln is recursive reln of another,,..I have solved basic n...
I already told you
dawn ridge
5,9,17,33
tacit arch
Plug a2 and a1 into the recurrence relation to see if it holds
a2 = 2 * a1 - 1
Repeat for a3 and a2
Once you're done with a few values, plug it in for general n and n-1
main zephyr
imagine a chess board and imagine there is only one bishop piece, given the current coordinate of the piece is (4,6) and the coordinate that the piece wants to go to is (3,7) determine whether the piece is moving diagonally
eternal spade
imagine a chess board and imagine there is only one bishop piece, given the curr...
chess math 
hold on
lone heartBOT
@main zephyr Has your question been resolved?
vale wigeon
"determine whether the piece is moving diagonally"?
what's there to determine?
bishops always move diagonally by definition, do they not?
@main zephyr can you clarify your question
icy latch
bishops always move diagonally by definition, do they not?
ikr, maybe it's a gradient type question?
vale wigeon
can you show the problem EXACTLY as it was stated
lone heartBOT
icy latch
can you show the problem EXACTLY as it was stated
it's probably to define through gradient and coords whether in this case, if the bishop does a legal move to said square
lone heartBOT
Available help channel!
abstract skiff
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abstract skiff
this is right?
ocean sealBOT
Result:
-4
,calc 3*2 - 2
ocean sealBOT
Result:
4
looks like your answer is incorrect
vale wigeon
how did you arrive at x=2, y=4?
abstract skiff
wait ill check
vale wigeon
show your work here so that we can look for your error(s)
vale wigeon
...?
abstract skiff
So basically
vale wigeon
do you have your work written out on a piece of paper?
vale wigeon
ok so all you did was write out a bunch of expressions with no rhyme or reason behind them
not a single equals sign in your work
abstract skiff
Just put y =
vale wigeon
are you allergic to equals signs?
vale wigeon
you want to put y= at the start of every line?
vale wigeon
but then that won't make any sense
abstract skiff
why not?
vale wigeon
surely, if you want to multiply both sides by 3 in the equation y = -5x + 6, the equation ought to become 3y = -15x + 18?
vale wigeon
that, and also there's a somewhat simpler way to do this
and you have no instructions forbidding you from doing so
just solve the equation -5x + 6 = 3x - 2
abstract skiff
alright
-5x + 6 = 3x - 2
-5x + 5x + 6 = 3x + 5x - 2
6 = 8x - 2
8 = 8x
X = 1
Y = -5 + 6
y = 1
knotty spire
,w solve -5x + 6 = 3x - 2
ocean sealBOT
knotty spire
congratulations
vale wigeon
be mindful of capitalization
also, while we're at it
with sufficient correction, your way could've solved the system too: you would have the equations 3y = -15x + 18 and 5y = 15x - 10 which you could then add to get 8y = 8 whence y = 1
main zephyr
<@625305547629133825> can you clarify your question
in my situation, im making a game similar to chess but all pieces can only move diagonally, the board's layout is the same as the chess board. Lets say that the piece that sits at (4,6) wants to move to (5,7). I want to know if the piece if moving diagonally before updating the piece's position
vale wigeon
i don't understand still
"all pieces can only move diagonally"
"i want to know if the piece is moving diagonally"
main zephyr
well im programming the game
vale wigeon
you just said all pieces in your game are moving diagonally
clear stump
isnt that just checkers
main zephyr
you _just_ said all pieces in your game are moving diagonally
thats the rule ye so i wanna implement it into my code
icy latch
check if gradient is 1 or -1?
main zephyr
isnt that just checkers
its called checkers? oh
vale wigeon
"i want to know if the piece is moving diagonally" implies the answer could be yes or no depending on some circumstances
but in your case the answer seems to always be yes
main zephyr
check if gradient is 1 or -1?
oh
vale wigeon
so i fail to see the point
main zephyr
but in your case the answer seems to always be yes
why would it always be yes?
vale wigeon
all pieces can only move diagonally
main zephyr
that is the rule im going with
vale wigeon
ok let me try this again
what part of the code is this check supposed to be in, and what is it responsible for?
main zephyr
i cant just write "all pieces can only move diagonally" into my program, i need to know the math to return a value of "true" or "false"
main zephyr
what part of the code is this check supposed to be in, and what is it responsibl...
validating whether the move is diagonally
its like a function that i provide 2 coordinates with
vale wigeon
ah
so you have a function that takes in a start point and end point that you need to return true if and only if the move thus described is a valid diagonal move
main zephyr
yes
vale wigeon
then yeah, check if the gradient is equal to ±1
main zephyr
oo
btw can u explain, in simple terms, what is a gradient
my teacher teached me its formula but never really explained what its used for
vale wigeon
the gradient, or slope as i've seen it called more often, is the measure of how steep or shallow a line is on the plane
main zephyr
she did say that parallel lines have the same gradient so i assume its the direction of a line?
main zephyr
the gradient, or slope as i've seen it called more often, is the measure of how ...
ah
vale wigeon
kind of.
i would not call it the direction per se
but it is a function of the direction
earnest tiger
Just make the absolute value of slope = 1
lone heartBOT
@main zephyr Has your question been resolved?
hollow pasture
alpine sable
hi
alpine sable
so i have a pde
ut + H(Du) = 0
where u is a function of x, a n dimensional vector
the book says u write the 2(n+1) +1 = 2n+3 odes for the characteristic system
i dont get where the 2n+3 comes from???
also it says that u can decouple the system of characteristics into two systems
dxi/dt = dho(H)/dho(pi)
and dpi/dt = -dho(H)/dho xi
where pi = dhou / dho xi
and xi are the components of the vector x
how do u decouple the system-??
sand pawn
could you upload an image please for visualizing your problem? @alpine sable
lone heartBOT
@alpine sable Has your question been resolved?
slender mantle
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slender mantle
I've used the midpoint formula and found that P is (2,0) by doing (midpoint of RS = ((-2+6)/2), ((4-4)/2)) = (2,0))
if I used the mid point formula, it must mean that P is collinear with R and S, yet part (ii) requires me to explain why they are not collinear, which means my answer must be wrong
Please help!
chrome plank
"its x coordinate is twice its y coordinate" that's not true for the point you found
Also, the midpoint between two points is not the only point that is equdistant
slender mantle
does that mean that P(2,0) fulfills the being equidistant part but does not fulfil the "x-coordinate is twice its y-coordinate)?
So I will have to find another point using another way that fulfills both conditions
chrome plank
yes
slender mantle
Okay, I will try again and update you, thank you
chrome plank
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fierce plaza
does anyone how to make any of the following? pareto chart, histogram , frequency graph, sector graph, stastical display if so dm me please
alpine sable
does anyone how to make any of the following? pareto chart, histogram , frequenc...
what's the context of "make"
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@fierce plaza Has your question been resolved?
lone heartBOT
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potent rain
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potent rain
I'm confused on how to find the opposite of cosine. I tried using the fact that cosine is an even function to ignore the negative.
I also tried to just move theta to the negative x value and then moving it by the xpi factor but that doesn't work either
crisp grail
use that cosine is the projection on the x-axis
potent rain
I will give an example on paper one second
crisp grail
use that cosine is the projection on the x-axis
crisp grail
the upper one is one of the solutions
and cuz its an even function the other solution is $\cos(-\right(\frac{\pi}{2}-\theta\left))$
ocean sealBOT
VincentBH
potent rain
and cuz its an even function the other solution is $\cos(-\right(\frac{\pi}{2}-\...
Ok my confusion comes when I do pi-t and pi+t
Technically it's the same thing but then that's 3 solutions 💀
It can't be 2pi-t because it leaves it in the same quadrant, quadrant 1
And that's positive so it can't be opposite
potent rain
the upper one is one of the solutions
Are you still here? 😫
Who can help me? I'm confused
.close
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potent rain
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urban pine
opposite here just means negative right?
potent rain
opposite here just means negative right?
Yes, I believe so.
It's weird terminology right, no one else uses it.
urban pine
just making sure i'm not overthinking it
potent rain
Very frustrating when someone wants to suddenly reinvent the wheel lol
urban pine
lots of opposites in math lol
for this i like to look at the angle and then move the theta from there
potent rain
Yeah so I'm confused because 2pi-t can't be it because obviously that leaves it in the same place it was before in quadrant 1 so it's not opposite
Then pi-t and pi+t are both potential solutions since it leaves you with a negative cosine
But the guy here says pi/2-t is one solution
So they can't be both the solution
urban pine
so cos(pi/2 - t) will always be sin(t)
that's an identity
and sin with SOHCAHTOA is the opposite, so that's why i was checking earlier lol
for these i like to start with the angle then move by theta
so cos(t) is starting at angle 0 (x-axis)
and cos(pi/2 +- t) is starting at angle pi/2 (x-axis other side)
and hopefully you see they go up/down theta either way, but the projection is still the same, just on the negative side of the x-axis
we can see the 2pi like you said it's the same as 0
urban pine
yeah you can visualize it like that
potent rain
I thought I started with theta and then moved with the pi factor.
urban pine
both work, i like to do the constant first and then kind of wiggle the variable in my head
whatever works for you
potent rain
But either way if I don't then I'm confused because pi+t and pi-t obviously start in quadrant 3 it's the same thing
urban pine
correc
well not quite Q3
the negative x-axis
one will go up to Q2, the other will go to Q3
urban pine
careful
yes
but
cos(a - t) = cos(-(-a + t)) = cos(-a + t)
can't just grab any theta in the argument and switch the sign
i.e. cos(a - t) /= cos(a + t) in general
potent rain
I'm sorry I just don't understand.
urban pine
nw
you're correct that cos is even
if a function f is even then f(-x) = f(x)
that's the def
but notice we have to be careful once the arg of the function is more complicated (including other terms)
f(a - x) is not necessarily f(a + x)
quick example x^2 is even but (a - x)^2 = a^2 - 2ax + x^2 and (a + x)^2 = a^2 + 2ax + x^2
not the same
not sure if i'm addressing which part you're confused about exactly
potent rain
Not really honestly this seems quite advanced
urban pine
not trying to attack you with old algebra stuff :p but just a quick example, the gist is that you can't just reach in and pick and choose what is positive or negative
potent rain
Hmm
urban pine
the entire input of the function can be negated without any effect
all or nothing
SO anyway that's all just to say that cos(a - t) and cos(a + t) are usually distinct; and they are for our case a = pi
potent rain
Ok and I have to use the former formulae to find that out?
urban pine
how do you mean?
which formula?
definition of even?
for now i wouldn't worry about it. it's prob best to get comfy with your unit circle instead of proving all this algebraically
potent rain
The one you said earlier with x^2 etc.
urban pine
sure that was a counterexample to being able to switch signs wherever you want (you can use the same to show that the negative of the whole thing is good to go tho)
i made a little visual for the cosine prob
play with the a and t sliders
couldn't make the triangles nice, so you'll have to imagine them lol
potent rain
I tried using desmos app on my phone; I'm at work rn
It is not very good it seems
It just shows a line when I put like x = cos(pi-t) for example.
urban pine
not missing much; it just plots cos(t) and compares to cos(pi - t) and cos(pi + t)
oh yeah when you type that it's a line equation so it'll give a line
if you wan't to plot points on a unit circle you have to give it a point like i did (cos(a - t), sin(a - t))
then it'll give the (x, y) coord for that
urban pine
no those will be two lines
in the same field put a coord in (something for x, something for y)
i'd recommend taking a look at mine to start
potent rain
Oh ok
urban pine
brb
lone heartBOT
@potent rain Has your question been resolved?
tidal zealot
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knotty spire
what have you tried?
knotty spire
I honestly have no idea what is going on
tidal zealot
im integrating
knotty spire
here
real gazelle
No
tidal zealot
why not
knotty spire
expansion si the easiest way forward
you get three terms
which you can integrate within seconds
tidal zealot
which you can integrate within seconds
yeah ik
but i want to know why can i not do reverse chain rule
why cant i do wht i just did
abstract fractal
What you did isn't reverse chain rule
Reverse chain rule is just another name for u substitution
AFAIK, anyway
knotty spire
well it definitely wasn't u-sub either
In this case, well, I don't think it would help
but you are welcome to try
this is why integration is generally difficult; not every way works
tidal zealot
real gazelle
Can you explain your thought process for what you did here
knotty spire
what you did is a u-sub in disguise
tidal zealot
The x^2 has derivative 2x
so?