#help-42
1 messages · Page 56 of 1
,w \sum^{n}_{k=1} (2k-1)^2
also is there a better way to do this
the final answer is right
oh wait you can do that?
but yeah the typical way is to use your summation formulas - idk of a better way than that
tysm
yeah you can do that in #bots
,w [your thing]
you can just type
,w sum of (2k-1)^2 from 1 to n
if you don't know latex
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I need help with this question.
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Need help on this
By setting the price of adults to x and price of children to y
We get two equations
Solving them might help
How do we solve them?
Have you learned how to solve equations?
Yeah but I just need a refresher
Ok
In the first equation
We can simply divide both sides by 50
Therefore x+y=16
Still with me?
Yup
Alr
=1050
However, we have an extra 10 children here
And the price is now 1100
So we know 10 children must cost 50
And you can continue from here
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I tried finding the lambda value which I found -3 and 2
But after following YouTube tutorial I am completely lost 💀
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Could anyone check my proof for this problem please?
this sentence is sloppy
yea it's all wrong
Really
I mean we can interchange the limit of the sum with the limit of the integral
because the series converges uniformly
Is it actually wrong?
typo here
How do you recommend I say this then?
i'm just doing some hilarious trolling i didn't even look at it
We can interchange integral with the infinite sum because it converges uniformly?
Normally I would've figured but riemann was also noting some things so I got legitimately worried
i'm not convinced you've proven the new series with sin(x) multiplying converges uniformly
actually this isnt true
justified by what
sin(x) is not dependent on k
so we can interchange it in the limit
if sin(x) = lim k-> inf (thing) uniformly
(by assumption)
then sin(x) sin(x) = sin(x) lim k-> inf (thing) uniformly
and then we may bring the sin(x) inside the k limit
Is my justification
yea try writing that up more carefully
because this sentence isn't rigorous enough
Okay I'll add a sentence there and at the beginning then
Thanks @leaden thunder
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.reopen
✅
<@&286206848099549185>
!1c
Please stick to your channel.
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SNIPED
Ok
this is the third time ;-;
What should I do now lol
Here?
Which part did you need help with?
All
For question a, do you know the definition of a conservative vector field?
No can u give me a rough idea...like I have to submit this in 15mins
Or I don't meet the attendance criteria
And gotta leave the course
If F is conservative, the following must be true:
Pls
Αρχιμήδης
Ok
Where f is the potential function.
To determine if this is true, you must take the partial derivative of P with respect to y, and the partial derivative of Q with respect to y of the following.
Αρχιμήδης
P is the function in the i direction, and Q is the function in the j direction.
Integration, either integrate P wrt x, or Q wrt y.
Assuming it is conservative, integrating P will give:
Αρχιμήδης
Then you have to fund your function h
And the reason we have a function of y is because we're working with partial derivatives.
I also forgot to mention, if it is conservative, the partial derivatives should equal.
No worries
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could anybody assist me please
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whats ur rank
in val
Like Iron 3 i think
NO WAYYY
i went up a lot recently
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please don't ping us several times in only a few minutes.
yeah sorry i thought it was fine because i posted my q25 mins ago
Isn't that yr college assignment
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Would they expect me to have the solution for F aswell?
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for
how do u derive those parameterisations for the unit vectors?
You're talking about polar coordinates?
but i cant recover the above
,w cross product (cos(theta), sin(theta), 0) and (0,0,-1)
taking the cross product with -k does get me A_theta if i know the first
so thats fine
so i guess i just need to know how to find the first
In Polar coordinates you make the transformation (r*cos theta, r*sin theta), the two unit vectors are the partial derivatives and then we norm them
If you take the partial derivative of this with respect to x you get u_r
If you take the partial derivative with respect to theta you get e_theta*r and you norm it to get rid of the r
ok so just to be clear
we have [
\vj r(r, \phi) = r\6\cos\phi\vc*\imath + r\6\sin\phi\vc*\jmath
]
by definition of polar coordinates
the partial derivatives will point at the direction of the unit vectors
so
[
\pdv[\vj r]r = \6\cos\phi\vc*\imath + \6\sin\phi\vc*\jmath \
\pdv[\vj r]\phi = -r\6\sin\phi\vc*\imath + r\6\cos\phi\vc*\jmath
]
There's an r missing in the line below
yeah thank you
so
taking the norm
first is just 1
so the unit vector is the same
the second will be r
assuming the positive case
divide by r and it gets u that
gee neat
okay thanks a lot!
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yeah thats super helpful actually
Yes, especially if you are studying physics with maths 😂
yeah thats what imd oing LOL
But tbf, this trick does only work for like spheres or circles. If you parametrized a parabola or sth the partial derivatives wouldn't be orthogonal
oh right thats the catch
is there like anything that lets u derive them
more general and by definition maybe
I mean you have to define one of those as a unit vector. Let's say you fix e_r as it is. Then you can construct e_theta as the unit vector orthogonal to e_r
But there would still be two possibilities
So even if you defined e_r you wouldn't even get a unique choice of e_theta
i mean assuming we are following a right hand coordinate system
then e_theta would just be this i guess?
Then theta is unique
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$\sqrt{9-8\cos\left(40\degree\right)}=a+b\sec\left(40\right)$
Why am. I here
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$\sqrt{9-8\cos\left(40\degree\right)}=a+b\sec\left(40\degree\right)$
Why am. I here
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it should be 40 deg
find |a+b| if a and b are both rational
I thought of squaring it first
not sure what to do from there
$9-8\cos\left(40\degree\right)=a^2+b^2\sec^2\left(40\degree\right)+2ab\sec\left(40\right)$
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u can compare both the sides
like u do for complex numbers
why would that work here
both a and b are rational
unlike in complex numbers where one part is imaginary
Im not toally sure
but here
it might work
like a^2 = 9
and b^2 + 2ab = -8
hmm
|a+b|
check the combinations then
hmm, if b=-3
u mean a
then ,w b^2-6b=-8
,w b^2-6b=-8
I didnt notice
that its cos theta on one side
and sec theta on the other side
we cant compare them like that-
so I have to evlavuvate cos(40)?
hmm, maybe I can factor out 9 from teh sq. root
Yeah
that should most probably work
cos theta = x
sec theta = 1/x
that should give u a cubic polynomial
cos(40)=x , where x is a constant, right?
hmm, so 9-8x=a^2+b^2x^2+2abx
that looks nasty TBH
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,w 9-8x=a^2+b^2x^2+2abx
where did the cube come from
obv its gonna be a cubic
wait how did u not get a cube
sec theta gonna be 1/x broo
yeahh
,w 9-8x =(a+b/x)^2
OH MY WTH
lemme try comparing wait
but I most probably think that should solve it
we just need to solve the thing
I mean it would probably be easier to find cos(40)
cos(40)=cos(30+10)
cos(10)=cos(30/3)
,w cos(40deg)
,w cos(10deg)
what sorta aproximation is that
decimal
so now I have to solve
/sqrt{3}/2= 4cos^3(x)-3cos(x)
nah
that won't wokr
*work
u see the cubic
we know that a = 9
I mean 3
for a being 3
t^2 = 0
so b = 0
so |a+b|=3
Yessir
my book says the answer is 2
wait, let me check the offical answer key(This is from a past exam)
we can
compare
I used that even in seq and series complex num trigo etc
I mentioned seq and series and trigo as well
y oyo
yo
cos(3theta) where theta = 40
use that
it solved it
thought of that
but the cubic is ugly
very ugly
u want the justification?
$\ -\frac{\sqrt{3}}{2}=4x^3-3x$
cos ( 120 ) = - sin 30
Why am. I here
yeah, I know why, I'm just trying to figure out how to solve the cubuc
then use the formula
we know the value of sin 30
use the cos 3 theta
if u know that
cos(3tehta)=4cos^3(theta)-3cos(theta)
yeah, the cubic isn't solvable
dont change it
Bro I already solved it
Im trying not to give direct answer
4cos340 – 3cos 40 = -1/2 compare with 8x^3 + x^2(a^2-9) + 2axb + b^2 = 0
ah, ok, so $8x^3=4cos^3(40)$
Why am. I here
how did u do that-
2axb=0
right?
also,I'm not really sure you can just compare the expressions like this
I'm not convinced
lemme send u a pic
compare these and tell me
what u getting
try once again
cos^2 term is zer in the other equation
so a^2 - 9 = 0
justifies?
,rotate
yeah, pretty much, snowflake suggested comparing both sides
b^2 is the only constant so b^2 = 1
I;m thinking, just a him
that sort of makes sense
yes
so b=-1
b = +-1
a = +-3
got it, thanks!
and what was that other formula u mentioned
this was my way of solving it
it took ridiculous amount of tries tho
I have no idea what that is
that would require solving a bunch of simultaneous equations
is my method harder than that
?
then probably I might learn vietas as well
at first I thought it was cos x on both sides
It got me whole wrong
That was my fault
not reading the question properly
vitaes is basically the relation between the roots and the coefficent of a polynomial
That can be extended for an nth degree polynomial
we learned it in qudratic
yeah but we learnt it first in quadratic
its all about the roots
why do we discard b=1 though
theres only 1 term without cos theta in the whole equation
meaning only 1 constant term
and in the second equation as well theres only 1 constant term which is 1*
so b^2 = 1
I'll close this now?
Yeah
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thanksa again!
got it, thanks!
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Yoo
I need help
Determine the vertex and the direction of opening for cach quadrau
function. Then state the number of zeros.
2x² - 3x = x² + 7x
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No
@wintry copper Has your question been resolved?
use this formula for the vertex:
the number of zeros is equal to the highest power of x (im excluding complex zeros as an answer since i dont think you guys have done that yet)
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What do you need?
The answer
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can anyone help with this please
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Could someone explain how to do these problems properly/where I lost points?
second line seems wrong, how did you get +16u
I'll go through one with you
3x here is not a constant
over here
I think you didn't show du = dx and stuff
also you can't just drop "du"
in the first line
the rest is just formatting issues
you should use the bar when possible
@solar steeple
so when do i add the bar
when ur evaluating an integral across bounds given the anti derivative
so on every line?
only when you evaluate it
so here
o just there ok i see
mhm overall not too bad
just remember can't pull out stuff that's not constant
so here
wdym
where is "du" here @solar steeple
mhm
and i should put the bar on steps 4. and 5. here?
you don't need the bars on indefinite integrals
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for part b, would a normal vector to the y-axis be <1,0,0>?
so could I use that to write the equation of the plane
orthogonal to the y axis means, use a vector pointing in the y direction as your normal vector
<1,0,0> doesn't point in the y direction
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but don't I have to find a vector that is perpendicular to the y-axis
oh
is it because the point (1,0) is the y-axis
no, the plane itself should be perpendicular to the y axis
so the plane's normal vector is parallel to the y axis
a bit confusing admittedly haha
(and not even necessarily true if you go to greater than 3 dimensions)
I'm kind of confused
oh wait
I think I get it now
its asking orthogonal to the y-axis but the normal is parallel to it
thats such a weirdly worded question
so would a vector be <0,1,0>?
well the normal vector for the plane be <0,1,0>?
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I have a question for all of these problems do we check for absolute convergence first and if it’s divergent we check for conditional convergence?
In another words if it’s not abs convergent we check for conditional convergence
If it’s abs convergent we are done
yeah that's a way to do it
sometimes the problem will be easier, i.e the series can grossly diverge
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i think its a am i right
i would say yes, but B is also technically correct
hm
because B is saying
(sqrt of 1 * x + sqrt of 49)^2
which is just (x+7)^2
but, since we have a coefficient of 1 at A, taking the square root of a is not needed
option A would be the best one
yeah i guess
thanks
i have a couple more
im unsure about
i think this one is a too
is the function negative or positive?
I wouldn't say function, rather the "a" value in the vertex form: y = a(x-h)^2 +k
yea true
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This is a stats with calc.
I'm just asking if I set this question up correctly
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how would i do this? im not sure where to start
@karmic ridge Has your question been resolved?
is this a problem from a set that's attached to a topic or smth
there exists a fairly easy way to prove this so i'm assuming just use that topic as a reference idea (if it exists)
if not, then my honest recommendation is to just try what you know (imo there's not much to be said here without giving away the approach)
hint that's not really a hint but more like friendly advice: ||you don't want to do anything with trig or excessive pythag calculations; the solution is clean and accessible||
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can you help me solve this(i have no idea where to start)
You can use the fact that the ratio of the bases is the ratio of the areas, if the heights are equal
i am sorry but i am in grade 10 i dont know what that means
yes ?
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@remote mural Has your question been resolved?
, rcw
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So, I got stuck on this and it's been a little task that me and some others have been tasked with. I have no entire clue where to start and I got 1 more day to somehow complete it.
9^14^22^18^13^28^33^27^30^19^36^38^20^12^16^27^49^13^27^30^14^38^10^19^14^35^45^20^12^23^20^19^17^36^46^14^10^18^14^22^18^17^40^15^18^27^48^10^14^26^39^10^14^38^10^19^16^37^35^27^40^18^14^22^16^25^20^19^36^38^20^13^36^37^30^18^17^39^34^36^24^10^18^16^30^17^46^35^38^33^20^18^14^44^17^40^12^28^30^19^13^20^13^16^30^18^26^23^37^47^38^12^16^23^10^18^14^23^20^12^36^47^15^33^29^24^38^19^30^16^33^30^18^14^44^17^40^18^12^17^45^20^12^16^23^10^19^36^38^27^30^15^34^36^14^38^17^40^19^14^38^14^44^16^20^18^14^44^17^40^15^24^36^23^10^16^33^30^17^44^38^32^18^14^36^46^17^40^13^32^17^33^29^13^25^45^2
nah
Nope.
All I was given was.
"Hint: Exponents"
I'm either guessing it's just work it out one by one then power it by the next number or do that but backwards then power 9 by that number.
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lmao
You could go on using python and waste computing power but it's just a troll
So there's like no way to work it out?
Its too much computation for a human
1....
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Anyone who can help
@supple vector Has your question been resolved?
No, IT will never be resolved
@supple vector Has your question been resolved?
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shoot this is unclear sec
if (x-3.5)^ = 0 then the + or - shouldn't change after the root right?
here is the og here is the og problem
I factored f(x) and then i'm supposed to determine if it's + or - inbetween each of the roots, but it should be - + - + + and geogebra gives a negative numbers for f(x) when x is between 2 and 3.5
f(x)=2 x^(5)-5 x^(4)-31 x^(3)+92 x^(2)+4 x-112 and here is f(x) directly copied and pasted from geogebra
@green night Has your question been resolved?
hmm
ok I'll give it a shot
I don't have the premium to give it photos haha
wait maybe I can
.close
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hi
can someone tell me how to solve this
14
this is school math?
im stuggling bro my head is going crazy
brother just relax
and think for each info that the exercise gave u
lemme help you
so when we have km/h we cant multiply it with minutes
right
so 35 minutes = 7/12 hours
first thing you do at this kind of problems
so what can u do with that info
xD
im on 40th question
oh
ok
tag me so when i reopen discord i can find u easily
ok
doing it
So we know that Sanjit drove at 54 km/h from York to Leeds. Now, it took him 35 minutes to drive 42 km from Leeds to Skipton.
right
yes
so, your given kilometers per hour
yes
imma wait if u understand by Azar
so, what do you need to divide in order to get kilometers per hour (hint, its in the units)
kilometers per hour so it has to be the distance he traveled 35 kilometers divided by what?
remember, our D is 35 kilometers
35 minutes is it?
imma just do it
We already know the speed between York to Leeds, its 54 km/h
may you please tell me the answer pls
we need the speed from leeds to skipton
sorry, i made a mistake, he traveled 42 kilometers from leeds to skipton
so 42/time it took to go to skipton
ok
so you make it in to an hour
yes, convert it into a hour
that if a hour is a 100 minutes
no wait its not
but its not
he almost got it
good*
you can do that
total distance/total time
This is my solution
150? boy he must've gotten a few tickets
what is it arsi
i got the same
so wait whats the answer
my answer was 61,7km/h
Why, what should be the solution?
you can get the speed by averaging the speed from york to leeds and the speed from leeds to skipton
where do you have to enter the answer, maybe it is a decimal place
uh
48,78504672897196 try it
lol
or just 49
idk why thats the answer
maybe thats it or im wrong
@silk horizon
wrong
try 61,41km/h it´s an more precisely sulution, than before
i wrote 48.8
yay
correcto
can we please do 2 more
bruh
why the heck mine is wrong
also @hoary silo can you try working this out
send me the answer
im confused
there is the sulution, but with inaccuracies
hard ones 🙂
huh
sorry, I don't have any more time
oh
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prove that 1 + 1 is 2
prove it
i don't think it's possible, I think it's just taken for granted
no because it isn't
1 has an assigned value that when you add 1 and 1 together you get 2 idk man
but I'm curious what people who know more will say
Principia Mathematica
is a book
where two people took around 1000 pages to prove 1+1=2
hahahaha lol
based on euclids postulates
aint that some shit
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$a - \frac{a^{\frac{1}{3}}{\frac{1}{3}\cdot a^{\frac{-2}{3}}}}$
so i set a = -2, and my ti nspire calculator spit out 4 - 1.700893e^-13 *i. what does this mean
Aurora
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bruh
whats the q
too lazy to debug latex
use newton's method to estimate the roots of the cube root of x, with an initial estimation of 1
which brings the question wtf
why the -1.700 e^-13 i
Probably rounding error
how did the rounding error produce i tho
Google how your calculator model works
This is a math server not a calculator software server
cuz i only see a third root which doesnt cause i
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Good on you for realising
.close
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Doubles every four hours how can I convert that so the equation can commence?
I think o have to use geometric sequence or series
divide the power by 4
Divide n by four?
It’s the formula
For geomtric
For geometric sequence
I think that’s what I’m supposed to use
It’s $an=a1(r)^n-1$
micock
n-1 is the exponent but yeah
Our unit formulas didn’t have that
I think we are supposed to utilize the geometric and arithmetic sequence formulas
so y = (3,000,000) * 2^(n/4) where n is in hours
is it because its in a series like:an = a11(r)^((n-1)/4)
Or series formulas if it’s asking for the sum
Idk if it’s in a series or sequence