Moosey
#help-19
clever fjordBOT
sullen ferry
$du=\f{\sqrt{u^{2}-16}}{u}dx$
clever fjordBOT
Moosey
sullen ferry
$\frac{u}{\sqrt{u^{2}-16}}du=dx$
clever fjordBOT
Moosey
odd edgeBOT
@old whale Has your question been resolved?
odd edgeBOT
shy smelt
What have you tried so far?
wooden python
!status @blazing barn
odd edgeBOT
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
blazing barn
wooden python
ok
blazing barn
sorry i forgot i put this in im all good
wooden python
do you have anything else to ask?
soft ridge
how do i make a help channel
odd edgeBOT
how do i make a help channel
soft ridge
how do I solve 50cos^2(x) = 25 + 16x^2
wooden python
you just did
soft ridge
oh
wooden python
making a help channel just means posting a message in it
and usually you're supposed to have your first message contain your question
(but DON'T delete your first now. if you do it'll autoclose)
anyway...
$50 \cos^2(x) = 25 + 16x^2$ ?
clever fjordBOT
Ann
soft ridge
so what do I do now
worthy moat
Plug that in a calculator?
soft ridge
but how do I solve it on paper
worthy moat
Use netwon's method
soft ridge
i have no clue what that is
lavish kite
i asked wolframalpha and it just produced numbers, and the extremely unhelpful exact form of "the root of 16x^2 - 50cos^2(x) + 25 near [number]", so probably there isn't a reasonable way to find an exact solution
so basically what you would do is just try various numbers to find something really close to a solution
which... sounds really annoying to do on paper because how do you even compute cos^2(x) by hand
where did you get this problem from...?
soft ridge
interesting. I thought there would be some complicated way to solve it
soft ridge
where did you get this problem from...?
was just doing a 3d vector question
then I eventually got this
should I just send the question ?
lavish kite
yes
grizzled tide
!xy
odd edgeBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
grizzled tide
oh i wish it linked the website
lavish kite
i think probably you got something wrong earlier in the question and the thing you're actually meant to be solving at this point is far more reasonable
soft ridge
soft ridge
i think probably you got something wrong earlier in the question and the thing y...
yeah they meant the plane xy
but I thought they meant like the line x
part 3
i was initially trying to make the position vector to be at an angle 45 to the vector (0, 1, 0)
odd edgeBOT
@soft ridge Has your question been resolved?
odd edgeBOT
restive delta
!status
odd edgeBOT
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
Try to write the denominator as a perfect square
Lol
It can be written like that, actually
Write 1 in terms of sin and cos
Yes
Do you remember the integration for secx? Just askin
I see
There are two approaches
One is longer
But if you don't remember the integration of sec x then the other method is as long too so idk
You can substitute u=x/2
And then use half angle formulae
$$sin{x} = \frac{ 2\tan^2 {x/2}}{1+ \tan^2 {x/2}}$$
$$cos{x} = \frac{1- tan^2 {x/2}}{1+ tan^2 {x/2}}$$
clever fjordBOT
Lorentz
restive delta
Or that, yes
In this case that would be easier
This, I mean
If you wanna find the integral of csc x, just multiply the numerator and denominator with cot x - csc x
I gtg now but you should get the ans if you follow that
restive delta
If you wanna find the integral of csc x, just multiply the numerator and denomin...
Note that this is for csc x
blissful whale
Help me
south plume
synthetic division / polynomial long division is what you need to do
blissful whale
How does that work
cold urchin
It'll be easier for you to look it up on Youtube.
blissful whale
Mmmm ok, but is there like a formula? Or do I always have to test it out?
ashen beacon
How does that work
go through this https://www.purplemath.com/modules/synthdiv.htm
blissful whale
Just like try stuff till I get it eight
cold urchin
,,\polylongdiv{3x^3+2x^2+5x+3}{x-1}
clever fjordBOT
Pure
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cold urchin
lol
cold urchin
odd edgeBOT
@blissful whale Has your question been resolved?
blissful whale
Yup
odd edgeBOT
odd edgeBOT
Available help channel!
eternal cave
Let $a,b,c$ is real positive that sastify $abc=1$.
Prove :
$\left(a+\frac 1 b\right)^2+\left(b+\frac 1 c\right)^2+\left(c+\frac 1 a\right)^2\ge 3(a+b+c+1)$
clever fjordBOT
ChemicalMendeleev
odd edgeBOT
@eternal cave Has your question been resolved?
eternal cave
<@&286206848099549185>
lime turret
This is hard
tepid acorn
Homogenize by substituting x/y, y/z, z/x
mystic saffron
**ChemicalMendeleev**
try playing with AM GM HM inequalities
odd edgeBOT
odd edgeBOT
Available help channel!
tall veldt
Q: Is binary search the most efficient way (on average) to guess a number someone is thinking of between a specified range by just yes/no questions?
Context: Played this game with some 10-16 year olds today and on the first round they quickly discovered binary search after a couple questions like "is it odd". So then I banned questions like "is it bigger/less than x" on the next round and they resorted to asking about digits e.g. "does it contain a 3?".
I feel like it is the most efficient way but i wonder if there are any sneaky tricks you could deploy.
lavish kite
the optimal method is anything that cuts the space of possibilities in half each question
tall veldt
ah of course yes, so binary search is an optimal route. do there exist other lines of questioning that are optimal?
lavish kite
depends what sort of question is allowed
most obviously there's parity
"is it even?" "is it [number] mod 4?" "is it [number] mod 8?" etc.
tall veldt
ah thats nice
lavish kite
you can also just pick some arbitrary set
like if you know the number is from 1 to 10, you can ask "is it any of 3, 4, 6, 7, 8?"
tall veldt
thats also true, but i guess less feasible when we did 1 to 10000
lavish kite
you can also just pick some arbitrary set
like if you know the number is from 1 ...
or in a similar spirit you can just keep adding small corrections until you end up with exactly half
"is it a multiple of 3, or a prime number, or a square number, and not divisible by 37, ..."
raw palm
you can also just pick some arbitrary set
like if you know the number is from 1 ...
this will not be accepted by the one being asked ig
tall veldt
they never really thought to ask questions with a bunch of OR clauses, it would be interesting to see whether they could ever arrive to something like that
low locust
I feel like you could do some very efficient stuff with Chinese remainder theorem. depends on whether you are allowed to ask questions like "what is the remainder when divided by n"
lavish kite
i think it's just yes/no questions
low locust
of course that would make the question trivial if you allow n to be too big
tall veldt
it was just yes/no yeah
tall veldt
"is it even?" "is it [number] mod 4?" "is it [number] mod 8?" etc.
so if you wanted to go a mod route this would be the way
i guess a follow up question would be: what kind of questions can you ask that would split a given range in two?
low locust
is it a square residue mod next prime
tall veldt
- less/bigger than [mid point]
- is it even etc
tall veldt
is it a square residue mod next prime
is this easy to see? i forget about residues
low locust
not really. and it also doesnt split the range into subintervals, so you couldnt iterate it
tall veldt
would be useful for an evil version of the game where you cant ask the same type of question twice
okay thanks for the insight gang
.close
polar locust
Let $a, b \in \mathbb{R}$, and $a>1, b>0$. CDF of random variable $X$ is $F(x)=0$ for $x \leq b$ a $F(x)=1-(b / x)^a$ for $x>b$. Find values of $a, b$. Find a density function and expected value of random varaible $X$. Solution: Density is $f(x)=0$ for $x \leq b$ and $f(x)=a b^a x^{-a-1}$ for $x>b, E(X)=a b /(a-1)$.
clever fjordBOT
Michal
polar locust
can someone explain me how to get the solution?
It says that find values of a and b, but the solution does not have it.
modern hamlet
That's odd, I don't know what it means either. Do you have the original question?
polar locust
That's odd, I don't know what it means either. Do you have the original question...
yea, but its not in english
modern hamlet
that's probably what's going on then, a translation error
polar locust
CDf = cumulative distributive function
modern hamlet
because it's clear the solution is wanting you to find the pdf from the CDF
polar locust
i dont think so
polar locust
because it's clear the solution is wanting you to find the pdf from the CDF
exactly
modern hamlet
that's what the solution is saying though
Do you know how they got $ab^a x^{-a-1}$?
clever fjordBOT
BLONK
modern hamlet
Ok then you seem good
modern hamlet
they seem to arbitrary
polar locust
hmm
odd edgeBOT
@polar locust Has your question been resolved?
trim owl
Where do I get started for 3b?
odd edgeBOT
Where do I get started for 3b?
viscid grove
How does this solutions key find out that (1+r) = 1/a?
wide jackal
How does this solutions key find out that (1+r) = 1/a?
first line
a (1+r) = 1
1+r = 1/a
odd edgeBOT
odd edgeBOT
Available help channel!
crisp flume
this is basis of vector space W
odd edgeBOT
this is basis of vector space W
crisp flume
how do i find some basis of $\mathbb{R}^{2 \times 2}$ which includes basis of W in itself?
clever fjordBOT
Slowaq
wooden python
so you want to extend this basis to one of R^(2×2), yes?
crisp flume
Yes
wooden python
right
dim(R^2×2) = 4, so you need one more vector
i.e. one more matrix the addition of which wouldn't render this set LD
try finding one
crisp flume
Well that is the thing I don’t know I know that it is one of these (10/00)(01/00)(00/10)(00/01) but dunno how to determine which
@wooden python
wooden python
idk row-reduce your thing or something
turn them into rows, package them into a 3x4 matrix and do row reduction on it
odd edgeBOT
@crisp flume Has your question been resolved?
odd edgeBOT
@crisp flume Has your question been resolved?
rare marten
Hey guys, anyone here who knows line integrals?
odd edgeBOT
Hey guys, anyone here who knows line integrals?
odd edgeBOT
Hey guys, anyone here who knows line integrals?
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
rare marten
Okay, I have this line integral, it is in a conservative vector field, hence, independent of path. Now I want to know if I can calculate the straight line from the first point to the last by setting x's bounds from -1 to 5, and substituting y = 1 into the given function. hence getting ∫(e^x+x+sinx) dx + 0 since dy is 0
quasi sparrow
Okay, I have this line integral, it is in a conservative vector field, hence, in...
Oh you're taking a test?
rare marten
Oh you're taking a test?
Nah, just practicing with last year's exam
quasi sparrow
Are you doing a or b
rare marten
Are you doing a or b
b, already did a and found that it is a conservative vector field
odd edgeBOT
@rare marten Has your question been resolved?
quasi sparrow
b, already did a and found that it is a conservative vector field
Just use the theorem
And do
Example 16.3.10 : Using the Fundamental Theorem for Line Integrals
rare marten
And do
Example 16.3.10 : Using the Fundamental Theorem for Line Integrals
That takes kinda long, and I think I am on the right track, just need someone to confirm what I'm thinking is correct. We have done similiar stuff in that way during the lectures.
forest sky
you can integrate along any path that takes you from the same start point to the same end point if it is conservative
odd edgeBOT
Available help channel!
white olive
Hi, apparently I made a mistake somewhere in here but the thing is idk where. The correct answer for y domain should be (0, e) and I have (0, e^2) 🤔🤔🤔
leaden quiver
Hi @white olive are you trying to find the derivative of $y=\textrm{e}^{\frac{2}{\pi}\arccot(\sqrt{x})}$?
clever fjordBOT
white olive
Yes
leaden quiver
ok I see you are using log differentition, nice
leaden quiver
The domain of the derivative?
white olive
Yes
leaden quiver
Ok well we need to find the derivative first 🙂
white olive
Oh it’s not found yet?
white olive
arctg?
Btw that’s the answer
But our book is so stupid it doesn’t have explanations
leaden quiver
Ah, I see youre trying t find the inverse of the original function
I apologize. I understand now
leaden quiver
We know that arccot is defined for all values of x, so what is the domain for $\sqrt{x}$?
clever fjordBOT
white olive
x >= 0?
leaden quiver
Right. And if you know that arccot will be decreasing, then the maximum $\arccot(\sqrt{x})$ can be is when $x=0$
clever fjordBOT
leaden quiver
white olive
Huh I don’t understand this
leaden quiver
So the biggest the range of the original function can be is $\textrm{e}^{\frac{2}{\pi}\arccot(0)} = \textrm{e}^{\frac{2}{\pi}\frac{\pi}{2}} = \textrm{e}$
clever fjordBOT
leaden quiver
Im trying to argue that the range of f is $(0,\textrm{e}]$. If you know this is the range of the original, then this whould be the domain of the inverted function
white olive
Is it bus x can’t be lower than 0?
clever fjordBOT
white olive
bcs*
leaden quiver
Is it bus x can’t be lower than 0?
yes so this restricts the domain of the original f
white olive
Im trying to argue that the range of f is $(0,\textrm{e}]$. If you know this is ...
What if we had different x domain
leaden quiver
I'm not sure I understand what you are asking
white olive
Im trying to argue that the range of f is $(0,\textrm{e}]$. If you know this is ...
Well nvm but (0, e) according to my book is incorrect as it should be (1, e)
leaden quiver
Ah I see where I messed up. As $\arccot \sqrt{x}$ gets large, it will tend toward 0. This means that $e^{\frac{2}{\pi}\arccot\sqrt{x}}$ will tend toward $e^{0}$ as a lower bound, giving $(1,e]$.
clever fjordBOT
leaden quiver
This is a really tough question unless you know what arccot looks like :3
white olive
This is a really tough question unless you know what arccot looks like :3
Yea
Is it possible to do this in another way?
Bcs I can’t use graphs during the exam
leaden quiver
we could try to analyze cot^2 but that might be harder 🙂
leaden quiver
Gimme a second to think about how to explain this one
white olive
Okay np and thx
leaden quiver
Since cot^2 is defined for all x values except multiples of pi, I get this as the domain of the inverse function
Anywa, that seems way off from the book. So my guess is that you will need to analyze the original function to get the information you need. Just looking at the inverse function will not be helpful
white olive
Okay and thanks for your time
elder egret
odd edgeBOT
elder egret
how did we get from the first line to the second line?
south plume
how did we get from the first line to the second line?
product rule but backwards
marsh crown
@toxic monolith
odd edgeBOT
<@1035542975503138836>
marsh crown
can i still ask you more?
previous channel got closed
well anyways
is it better to use long divison in this case?
im getting annoying fractions
in this synthetic division
ok
i just solved the problem using long divison
but i still wasn't able to use synthetic division
cuz of fractions that i get during the process
<@&286206848099549185>
odd edgeBOT
@marsh crown Has your question been resolved?
toxic monolith
<@&286206848099549185>
I'm sendign you mesage on DM, with instruction
odd edgeBOT
rich phoenix
What is the question?
tall veldt
Manipulate it to look like a standard geometric series
?
Make it look like (something)^n
Use power rules
What
Manipulate the expression in this sum to look like (something)^n, since that's what geometric series look like
Use power rules
Not at hand no
You can theoretically use any of them, whether that's going to get you closer to (something)^n is something you need to experiment with to find out
Experiment and find out
Just literally try something, anything, with the goal of making things look like (something)^n
If something you do looks like it doesn't work then try something else
half garnet
does the center of a group only contain the identity element ?
south plume
not necessarily
south plume
does the center of a group only contain the identity element ?
i mean it always must have it
but it can be more than just the identity
if identity is the only element of the center, then the group is called centerless
half garnet
do you have an example ? because I don't see how it's possible
south plume
well for an abelian group $Z(G)=G$
clever fjordBOT
artemetra
south plume
for a D_2n the center is not trivial
half garnet
sorry I don't know already this notation I'm a very beginner in this, I tried an exercise which say to prove that a subroup is the center of a group but when I saw that I thought it can only have the identity element
south plume
"subgroup is center of a group" or "center is a subgroup of a group"?
half garnet
ohh okay I see I think
south plume
the first one is not true in general
half garnet
ye but in the exercise it was a particular group
half garnet
like in (Z, *) for example 1 and 0 commute but 0 is not the identity element
south plume
* is multiplication?
half garnet
yes
south plume
is this a finite group or an infinite group
half garnet
? I don't know why
south plume
$(\bZ, *)$ is not a group
clever fjordBOT
artemetra
south plume
no multiplicative inverses
half garnet
oh yes maybe$ (R*, *)$
south plume
maybe?
odd edgeBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
south plume
@brittle beacon genuine thank you for the reactions lol i am practicing my group theory skills
south plume
I mean R with no 0 and the multiplication
i see
half garnet
-1
half garnet
oh yes, sorry
half garnet
yes i think
half garnet
center is the whole group
?
brittle beacon
reals with multiplication is abelian
(Was wondering which group was being referred to 
was about to say!)
tall veldt
Another example: group of 2x2 matrices under multiplication. Centre contains scalar multiples of the identity
half garnet
yes but the center is not the whole group
south plume
and if everything commutes with everything then the center is the whole group
south plume
yes but the center is not the whole group
why not? :^)
south plume
any more questions
half garnet
nope maybe later, thanks a lot 🙂
south plume
no problem
odd edgeBOT
odd edgeBOT
Available help channel!
mystic goblet
how am I supposed to know the laplace transform of sin(t-pi)?
mystic goblet
in my laplace table, I have the laplace of sint and of a normal unit step function, but not of a trig unit step function. so what the heck am I supposed to do
echo ginkgo
u_a(t) f(t-a), that's exactly what you have here
@mystic goblet
f = the sin function, a = pi in your case
mystic goblet
okay but f(t-a) becomes F(s) according to the table right?\
so we have the laplace transform of sin(t-pi)
which I dont see
odd edgeBOT
@mystic goblet Has your question been resolved?
odd edgeBOT
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Available help channel!
digital jacinth
can someone help me with this
odd edgeBOT
can someone help me with this
digital jacinth
i know the 2 and 3 are true identies but im quite confused in 1 and 4
chilly epoch
u can use cos (a+b) formula
digital jacinth
i dont know how to use it
chilly epoch
do you know the formula?
digital jacinth
nope my teacher didnt even discussed this but we are required to answer this
chilly epoch
So π/2+ θ angle lies in 2nd quadrant
digital jacinth
oh ok
lilac wharf
These formulas are not necessarily needed
For example you can substitute t = pi/4 and try to find if all the formulas hold
digital jacinth
is no.1 the imposter here?
lilac wharf
is no.1 the imposter here?
It is
digital jacinth
yeah finally i solved it
toxic crane
For example you can substitute t = pi/4 and try to find if all the formulas hold
That's the easiest way too~
digital jacinth
how about this
lilac wharf
What if you substitute u = 0 in each of them to see if all of them hold, at least for u = 0?
digital jacinth
im honestly confused wait
lilac wharf
Replace all u you see by 0, and see if the equations are true or not
You know that sin(0) = 0
cos(0) = 1
tan(0) = 0
lilac wharf
It should be 🙂
odd edgeBOT
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Available help channel!
viral plinth
can't i for the sum just take the basis as S and thats it?
oblique rapids
How this not 0
odd edgeBOT
How this not 0
quasi sparrow
How this not 0
Why do you think it's zero
oblique rapids
Why do you think it's zero
I converted it to degree and used 300+315 and converted it
quasi sparrow
I converted it to degree and used 300+315 and converted it
Where did 300+315 come from
odd edgeBOT
@oblique rapids Has your question been resolved?
oblique rapids
Where did 300+315 come from
Degree form is 615 so I added those 2
Cus they’re in the unit circle
latent scaffold
If you're trying to reduce the angle so that it sits between 0 and 2pi (or between 0° and 360°), you subtract 2pi or 360°, not 300°.
You want to "unwind" the angle a full turn.
oblique rapids
If you're trying to reduce the angle so that it sits between 0 and 2pi (or betwe...
Wdym
Oh I was doing cosacosb-sinasinb
So I used the 300 and 315 cus it added up to 615
Was that wrong?
latent scaffold
I mean if you really want to use the sum formula, at least make sure your decomposition has at least one angle you know the value of. 315 and 300 are not "easier" to deal with.
I'd make one be 360, and the other be 615-360
latent scaffold
Oh I was doing cosacosb-sinasinb
Also, are you sure that is what they mean by addition/subtraction?
oblique rapids
Not sure
latent scaffold
It seems rather unnecessary
oblique rapids
So what was the easy way
oblique rapids
I'd make one be 360, and the other be 615-360
255 isn’t in the unit circle tho
oblique rapids
If you're trying to reduce the angle so that it sits between 0 and 2pi (or betwe...
So I was suppose to just do 615-360 and that’s my answer?
latent scaffold
I mean you can probably do it your way tbh
oblique rapids
But I got 0 and it said it was wrong
latent scaffold
I don't think you should be getting 0 even if you go at it your way with 300 and 315
oblique rapids
I don't think you should be getting 0 even if you go at it your way with 300 and...
Oh ur right I got it now idk how I got 0 last time
Ok it was cus I input the wrong fractions
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic goblet
for an exercise like this we can always say that whatever is inside the brackets is equal to 0?
odd edgeBOT
@mystic goblet Has your question been resolved?
quasi sparrow
for an exercise like this we can always say that whatever is inside the brackets...
Your phrasing is confusing
Can you write out what you mean exactly with equations
brittle beacon
shouldn’t have taken that outside the summation 
But you can determine that when n>=1, the coefficient of x^n would be zero sure
mystic goblet
okay clear
mystic goblet
Can you write out what you mean exactly with equations
I didnt say equations but I assume you mean exercise?
anyhow i think I understand it. What I dont understand is:
I mean if everything i wrote it correct than i have no further questions on this exercise
brittle beacon
I didnt say equations but I assume you mean exercise?
[as in, did you mean “is [the stuff in the picture] = 0?”]
mystic goblet
yeah and you answered that everything with the power of x^n=0
ok great thanks
.close
odd edgeBOT
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Available help channel!
oblique rapids
Can someone explain why the interval is only (-1,2)??
oblique rapids
Why the infinities not included
sullen ferry
what happens when x<-1?
when you plug it into (x+1)(x-2)
what happens when x>2?
(you want (x+1)(x-2)<0 )
sullen ferry
ok, think more this more visually
this is an upward facing parabola yes?
and it has two zeros, -1, and 2
oblique rapids
Yea
sullen ferry
so it'll look like, this, yes?
now, we can interpret (x+1)(x-2)<0 as, 'when is this parabola below the x-axis', if it were (x+1)(x-2)>0, it would be 'when is this parabola ABOVE the x-axis'
odd edgeBOT
@oblique rapids Has your question been resolved?
oblique rapids
now, we can interpret (x+1)(x-2)<0 as, 'when is this parabola _below_ the x-axis...
I don’t get it
sullen ferry
x^2-x-2 is the y-value output of this parabola
we want x^2-x-2<0, y-value below zero, below x-axis
odd magnet
for all x in r (except -2), if the absolute value of that gigantic disasterpiece of a division is less than 2, then x must be between 1/2 and 1
clever fjordBOT
Ransik
zinc snow
I just dont know where to start or what to do, im pretty sure its 50.5mm but i want to know how if thats true.
long seal
I just dont know where to start or what to do, im pretty sure its 50.5mm but i w...
That’s 5.05 not 50.5
wicked kestrel
do you know what it means for two shapes to be similar?
usually it's in the context of triangles (ie "similar triangles" is a term you've hopefully seen before) but it applies to other shapes easily enough
zinc snow
usually it's in the context of triangles (ie "similar triangles" is a term you'v...
so how would i solve that
OHHHH
OHHHHH
@wicked kestrel
wicked kestrel
what
odd edgeBOT
@zinc snow Has your question been resolved?
hoary crescent
i was using usub to solve this, but i got integral 1/x du
hoary crescent
with u is equal to lnx
how do i get rid of the extra x so i can finish the integral ikn terms of u?
mystic saffron
I believe you have to do integration by parts for that really
$\ds \int \m\ln x\cd \f1{x^2}\dd x$:
\vs{3 mm}
\env{alignat*}{{2}
v &= \m \ln x &\qq \dd u &= \f1{x^2}\dd x
}
clever fjordBOT
mystic saffron
I need help with this question below, please describe it step by step if possible.
Boys length can be descried with the simple model f (x) = 78 ⋅ e^0,07x where f(x) is the length in centimeters and x is the boys age in years.
A) Decide at which age boys are 125 cm long according to the model.
B) Use the model and decide how fast boys grow when they are exactly 6 years old.
C) Is the model also compatible with boys that are 18 years old?
mystic saffron
anyone that knows how to solve it?
modern hamlet
Yes, what's your main point of confusion?
modern hamlet
f(x) tells you the height of boys. so in A it's figuring out what age f(x) = 125. Do you know how to solve f(x) = 125?
modern hamlet
are you allowed to use a calculator?
mystic saffron
yes
modern hamlet
125 = 78*e^(0.07x). Do you know how to solve for x?
mystic saffron
ok
modern hamlet
so you would get
125/78 = e^(0.07x)
and then next is more advanced. you have to take the natural logarithm of both sides
mystic saffron
so it's 1,60 = e^0.07x ?
modern hamlet
Yes
pure yoke
How do I get this into triangular form, I don't think I can combine any equations?
pure yoke
row echeclon form
desert marlin
xyz doesn’t need to be included
But that’s right otherwise
What have you tried? Why are you stuck?
desert marlin
What have you tried to make it into that form
Yes there are
Divide row 1 by 4 to begin
pure yoke
so x -1/4y +1/4z =7/4
so from here, I don't think there is equations to combine, I don't think I can combine r1 and r3 since r3 don't have y
loud haven
Hi I'm trying to figure out how to use the Conservation of Energy Equation, Ekinitial +Eginitial = Ekfinal + Egfinal, and the equations that make it up to solve a problem. The values of the answers are provided, the question is to find out how to manipulate the equation to find the answer. I can figure out the Potential energy easily enough with m(g)(h); The problem is when I try to figure out the Kinetic energy or the speed when I don't know either.
Help needed urgently, please!
hexed girder
It's definitely unfortunate that you don't know the launch angle
loud haven
It affects the velocity, right?
hexed girder
Well, horizontal velocity should stay constant throughout the entire movement
It would be helpful to know the horizontal velocity because it would be the only velocity at the height of the launch, so then you could figure out the total energy in the system
oh wait
You're going to want to figure out the total energy in the system from the amount of kinetic and potential energy at launch, and use that total to determine the individual energies at later points
@loud haven
You know the equation for kinetic energy right?
loud haven
1/2 (m)(v)^2, right?
hexed girder
Yup. So once you know the kinetic and potential energies at launch, you will be able to use the total energy in the system and the easily determined potential energy at each point to determine the kinetic energy at each point. Then you should be able to work from there to solve the rest
hasty dome
You can pretend you dropped it from rest at 12m height and see what the velocity would be when it's 2m from the ground to see what the vertical velocity was at the start.
The starting velocity will be the same, but in the upward direction.
From that, you can determine the angle or horizontal velocity or whatever.
hexed girder
Yeah I figured out you don't actually need that
hasty dome
Oh, OK.
hexed girder
It's been a while since I've taken a physics course, forgot you're supposed to use total energy in the system to solve a lot of problems
loud haven
So sub in the total energy from the first part into the second part, then manipulate the equation to single out the velocity, then move on to solve for the Kinetic energy of the second part?
If that doesn't make sense I'll try to type it
hexed girder
no, you manipulate to solve for kinetic energy
In this system, the total energy at a point = kinetic energy + potential energy
and the total has to be the same at each point
loud haven
So how would I figure out the Kinetic energy if I don't have the velocity?
Oh wait hold on
So take the total energy and subtract the Potential energy that I've already solved for
hexed girder
you have the initial velocity
yes
but first, you have to use the first point to find the total energy
since you know the velocity at the first point, you can solve for both kinetic and potential there
ruby nacelle
,rccw
clever fjordBOT
odd edgeBOT
ruby nacelle
can anyone help me with 40b?
i kinda forgot how to find the slope with given inclination
odd edgeBOT
Available help channel!
ruby nacelle
idk
sullen ferry
!original
odd edgeBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
sullen ferry
ah wait
odd edgeBOT
@ruby nacelle Has your question been resolved?
forest nest
what's the proper way of writing set to express the domain of f(g(x))
would something like this be syntaxically correct?
summer cradle
this does not look right and is also syntactically off
for the syntax, just write = if you want to say two things are equal (not :)
and when you intersect two sets A and B
their intersection is just A intersect B
not {A intersect B}
is $I_{f(x)}$ supposed to be the image of $f$? what relevance does that have to the domain of $f\circ g$?
clever fjordBOT
chmonkey #1 simp
summer cradle
no
well
yes
lol
it's better
the domain of f o g is just the domain of g
there are conditions under which f o g makes sense for given function f and g
and under those conditions, the domain of f o g you'll find could be nothing but the domain g
forest nest
the domain of f o g is just the domain of g
but don't u also have to make sure that every image that the g(x) comes up with can be plugged into f(x)?
summer cradle
that's built in to f o g making sense as a function to begin with
forest nest
oh
it's just like a rule you have to follow
like here would i just not be able to write f(g)?
summer cradle
i probably wouldn't describe it as a "rule to follow" but ok sure
here, it's nonsensical to try to compose them in the first place
summer cradle
for f o g to "make sense", we need that the image of g is a subset of the domain of f
forest nest
it's just defined like that okidoki
summer cradle
yes
forest nest
merci :)
summer cradle
:)
forest nest
.close
jade cloud
how’s the answer C
odd edgeBOT
how’s the answer C
jade cloud
idk how they got it that way.
modern hamlet
do you know the chain rule?
summer cradle
modern hamlet
ok, so what did you get?
jade cloud
i’ll write what i did
hold on
wait so
with chain rule i got 7(5x^5+1)^6 • 25x^4
and then i got 175x^4(5x^5+1)^6
and when i did deriv again. i like brought the six down and multiplied by 175 and got a bigger number than what the answer shows
modern hamlet
keep the 175 out front and move other numbers to later terms
what did you get for the second derivative?
jade cloud
ngl i stopped there bc i got stuck
💀
let me work it out
one more time
ill@show work
summer cradle
another pfp twin
summer cradle
@pearl patio
summer cradle
there's someone else with a kuromi pfp but i can't remember her name
summer cradle
jade cloud
keep the 175 out front and move other numbers to later terms
hey !!
i did
something but
idk if i did it rigjt
jade cloud
💀💀😭
summer cradle
it appears you should use product rule to differentiate f'
i am not sure what you did but it does not look right
jade cloud
oh what
OHHH
PEODUCT RULE
RIGJTT
JOKD ON
I WAS DOIGN CHAIN AGAN
wait what.
If i did product rule right!
how will the answer come to C
bc it
like
yk
summer cradle
idk, maybe a nice factorization will come up
odd edgeBOT
@jade cloud Has your question been resolved?
odd edgeBOT
@jade cloud Has your question been resolved?
royal dragon
how’s the answer C
you can use any CAS (computer algebra system) to do formal derivatives
so that you don't have to wait for human response, and you get the solution in seconds
mystic saffron
hi
mystic saffron
why is it d divided by
not d multiplied by
the book shows a weird method of doing it as well
Edexcel
y^2 was being divided by d so we multiply both sides by d, not divide
am I wrong
modern hamlet
this step is wrong
modern hamlet
Because it doesn't follow the correct rules, you need to explain why you did that
mystic saffron
Because we are trying to isolate Y
modern hamlet
Because we are trying to isolate Y
yes, so multiply both sides by y^2
then you get what
lavish falcon
d is on top you cant just multiply it out
lavish falcon
yes
modern hamlet
you can do whatever you want
you could multiply both sides by d, it just won't help
mystic saffron
so we need to isolate y by multiplying it into the other side and then moving the other items to the other side
modern hamlet
the optimal thing here is to multiply both sides by y^2, then 1/(a-c)
lavish falcon
yeah you can multiply it by d it just doesn’t make the equation cleaner
mystic saffron
but then it would be d^2 right
lavish falcon
yeah which just adds a bunch of problems
odd edgeBOT
odd edgeBOT
Available help channel!
stark veldt
odd edgeBOT
odd edgeBOT
@stark veldt Has your question been resolved?
burnt zealot
If y=1/t what happens when I differentiate with respect x
drowsy root
becomes 0, because with respect to x its all constants
nimble blaze
use chain rule
burnt zealot
so dy/dx = -1/t^2 dt/dx. ?
nimble blaze
yeh
astral moat
hi any clue what this notation means? i dont understand it
If m = a0a1a2a3a4, n = a4a3a2a1a0
Suppose 9 | m, then
{summation from 0 to 4} (10)^k ak (mod 9) = 0 (mod 9)
{summation from 0 to 4} ak (mod 9) = 0 (mod 9)
{summation from 0 to 4} (10)^(4 - k) a{4 - k} (mod 9)
= {summation from 0 to 4} a{4 - k} (mod 9)
= {summation from 0 to 4} ak (mod 9)
= {summation from 0 to 4} (10)^k ak (mod 9)
= 0 (mod 9)
mystic saffron
\textbf{Question:} If $A$ is a normal subgroup of $G$ and $B$ is any subgroup of $G$, prove that $AB$ is a subgroup of $G$.
\vs{3 mm}
\textbf{My solution:} Let $a_1b_1$ and $a_2b_2$ be two elements in $AB$, where $a_i \in A$ and $b_i \in B$. Then:
\env{align*}{
a_1b_1\p{a_2b_2}^{-1} &= a_1 b_1 b_2^{-1}a_2^{-1} \
&=a_1b_1b_2^{-1}a_2^{-1}\p{b_2 b_1^{-1}}\p{b_1b_2^{-1}} \
&=a_1b_1b_2^{-1}a_2^{-1}\p{b_1 b_2^{-1}}^{-1}\p{b_1b_2^{-1}}
}
Then we can say that [
a_1b_1b_2^{-1}a_2^{-1}\p{b_1 b_2^{-1}}^{-1}\p{b_1b_2^{-1}} \in AB
]
Because [
a_1b_1b_2^{-1}a_2^{-1}\p{b_1 b_2^{-1}}^{-1} \in A
]
clever fjordBOT
odd edgeBOT
iron bear
yeah gotcha thank you
mystic saffron
<:thonk:406575732563902485>
wot
iron bear
what you did is sufficient
odd edgeBOT
✅
mystic saffron
[0.7\textwidth]Let $G \le S_n$ be a subgroup of the symmetric group on $n$ letters. Show that either every permutation in $G$ is even or exactly half of the permutations in $G$ are even
clever fjordBOT
spiral basalt
Is the signature reduced to the identity or not ?
mystic saffron
Is the signature reduced to the identity or not ?
Is that meant to be a question directed at me or clarification for the question?
spiral basalt
A hint
spiral basalt
Looks like 2 cases to me, if you see what I mean
mystic saffron
i havent studied the alternating group just yet to be fair so idk if i can do this question
spiral basalt
You don't need it
mystic saffron
oh you dont?
spiral basalt
You don't
Though ofc the understanding related to the overall study of the signature, and by extension the alternating group, may help figure out the solution here.
But you don't need it
This is very strongly inspired from the proof of |An| = n!/2 though
mystic saffron
i think i kinda see what u mean but i will study a bit first and get back to this maybe
iron bear
spiral basalt
The idea, for the nontrivial case, is to ||exhibit the right bijection||
iron bear
all you need to know is that group elements are all invertible and that odd + blah changes parity
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
Is there an A ⊆ N with the property: (a) A is finite, Ac is infinite? (b) Ac is infinite, Ac is it finite? (c) A and Ac are both infinite? (d) A and Ac are both finite?
hasty dome
What do you mean by "is it finished"?
mystic saffron
Whoops typo
hasty dome
Is N the natural numbers or just an arbitrary set?
mystic saffron
Natural numbers
brittle beacon
Or do I need to prove every part
You should, though you might not need to in your exercise
(find examples or argue why not)
hasty dome
OK, so let's look at a.
What is a finite subset of the naturals?
Like an example.
<@&268886789983436800>
mystic saffron
(1,2,3) is a finite subset of N
hasty dome
OK, is its complement finite?
mystic saffron
Well I assume since its a closed subset
mystic saffron
No sorry
I didn't actually need help with this
I just wanted to know do I need to prove it
hasty dome
Oh, OK.
hasty dome
You said the complement of {1, 2, 3} was finite, right?
You should prove that one, by showing that the complement is finite.
The complement is the natural numbers with 1, 2, and 3 taken out.
How many natural numbers are left over?
Like you have 4, 5, 6, 7, etc.
hasty dome
Right, A is {1, 2, 3}. The complement is all naturals not in A, so {4, 5, 6, ...}.
mystic saffron
Yea it's infinite
But I know that the point was it's easy to be seen without proof
hasty dome
Oh, OK.
mystic saffron
However since you're being so nice
I do have a question
The equivalence relation on the set S determines the partition of the set S (on the equivalence class). vice versa, each partition F = {Si | i ∈ I} of the set S determines the relation ∼ in the following way: x ∼ y ⇔ (∃i ∈ I)(x, y ∈ Si). Prove that the relation ∼ defined in this way is an equivalence relation whose equivalence classes are sets Si , i ∈ I
I don't even know how to start this
Also this is Google translate cuz I'm too lazy to translate that huge chunk myself but I think the translation is good
I just need a push I don't know how to start
hasty dome
OK, so you need the definition of equivalence relation.
It needs to be symmetric, reflexive, and transitive.
mystic saffron
Yea that I know
hasty dome
So, you'd prove symmetric by starting out "x ~ y <=> exists i in I such that x, y in Si". So, if it only checks whether both are in Si, then y~x is also in Si, since x and y are both in Si.
And so forth with the other two.
mystic saffron
So, you'd prove symmetric by starting out "x ~ y <=> exists i in I such that x,...
Now you lost me
hasty dome
Well, there exists an i such that both are in Si.
So, if both x and y are in Si, then both y and x are in Si.
So, x ~ y <=> y ~ x.
Does that make sense?
mystic saffron
Sure it does I think I don't understand how this relation is defined
What's Si and i, I mean obviously sets
But what kind of sets
hasty dome
i is just an index (the Ss are numbered and i is the number).
It says S is partitioned into S1, S2, etc.
Which means that each of the elements go into exactly one Si.
mystic saffron
Ohhh I see yea I'll have to redo relations I've been struggling with that
hasty dome
Partitioning S just means you get some subsets of S and each element in S goes in exactly one of those subsets.
mystic saffron
So how would you check symmetry in proper notation
hasty dome
x ~ y => exists i in I such that x, y in Si => exists i in I such that y, x in Si => y ~ x
Something like that.
You can also get more in detail.
x ~ y => exists i in I such that x in Si and y in Si => exists i in I such that y in Si and x in Si => y ~ x
Since and is commutative.
Does that proof make sense? I can explain it more.
mystic saffron
Yea it does tyvm
hasty dome
No problem.
mystic saffron
I'll skip that for now and do induction
hasty dome
Oh, it looks like partitions need to have nonempty subsets.
thin anvil
odd edgeBOT
hasty dome
,rccw
thin anvil
When converting this question vertex form
clever fjordBOT
thin anvil
When converting this question vertex form
I’m getting 3/4 positive
But some people from class are saying it’s negative -3/4
I’ll send my answer
Idk what’s wrong
thin anvil
My answer is correct?
signal oar
,w 2x^2 - 3x + 21 simplify
solemn jay
ur answer is correct
thin anvil
Let’s goo
signal oar
See the second result
brittle beacon
But some people from class are saying it’s negative -3/4
What’s “it” referring to, for clarity?
hasty dome
Well, b is being subtracted from x.
You have x - 3/4, so b = 3/4 since 3/4 is being subtracted from x.
signal oar
Should be x+3/4
Nope, otherwise you'd get a positive coefficient for x. But it's negative, -3.
hasty dome
No.
See how b is being subtracted from x?
See how 3/4 is being subtracted from x in your shown work?
b = 3/4.
thin anvil
See how 3/4 is being subtracted from x in your shown work?
Yes
thin anvil
b is whatever's being subtracted from x.
So I’ll have to write it without sign
hasty dome
Yes, it's positive 3/4.
If it was a(x + b)^2 + c, it would be -3/4, because b would be whatever's being added to x, which would be -3/4.
But it's a(x - b)^2 + c.
So, here, b is whatever's being subtracted from x.
You can use \qty(stuff\).
That'll autoresize the parentheses.
clever fjordBOT
Chai T. Rex
\[2\qty(x^2 - \frac32 x + \frac{21}2)\]
signal oar
You can use `\qty(stuff\)`.
Thanks, I didn't know of that. From what package is that? Amsmath?
hasty dome
I think so. Let me check.
hasty dome
Sorry, I'm not sure.