And the second is maybe A
#help-0
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fluid ridge
So the main thing that sets these 3 options apart in the first question is this:
Experiments compare and contrast a control group with a study group. Observational studies use data gained strictly from observing the subjects, as opposed to asking them any questions. Whereas a sample study, if you look up online is just about, verbatim, a survey which may be conducted as a questionnaire of sorts, in person or over the phone.
For the second question A will never be the right answer. We need a statement that's verifiable. In theory they don't tell us how many people actually agreed, if only like 3 people agreed then the answer will probably be D, but if we assume a reasonable portion of the population agreed then it should represent a decent sample statistic, which would make the answer C.
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median oar
Hello
median oar
If I start here
What tells me I can slice the integrals into 3 parts like this?
Is that just a property of integrals? I’m separating the integrand into 2 terms that have countably many parts so idk if that makes things back
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fair vigil
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fair vigil
I drew the graph till 10, after it its just a straight line till 120
Is C the correct answer?
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sour yew
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sour yew
this solution does not put i next to 2?
warm copper
Since it's a cube root, signs will survive. If it were an even root like the square root, that might be a concern.
warm copper
Not always.
Consider that $\sqrt[3]{-54x^3} = \sqrt[3]{{\color{cyan}-27}(2){\color{green}x^3}}$. The ${\color{green}x^3}$ can come come out as ${\color{green}x}$ without trouble - cube roots and cubes reduce, right? Well, what about ${\color{cyan}-27}#?
ocean sealBOT
Shenzao
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warm copper
$27 = 3(3)(3) = 3^3$, so how could we get $-27$?
ocean sealBOT
Shenzao
sour yew
warm copper
Exactly, $-3(-3)(-3)=(-3)^3 = {\color{cyan}-27}$.
ocean sealBOT
Shenzao
warm copper
So we can take out the -3.
If we take out the x and take out the -3, we still have the 2 inside, so we end up with $-3x\sqrt[3]{2}$.
Does that make sense?
sour yew
yes
ocean sealBOT
Shenzao
sour yew
thank you
tall topaz
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lone heartBOT
keen plinth
tall topaz
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crimson crag
yo
crimson crag
what does it mean for something to be proportional
celest stump
it means its in multiple of that thing
say you have a square with dimensions of 1
a square with dimensions of 2 would be in proportion because its 2 times its area
crimson crag
wouldn't it be 4 times its area
celest stump
yes
crimson crag
celest stump
a segmented line can be
celest stump
yes but you're dealing with lines that are infinitely as large
i mean theoreticially by the definition i provided then it would be proportional
the length of the x axis is infinity
the length of the line is infinity
anything times infinity is still infinity
crimson crag
it is a segmented line
celest stump
that means it starts at a point and ends at another point?
crimson crag
celest stump
because each segment has the same slope
crimson crag
what is a segment
celest stump
so its just a streched/compressed version of each line
crimson crag
but this line has the same slope everywhere
so why is this not considered proportional
celest stump
crimson crag
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topaz phoenix
claim
topaz phoenix
someone help pls i gotta go to school in acouple minutes and this is last question
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robust geode
This is way too late
lilac thicket
I would just need some quick reassurance on how to do an induction proof on a tree or if I am wrong some correction.
So I wanna proof something for a tree regarding its relation to a certain matrix.
My induction goes over the number of vertices in the Tree.
Now my confusion is , is it correct that in the step I'd have to do something like
"let T be a tree on n vertices. T has a leaf l . Lets look at T' = T-l. Ok hypothesis tells us statement is true and then adding l back causes x to happen with the matrix. And then were done"
So we would add l back right were we deleted it or does it necessarily have to be an arbitrary vertex in T' that we add l to?
Someone told me we cant tell where we add l back. But in my mind that seems to be not true since we already made no assumption about T other then T has n vertices.
lilac thicket
because if we couldnt say we add l back right to the place we deleted it from, then I would say - why not immeaditely start with T' and construct a tree T := T'+ v. But thats not how I was taught induction on trees works
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willow marsh
!help
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willow marsh
i got be as
17m?
can someone tell me if thats correct
or not
i cant see asnwer
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vapid steppe
Let $R$ be the region bounded by the curves of $f(x)=\ln(x^2+1)$ and $g(x)=\cos x$.
ocean sealBOT
Jash
vapid steppe
The base of a solid is in the region R. Each cross section of the solid perpendicular to the x-axis is a rectangle with a base on the region and a height of 2x. Write an expression involving one or more integrals that gives the volume of the solid.
(calculater question btw)
is it just $\int_A^B (\cos x-\ln(x^2+1))2xdx$
ocean sealBOT
Jash
vapid steppe
where A and B are the x coordinates of the intersections
jagged timber
lone heartBOT
jagged timber
how should I paramaterize this region in terms of polar coordinates
my goal is integrating it over the function xy which is = (r^2sinthetacostheta)
it would be easy if it was bounded by the x axis
or should I use rectangular coordinates
ionic jewel
or should I use rectangular coordinates
can do either
is it not just r = 6, theta from 0 to pi/2
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jagged timber
is it not just r = 6, theta from 0 to pi/2
that would be a circle of radius 6 in quadrant 1
much larger
ionic jewel
that would be a circle of radius 6 in quadrant 1
this appears to be the same thing you have?
oh yours isnt a circle
wow im baited by the arc
robust geode
Yeah the radius is 3
ionic jewel
no his is an ellipse
robust geode
What no ?
jagged timber
robust geode
Move the graph at the axis intersection, maybe it will help
Since translations don't shift angles and length
robust geode
Why 3D ??
robust geode
Alright so "integrating over xy" means "integrating over x and y" ?
robust geode
Okay
ionic jewel
to be clear, you could do polar here if you really wanted though
robust geode
So f(x,y)=xy is your function you integrate, and the region R is the disk of radius 3 centered at (0;3) in the 0xy plane, right ?
jagged timber
to be clear, you *could* do polar here if you really wanted though
what bounds
for polar
oh
I could
do a polar for r = 6
then subtract
maybe
no I cannot
nvm
robust geode
do a polar for r = 6
The circle would have a wider circonference
jagged timber
yeah
robust geode
Let's just maybe start with the inequality related to this region ?
And then implement the parameter in the equation
I guess your values in y are shifted by 3
So instead of having (x,y)=(3cos(t),3sin(t))
You would have (x,y)=(3cos(t),3(sin(t)+1))
If I'm not mistaken
jagged timber
parametric equation
robust geode
Yeah but what parameters, aren't they the radius 0<r<3 and the angle 0<t<pi/2 ?
ripe ruin
Labelling the triangles
naive valley
lone heartBOT
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prisma wave
When entering this into my calculator I get -0.07, but that doesn't sound right
prisma wave
Anyone know what I'm doing wrong?
ocean whale
,w sind(tand(acosd(-0.23)))
ocean sealBOT
ocean whale
When entering this into my calculator I get -0.07, but that doesn't sound right
It's -0.07
barren bolt
The real question is what’s the point of this question if you have a calculator
I also got -0.07 on my calculator
fierce prairie
how come it doesn’t sound right lol
prisma wave
The real question is what’s the point of this question if you have a calculator
Very good question
prisma wave
It's -0.07
I entered it in chatgpt and it gave me like 200 degrees
barren bolt
Don’t use ChatGPT for math
It’s a writing tool
And it’s very good at confidently lying to you
lone heartBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
barren bolt
There was a case where a lawyer used ChatGPT in a real court case and chatGPT MADE UP case law that he trusted without looking into and got huge fines
fierce prairie
And it’s very good at confidently lying to you
and lying to itself lol
barren bolt
Its not an all purpose AI it’s an engine that is good at predicting the next word that will make its speech sound human
Frankly I don’t get why people so often use it as a reference it truly doesn’t seem better at that than google
For writing it seems great
But for research it’s a bad idea
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prisma wave
Oh ok thanks for the help
alpine sable
lone heartBOT
alpine sable
ok so i put this into the form of b^2 - 4ac < 0
cuz it has no solution
then i get
p^2 > 4/9
fallen verge
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
fallen verge
ah
alpine sable
so
but how can u show it in the set of possible values?
as p itself
?
do u draw a graph?
fallen verge
you can
alpine sable
so -2/3<p<2/3?
fallen verge
another way to do it is to do
p^2 - 4/9 > 0 and factor
fallen verge
so -2/3<p<2/3?
not quite, the inequality symbols are the wrong way around
alpine sable
another way to do it is to do
p^2 - 4/9 > 0 and factor
wait can u explain that?
alpine sable
not quite, the inequality symbols are the wrong way around
how do i acc do the inequality symbols
how do i know which way ?
fallen verge
how did you get the inequality in the first place so i can explain that first
fallen verge
so -2/3<p<2/3?
this one
fallen verge
where did p<0 come from?
fallen verge
ok im not sure what youre saying so let me just explain the algebraic version first
you got to the point p^2 > 4/9, which is correct
then we get
p^2 - 4/9 > 0
hwo can we factor this?
alpine sable
hwo can we factor this?
oh (p - 2/3)(p + 2/3)
alpine sable
is that the only way to find the inequality sign?
fallen verge
we will do the graph version in a sec
alpine sable
we have
(p - 2/3)(p+ 2/3) > 0
ok i understand this bit
u just plot it on the graph and since the graph is >0
we know that it will be seperated
fallen verge
slow donw
fallen verge
ok yeah that works
but if you were to do it fully algebraically, you can think about if each bracket is positive or negative
alpine sable
but if you were to do it fully algebraically, you can think about if each bracke...
like p in the bracket?
fallen verge
lemme use an example: if you have p = 1, you have
(1 - 2/3)(1 + 2/3)
positive*positive=positive
so we know p=1 works
the only time a sign will change in one of the brackets is when p is on another side of a root
fallen verge
are you familiar with the idea of a sign chart?
fallen verge
looks like this
alpine sable
YHH I DO
fallen verge
youre welcome
fallen verge
if you want the graphical version, you have to draw out p^2
alpine sable
got it!
brisk parrot
Hi can someone help me with 5
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fickle cipher
This is the encryption algorithm for RSA, can you find P given that you know e, n, and C?
ionic jewel
This is the encryption algorithm for RSA, can you find P given that you know e, ...
well the entire point of RSA is that you can't decode the message without the decryption key
"cant"
fickle cipher
well the entire point of RSA is that you can't decode the message without the de...
u cant solve this algebraically? P is the original text and C is the ciphertext
ionic jewel
... if you could, then the RSA encryption wouldn't work
the (unproved) idea is that there is not way to solve this besides brute force (which the number are too large to be feasable)
I don't want to explain the number theory, but the RSA algorithm is very well studied and well known, so you can find resources easily
sour verge
The only values that could help you compute d (and thus decrypt the message) would be the original prime factors you chose such that p*q = n. This is why the problem is hard in general (and why the algorithm works for encryption), because such a decomposition is unfeasible for large primes.
fickle cipher
... if you could, then the RSA encryption wouldn't work
is there a reason why? i wont ask you for an explaination if its too long but could you point me to any resources
fickle cipher
The only values that could help you compute d (and thus decrypt the message) wou...
im mainly wondering why u cant just work backwards from the original encryption algorithm which i uploaded
ionic jewel
the easiest answer is "why don't you try?"
perhaps itll be easier to convince yourself of it
sour verge
Because you throwaway the primes once you're done.
There is no working backwards possible unless you have them.
ionic jewel
There is no working backwards possible unless you have them.
probably*
sour verge
Yeah probably and for now.
ionic jewel
its unproven that breaking the RSA algorithm requires factoring
fickle cipher
the easiest answer is "why don't you try?"
is there like a name for the specific problem? chatgpt said its similar to the discrete logarithm problem but idk
ionic jewel
yeah the problem is "its really hard to factor large numbers"
maybe called the RSA Problem
ionic jewel
is there like a name for the specific problem? chatgpt said its similar to the d...
discrete log problem leads to a different cryptosystem
ElGamal is the one I know
sour verge
DH key exchange as well!
sour verge
Thanks for pointing that out btw, I didn't know that. Turns out the equivalent bit is just about finding the private key, which in itself may be harder than finding the plaintext to begin with.
Meant to reply to the earlier message about the prime factorization problem oh well
fickle cipher
yeah the problem is "its really hard to factor large numbers"
im sorry im really new to RSA and modular arithmetic but given these randomly assigned numbers cant u find a way to solve for P:
ionic jewel
these are weak numbers, so I suppose you could do it for these
wait whats the second line doing?
there are no solutions to the first line, and 4 solutions to the next one
ionic jewel
no solutions
the n is very easy to factor, (and the encryption exponent is low) so this one is solvable
fickle cipher
the n is very easy to factor, (and the encryption exponent is low) so this one i...
could u please explain how u would usually solve problems like these, maybe it well help me understand how the difficulty will increase as the numbers get higher
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tidal shell
<@&286206848099549185>
Per ChatGPT: The problem doesn't make sense because the remainder (100) is larger than the modulus (80), which contradicts the definition of modular arithmetic where the remainder must be smaller than the modulus. Additionally, in the context of RSA, the modulus is typically the product of two large primes, not a small number like 80.
fickle cipher
Per ChatGPT: The problem doesn't make sense because the remainder (100) is large...
can u come to help 2 pls
ocean hawk
Per ChatGPT: The problem doesn't make sense because the remainder (100) is large...
if you don't have a question, please close the channel
tidal shell
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craggy briar
How do I do this problem?
craggy briar
<@&286206848099549185>
ivory carbon
Do you do calculus, or is this meant to be non-calculus?
craggy briar
Do you do calculus, or is this meant to be non-calculus?
calculus
sorry forgot to specify
This is the work I have rn
Update: got a few numbers but they dont seem to be right
^updated work
<@&286206848099549185>
ivory carbon
you have to make the volume equation as a function of width and height, then subtitute in the are function as a function of cents. Then find the absolute minima by setting f(w, h) = 0 and solving for w, h
young bramble
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young bramble
Hey, this is the question and my working so far
I've skipped a couple lessons and don't have the catch-up resources so I'm trying to figure this out, would appreciate it if someone could just let me know if I'm doing this the right way
Thanks!
storm ridge
,rotate
ocean sealBOT
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young bramble
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young bramble
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young bramble
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young bramble
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young bramble
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young bramble
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dire tiger
trim pasture
How to solve this?
lone heartBOT
How to solve this?
trim pasture
This is the answer
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scarlet drum
The angle bisectors of A and B in triangle ABC form an angle of 150. Point K is diametrically opposite to A on the circle circumscribing triangle ABC, and is D the projection of B onto A.
a) Calculate the size of angle C of ABC.
b). Calculate the value of the AD/AK ratio.
scarlet drum
Can't get the drawing right.
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scarlet drum
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scarlet drum
what
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west girder
This is just angle chase, nothing special is required
lone heartBOT
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sour yew
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sour yew
how to solve for C
lone heartBOT
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tacit arch
how to solve for C
The question is cut off
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versed knoll
I have $Y = aX + bZ$, where $Y$, $X$ and $Z$ are random variables and $a$ and $b$ are constants.
I know what $a$ and $b$ are, and I know each random variable's variance.
versed knoll
I'm trying to find the covariance between $Y$ and $X$, assuming that $X$ and $Z$ are uncorrelated.
Is it as simple as simply knowing that if $Y = \beta X$ and $\beta = \frac{Cov(Y,X)}{Var(X)}$, then in my formula, $a = \frac{Cov(Y,X)}{Var(X)}$ ?
Because if I know what $Var(X)$ is, then, I can figure out that $Cov(Y,X) = a Var(X)$?
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odd sundial
How could u start on this question
lone heartBOT
How could u start on this question
fervent timber
it’s like a sudoku ig
use process of elimination and start filling the boxes
assume that you can’t have any 3 boxes that spell “B E E”
lone heartBOT
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odd sundial
@fervent timber but it seems like it’s near impossible as bee can be spelled out even with diagonal
prime badge
i agree, it really doesn't want to be solved
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alpine sable
x=a[cos t+log tan t/2] , y=asint
lone heartBOT
x=a[cos t+log tan t/2] , y=asint
pseudo ice
You’re supposed to wait 15mins before pinging helpers 
alpine sable
idk lol
pseudo ice
whats dy/dx?
Anyways, do you know the way to find it for parametric equations?
alpine sable
yee
pseudo ice
Yep, what would you do to find it? 
alpine sable
like u shud denote a varible as t
it depnds if its curve,parabola or etc...
eg if slope of tangent is 1/t
the paramatric eqn is = x=at2;y=2at
u there?
pseudo ice
Erm, well, there is a variable t in there
As in can you find dy/dx in terms of t? (Hint: chain rule ⛓️)
alpine sable
i got tan t as the answer
i got the answer but am not sure its correct
coz i dont belive in me lol
tidal shell
Still need help? @alpine sable
tacit arch
i got tan t as the answer
Show your work
alpine sable
like am using laptop
my phone is on charge
its simple nah i derived wrt t
and i converted tan as sin/cos
sec2 as 1/cos2
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tough dawn
For this problem I need to find the first 5 terms of the geometric sequence
tough dawn
I know the first one but how do I find the ratio so I can get to a_5?
foggy pecan
$r=\frac{a_{n}}{a_{n-1}}$
ocean sealBOT
Joanna Angel
tough dawn
Oh ok
tough dawn
$r=\frac{a_{n}}{a_{n-1}}$
So a_2 would be a_2/7?
foggy pecan
So a_2 would be a_2/7?
a_2 = 0.2 * a_1
upbeat wraith
lone heartBOT
upbeat wraith
How do I solve this?
I find the two derivatives, but I think I am supposed to multiply one by -1 and add the two derivatives?
But I always get the wrong answer somehow
foggy pecan
$\text{You have to solve the system of equations:}\\f_{x}\left( x,y \right)=0\f_{y}\left( x,y \right)=0$
ocean sealBOT
Joanna Angel
upbeat wraith
Wait.
Here is the example problem.
How do they get 6y-8y+30? I don't understand
foggy pecan
they used subtraction: the first minus the second equation, because it suited them in this case, but it is not a rule
they have noticed that
6x = 6x disappears
and they get only y
but in other similar situaiotn mayeb you will need to use diffeertn oepraiton
do you udnerstand ?
upbeat wraith
oh okay I understand
foggy pecan
🙂
upbeat wraith
But why 6y-8y and not 6y+8y?
foggy pecan
becasue they substracted all second equations means
-(6x + 8y) = -6x - 8y
btw:
do you know how to solve systems of equations?
your case is a very simple here, since there are two linear equations, you can solve them as you were doing ti at school
but often, if it comes to extremeum of function fo two variables
you can recieve systte with algebraic euqations
more complicated
all depends on partia derivatives
upbeat wraith
Okay so my two derrivatives are
10x+6y+32
6x+10y
foggy pecan
so you must write system:
10x + 6y +32 = 0
and
6x + 10y = 0
do it
and next
you should observe = njotice
that you can divide first equaiton by 2 and also secodn eq by two
upbeat wraith
right so I would get x=-5, and y=3
upbeat wraith
Ok I was just confused on what the example was saying where they combined the derrivatives,
Thank you for the help!
foggy pecan
yvw 🙂
sacred perch
lone heartBOT
sacred perch
Here they say find the real roots but what does it means?
do i just factor like a usual quadratic equation?
like 129 would be (x-3)*(x+4)
lament forge
well factoring is a good idea, but the actual answer they want is the roots
so for 129 the answer is x = 3 or x = -4
because those are the values that you can put in that make the equation true
3^2 + 3 - 12 is 0, 4^2 + 4 - 12 is 0
sacred perch
oh so like i factor like i did and then find the values of x that will lead to it being 0?
limpid turret
like 129 would be (x-3)*(x+4)
Yeah it basically means that.
The term real may be confusing in this context, because all roots in the problems will be real (I think). If they're not real, you will not be able to find them through factoring.
lament forge
a "root" is basically just a value that makes something zero
in this case it's the value of x that makes x^2 + x - 12 (or whatever) zero
it doesn't really have much to do with "square root"
hot trail
lone heartBOT
lone heartBOT
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upbeat wraith
How do I solve this?
lament wyvern
you...put the values of x and y in to f(x, y)?
and then solve it
f(4, -5) is solve sqrt(5y^2 + x^2) for x=4, y=-5
lament wyvern
yep
upbeat wraith
ok I don't know why I just had a brain fart I knew that
mental coral
lone heartBOT
mental coral
Tried doing secant secant theorem, hit a dead end after that, not sure where to go
maybe form a parallelogram with additional point above C but unsure
already known that point between A and B is similar to point between B and C and point between A and C splits AC evenly (i think)
not sure about how to get the diameter from that however
<@&286206848099549185>
west girder
maybe form a parallelogram with additional point above C but unsure
Close, consider the midpoint of AP, the midpoint of BC, P, and the circumcenter
vagrant falcon
lone heartBOT
vagrant falcon
am i missing something with exponents
cuz i thought for the first one you can multiply 1 by 2
and get e^2
but e^1^2 is not equal to e^2
but when I do e^2^2
and multiply 2*2 to get 4
e^4 does equal e^2^2
why is that?
humble ferry
1^2=1
coral thorn
1^2 is not equal to 2
vagrant falcon
oh
coral thorn
it’s just 1*1
vagrant falcon
i thought you would multiply the exponents
high rapids
2^2=4
humble ferry
x^2=x*x
coral thorn
(e^1)^2 = e^2
coral thorn
because then you have 1*2 according to laws of indices
humble ferry
Yes, BODMAS
coral thorn
vernal plover
Help
cinder temple
duh
junior vigil
what are you trying to do
junior vigil
well, just choose from a list of x-values to plug in. (be careful of domain restrictions)
i.e. if it's in a square root, then you want everything inside the square root to be positive
lone heartBOT
@vernal plover Has your question been resolved?
vernal plover
Yes
spare fern
Could someone help me out with this?
lone heartBOT
Could someone help me out with this?
spare fern
haughty sun
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
nimble fern
since csc(x) = 1/sin(x)
you may consider divide both numerator and denominator by sin(x)
alpine sable
Help, I don't know how to add and subtract a fraction using the least common multiple, tomorrow is my final exam and it's about that😭
gray isle
can you give a specfic example
alpine sable
two integers three quarters plus two integers five twelfths
gray isle
$2\frac34 + 2\frac{5}{12}$
ocean sealBOT
ℝαμΩℕωⅤ
gray isle
that?
alpine sable
im doing this with the translator
that's it, but instead of getting an equivalence, you have to get the least common multiple
and I don't know how to do it
alpine sable
oh thanks
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
yes
neon sun
lone heartBOT
tribal rose
is 0 odd or even
neon sun
n is larger than or equal to 1 btw
jagged cobalt
so, youve said that
$$T_1 +T_1 rT_1 r^2+...+T_1 r^{k-1}+T_1 r^k = \frac{T_1 (1-r^k)}{1-r}+T_1 r^k$$
$$\frac{T_1 (1-r^k)}{1-r}+\frac{(T_1 r^k)(1-r)}{1-r}$$
ocean sealBOT
AℤØ
jagged cobalt
by your inductive hypothesis
jagged cobalt
hm?
neon sun
i dont think its right
neon sun
i asked ai to solve it and they said it was wrong
jagged cobalt
dont use ai, theyre usually very off
neon sun
and also i dont know how to solve it at that point even if its right
jagged cobalt
**AℤØ**
from here just add them really
the numerator becomes:
$$T_1 (1-r^k)+T1(r^k-r^{k+1})$$
ocean sealBOT
AℤØ
jagged cobalt
well, youve proven that on the assumption its true for n=k, then its true for n=k+1
so youre done really
neon sun
i times everything by (1-r) ?
jagged cobalt
just need to write a statement
jagged cobalt
i times everything by (1-r) ?
nono
jagged cobalt
youre left with T1(1-r^(k+1)) /(1-r)
youre finished the moment you get this
just have to say its proven by induction
jagged cobalt
yeah thats just the numerator
jagged cobalt
**AℤØ**
the denominator 1-r is still under all this
$$\frac{T_1 (1-r^k)+T1(r^k-r^{k+1})}{1-r}$$
ocean sealBOT
AℤØ
jagged cobalt
once you simplified it to the required format you were done
jagged cobalt
you showed true for n=1
then assumed true for n=k
for n=k+1 you wanted to show you can get it into the form on the rhs of the equation at top
which you did by having:
$$\frac{T_1(1-r^{k+1})}{1-r}$$
ocean sealBOT
AℤØ
jagged cobalt
This second line you wrote is what you were showing
you were just showing the left could be written as the right under your assumption
jagged cobalt
well you couldnt write it directly like you did
jagged cobalt
**AℤØ**
this top line would be what youd write initially
then the second
then our simplifying into the required form
jagged cobalt
how what?
neon sun
my lhs still looks nothing like the rhs
neon sun
oh
jagged cobalt
youre showing the left can be written as the right
since thats what it wants you to prove
neon sun
yep
neon sun
youre showing the left can be written as the right
how do i do that though
jagged cobalt
by induction, you did the base case 1,
you then assumed it was true for n=k (top line)
jagged cobalt
**AℤØ**
then we did this
which was n=k+1, on the previous assumption
thats the whole process
jagged cobalt
which second line are you referring to
might be easier if i write this out for you more clearly
gimme a few minutes
lone heartBOT
@neon sun Has your question been resolved?
neon sun
thank you so much
lone heartBOT
@neon sun Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
hexed sonnet
How do I set this line integral up?
lone heartBOT
How do I set this line integral up?
hexed sonnet
I did this and got -32 but it's supposed to be +32
hushed locust
your parametrization for the curve seems to be incorrect
in any case if you need to find a path-independent line integral it's often simpler to set up a potential function
lone heartBOT
@hexed sonnet Has your question been resolved?
hexed sonnet
your parametrization for the curve seems to be incorrect
hmm im not sure why it's incorrect
I did x = 2-3t
y=-2-2t
and then dx/dt = -3 and dy/dt=-2
hushed locust
if you plug in your start and end-points for t, then you should get your start and end points
hexed sonnet
then i plugged that into the given equation
hushed locust
if you plug in your start and end-points for t, then you should get your start a...
try doing that and see what points you end up with
hexed sonnet
oh wait i see
hexed sonnet
in any case if you need to find a path-independent line integral it's often simp...
ah ok i see what i did wrong
thank you!
.close
lone heartBOT
lone heartBOT
Available help channel!
livid cedar
how do i compute the divergence in spherical coordinates, do i compute the derivatives first and then multiply it by the constants? or does it not matter because it is very confusing
lone heartBOT
how do i compute the divergence in spherical coordinates, do i compute the deriv...
@livid cedar Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wild coral
lone heartBOT
wild coral
i know you can use triangle inequality to solve for the lower limit
the upper limit is 29+56
but i dont understand why the vector can equal 85
also dont completely understand this one either
<@&286206848099549185>
lone heartBOT
@wild coral Has your question been resolved?
split mantle
but i dont understand why the vector can equal 85
Vectors are like lines, or rope. Doing A + B = 56 tells you what value b is restricted in.
split mantle
I'm not certain, but you need to define a positive direction, where as a velocity vector has the opposite direction, giving it the negative sign.
true geyser
why are we able to say h = 3
lone heartBOT
why are we able to say h = 3
true geyser
Like I understand that we just sort of plug in the answer to what (f'2) is into the limit definition of the derivative to get the secant line
but why and how does that h equal to f'(2)
tranquil charm
@wild coral B) is correct. the upper limit it 85 and lower limit is 27
cerulean karma
I can't seem to get this question right, it simply just hurts my brain to think about but I previously got 31.121 minutes as the answer, which was incorrect.
cerulean karma
If I remember I had previously gotten a ratio of 1/2
golden canyon
That checks out with your previous answer, yeah. How did you get 1/2?
*approximately
cerulean karma
I'm thinking that the rockets (red triangles) are two separate vectors. In the rocket going to B, we can see that if we add the vectors together the combined magnitude should be 2M. I'm not sure why I thought the combination of the two rockets towards A would be M/2 though.
golden canyon
Do you see how you get a right triangle if you add up the two rockets as vectors when going to A?
cerulean karma
Yes
golden canyon
So what would the total magnitude be? (in terms of M)
golden canyon
This would be a simplified diagram right?
cerulean karma
2/sqrt(2)?
golden canyon
*sorry, thought you meant sqrt(2)M
cerulean karma
Wait but isn't the outbound B rocket magnitude 2M?
And if inbound A rocket magnitude is sqrt(2)m, would the ratio be 2/sqrt(2)
cerulean karma
Oh yeah I see
golden canyon
Now try calculating the time again, I think the last part of your pevious method was correct, but the 1/2 wasn't
cerulean karma
I'm getting 22 but that shouldn't be right
golden canyon
I assume you are using this equation? $$\frac{1}{2}a_{1}t_{1}^{2}=\frac{1}{2}a_{2}t_{2}^{2}$$
ocean sealBOT
Jelle
cerulean karma
My teacher provided similarily 1/2at^2
golden canyon
Yeah, that's the distance and it holds for both spaceships so you can equate them
distance from A to B is the distance from B to A
golden canyon
Yes
cerulean karma
and then I would solve for t_2 ^ 2
golden canyon
yup
cerulean karma
So in this case would t_2 be 26.163 (rounded third dec up)
golden canyon
that's what I got as well
cerulean karma
Not really sure where to go here, me and my gf both worked on this and we previously chose option 3 as the answer but apparently that was entirely incorrect.
cerulean karma
Was using this image as a reference point to maybe figure out what each component would stand for
median dirge
You could just use dimensional analysis
Or basically check the units
Do you know wha dimensional analysis is
cerulean karma
Nope, this is a physics prep course at my university
Alg based is my weakest spot compared to calc based
median dirge
Oh well this is definitely physics
Okay one way to think of it is
Since you're getting acceleration in the LHS
You should also get acceleration on the RHS
You do this by checking the units on each side
The units of acceleration are m/s^2
So look on the right hand side and see what units do the terms give.
Also, remember that only quantities (terms) with same units can be added
vapid shuttle
don't try to close other peoples channels
median dirge
Lol.
alpine sable
dude its my channel
median dirge
What was that @alpine sable
alpine sable
this pple stole it from mee
vapid shuttle
dude its my channel
No one stole it from you, your question expired due to inactivity. If you have a question you must now open a new channel
alpine sable
dude just mind ur buisness nah
vapid shuttle
this one is being used by someone else
median dirge
We aren't. Just create a new channel and someone will help
alpine sable
thank you for the guide
cerulean karma
Anyways, what I try to think is that v=(x-x_0)/t which means that a=(v-v_0)/t but that isn't really shown
pale kestrel
Dimension analysis isnt a very deep concept to learn. Its about "matching units"
id recommend looking it up
id suspect khan academy would have it
but try any other resource if not, shouldnt be a long read
fair heath
How many four-digit numbers are positive integers that have the digit 1 but no digit greater than 2?
mortal trellis
so basically, including leading zeros, you can use the digits 0,1,2
lone heartBOT
@fair heath Has your question been resolved?
paper bough
(a*b)-(a^2-b^2)=900
a,b are greater than or equal to 1000
and less than 10000
means they are 4 digit numbers
find a,b...
paper bough
can someone tell me what do I do to solve it..
i simplified it but still..
paper bough
you need to find a and b respectively?
yeah
languid bolt
are you sure that's the whole question?
paper bough
are you sure that's the whole question?
yeah.. with an example
languid bolt
ab - (a^2 - b^2) right?
paper bough
ab - (a^2 - b^2) right?
yea
languid bolt
which becomes
ab - a^2 + b^2
paper bough
ooh
i forgot about this
so
-a^2 + ab + b^2 = 900
still how to solve :/
because its confusing when asking for solution with 4 digits
languid bolt
ngl, idk, wait for someone else
paper bough
ok..
zealous ingot
(a*b)-(a^2-b^2)=900
a,b are greater than or equal to 1000
and less than 10000
me...
are you taking a number theory class?
paper bough
are you taking a number theory class?
I remember its name, But forgot it. Anyways, this is my cousin question.. I dont think he know it
I tried my best but yeah I couldnt..
First college year cant solve this 💀
zealous ingot
i mean see if its just a high school question, then one can just use a calculator or plot a graph or smn
zealous ingot
First college year cant solve this 💀
haha its not particularly easy to establish a universal method to solve equations of the form Ax^2+Bxy+Cy^2 = D
paper bough
i mean see if its just a high school question, then one can just use a calculato...
90% its
But the question is asking for x, y then write it in [b+(10000*a)] form
paper bough
haha its not particularly easy to establish a universal method to solve equation...
:/ true
chrome tiger
because its confusing when asking for solution with 4 digits
Exactly, finding all real (a, b) is one thing, finding all integer (a, b) is another thing
paper bough
i mean see if its just a high school question, then one can just use a calculato...
How :/
I mean there is no calc with find x, y with a range [1000,10000)
paper bough
Exactly, finding all real (a, b) is one thing, finding all integer (a, b) is ano...
Oh
Im not really sure
Probably all integers
paper bough
Yep.. That's possible to be
Let me write the full q
The total value of a pair of numbers (a, b) is said to be the product of the two numbers from the difference of their squares. For example, the total value of the pair (4,7) is 5, because
(4x7)-(4²-7²)=5
Find any pair of numbers with a total value of 900, so that the number of digits of each number is 4, and if you find the pair, write the answer in the form
B+(10000 x a)
This is the question as sent to me
There is a possibility that (a) is a decimal
lone heartBOT
@paper bough Has your question been resolved?
lone heartBOT
@paper bough Has your question been resolved?
paper bough
No one..
Anyone
HELP PLEASE
chrome tiger
The total value of a pair of numbers (a, b) is said to be the product of the two...
Ok so if I understood this correctly they want integers
ocean sealBOT
EQUENOS
chrome tiger
If we want y to be an integer, x must be an even integer and 900 + 5k^2 should be a full square
balmy grail
This feels like a project Euler question, so that’s how I solved it. I wrote a python script to check every pair’s total value. It took 22 seconds to find an integer solution between [1000,9999] for both a and b.
balmy grail
If we want y to be an integer, x must be an even integer and 900 + 5k^2 should b...
But this is the more theoretical solution
paper bough
If we want y to be an integer, x must be an even integer and 900 + 5k^2 should b...
By 5k you mean 5000
chrome tiger
I mean 5 times an integer number k
paper bough
Oh
chrome tiger
**EQUENOS**
Substitute x = 2k here
paper bough
My brain stopped working 