Bob Goldham
#help-33
elfin berryBOT
elfin berryBOT
Bob Goldham
earnest sundial
no idea why they're using a >= relation instead of just saying it's =, but that probably makes sense in the context of that particular proof?
obtuse mural
isn't it simply this?
obtuse mural
no idea why they're using a >= relation instead of just saying it's =, but that ...
the formula we are trying to prove is f_n >= 2^0.5n for n >= 6
obtuse mural
**Bob Goldham**
i get the last part thank you, but for this part of the proof, i guess they are using the >= relation because 2^((1/2)+1) cannot equal 2 at all
??
earnest sundial
yes that's just root(2)+1 >2
obtuse mural
understood, so my overall question is when solving this proof, one should try to use inequality realtionships to eventually land on a formula that could be easily equated to the formula we need for our proof which is
i get the math but im kinda asking why we allowed to use this inequality? Isnt this inequality the only one that should be here?
obtuse mural
i get the last part thank you, but for this part of the proof, i guess they are ...
i get it now, its because the inequality is chosen specifically to reach the goal correct?
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marsh citrusBOT
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harsh radish
marsh citrusBOT
stoic saddle
|a| <= |a+b| iff b >= 0
is this true
harsh radish
Yes
stoic saddle
a = -5, b = 1...
devout mauve
what is (a+b)+(a-b)
harsh radish
2a
shrewd ivy
<@&286206848099549185> In how many ways can two letters be selected from the English alphabet if repetition is allowed?
Yah
spice cargo
harsh radish
Can you go to a different help channel
shrewd ivy
Bro just wait
harsh radish
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shrewd ivy
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arctic nacelle
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subtle fox
Hi there!
subtle fox
I really need help
waxen vector
waxen vector
What do you even need to do with all of this?
subtle fox
@waxen vector it's from my University. I missed 1 week lessons then here they are... I don't even understand any of these
waxen vector
I don't think anyone can without context
These are just a bunch of values for points/vectors and some constants
subtle fox
@waxen vector there is actually no context... it's from test book.
subtle fox
These are just a bunch of values for points/vectors and some constants
Yess. They are..😕
waxen vector
No one here is a magician sadly!
People can help you out but people cannot guess what you have to do
subtle fox
@waxen vector it's okay) thanks anyway!
waxen vector
Sorry 😦
subtle fox
@waxen vector don't be😊
Actually there is one more...
@waxen vector Can you..?
<@&286206848099549185> please?..
subtle fox
@night quail hi !
subtle fox
@night quail it's okay😊
subtle fox
@night quail can you help with this one)
night quail
just wait
subtle fox
@night quail thanks in advance 😊)
marsh citrusBOT
@subtle fox Has your question been resolved?
pseudo badger
$$\frac{\int_{0}^{4} \sqrt{y}\cdot \sqrt{1+16\cdot y^{3/2}} dy}{\int_{0}^{4} \sqrt[4]{y}\cdot \sqrt{1+16\cdot y^{3/2}}dy}$$
marsh citrusBOT
$$\frac{\int_{0}^{4} \sqrt{y}\cdot \sqrt{1+16\cdot y^{3/2}} dy}{\int_{0}^{4} \sq...
elfin berryBOT
xd_senBugha
pseudo badger
im stuck with this integral
we had to find the centre of mass of a bowl along the line y = x^4
devout mauve
well, two different integrals
you arent doing yourself a favor by trying to solve both at the same time
try u-subs
vernal forge
**xd\_senBugha**
i think last time you asked this i suggested you a u-sub u=y^{3/2}
have you tried it?
vernal forge
i think last time you asked this i suggested you a u-sub u=y^{3/2}
for the numerator one
marsh citrusBOT
@pseudo badger Has your question been resolved?
pseudo badger
i did but it leads to nothing
vernal forge
show
marsh citrusBOT
@pseudo badger Has your question been resolved?
pseudo badger
<@&286206848099549185>
marsh citrusBOT
@pseudo badger Has your question been resolved?
marsh citrusBOT
@pseudo badger Has your question been resolved?
marsh citrusBOT
@pseudo badger Has your question been resolved?
pseudo badger
<@&286206848099549185>
humble nebula
is that dv or du in the second line
pseudo badger
du
marsh citrusBOT
@pseudo badger Has your question been resolved?
hybrid wave
hello
main idol
pseudo badger
Not that denominator
pseudo badger
**xd\_senBugha**
This one
$$\int_{0}^{4} \sqrt[4]{y}\cdot \sqrt{1+16\cdot y^{3/2}}dy$$
elfin berryBOT
xd_senBugha
marsh citrusBOT
@pseudo badger Has your question been resolved?
pseudo badger
<@&286206848099549185>
rain cloak
pseudo badger
**xd\_senBugha**
I can't seem to solve it
odd crest
Are you sure that is the correct integral?
It says on wolfram alpha that the antiderivative includes a function known as the hypergeometric function
which i've never heard of
it also says that there is no precise value as the hypergeometric function is an infinite sum
as in the only precise value is 16/2 sqrt(2) [2]F1
pseudo badger
it is
it was a part of a physics question i had where i had to find the centre of mass of bowl whose walls were along the line y = x^4 and had uniform linear mass density
$$Y_{C.O.M} = \frac{\int(y dm)}{\int dm}$$
elfin berryBOT
xd_senBugha
pseudo badger
that integral above is $$\int(dm)$$
elfin berryBOT
xd_senBugha
agile steppe
it was a part of a physics question i had where i had to find the centre of mass...
I may be thinking about this wrong but to find y couldn't you just $\frac{1}{8}\int_{-4}^{4}{x^4}{dx}$
elfin berryBOT
Ninja
dusky trench
pseudo badger
I may be thinking about this wrong but to find y couldn't you just $\frac{1}{8}\...
You cant
It's an integral of dm and dm cannot be found in terms of x
$$dm = \sigma dA$$
And dA is in terms of y
elfin berryBOT
xd_senBugha
agile steppe
the way im thinking about it, if it has uniform mass density, then a little bit of mass (dm) scales the same way as a little bit of x (dx)
might just be me approximating too much though
pseudo badger
Even if you're right, the centre of Mass along the x axis will be at 0
agile steppe
yeah it will
so the answer to the integral i provided above is simply the y coordinate of the com
pseudo badger
So all in all we need to find the y coordinate
agile steppe
the integral is "weighing" each bit of dx by its y value at that point the same way a com calculation does, then by taking the average value of it you're dividing by the "total mass"
wait I have an easy way to check this i think
I mean it checks out as far as I can see, for ex, if I find the y value of the center of mass of a sheet modeled by a sine wave from 0 to 2pi, the average value for that is 0 and the integral also gives 0
wait @pseudo badger is the bowl even on the domain [-4, 4]?
pseudo badger
It is
agile steppe
ok I think thats it then
pseudo badger
Then where'd be the centre of mass for it?
agile steppe
the answer to the integral would give the y value of the center of mass
which is 51.2
and ofc x is 0
sacred kestrel
generalized inequality symbol i think
used when dealing with vectors, matrices, and other objects with dimension
ah looks like they can also be used to represent partial ordering
which in this context might be the more likely case
found an MSE answer dealing with this
whole sleet
They're trying to "wink wink nudge nudge this isn't ≥ and ≤ but they happen to act the exact same way"
We often just use ≥ and ≤, even when talking about partial orders
marsh citrusBOT
@compact portal Has your question been resolved?
devout mauve
well for sets we usually use $\subseteq$ in place of $\preccurlyeq$
elfin berryBOT
Denascite
devout mauve
not always tho, it depends on context
whole sleet
It looks like your book is comparing by subset. That is, A ≤ B if A is a subset of B.
You're choosing to compare element-wise, but haven't been told to
marsh citrusBOT
@compact portal Has your question been resolved?
elfin berryBOT
eph
whole sleet
They're using ≤ for a partial order of their choosing
They happen to be choosing the "subset" partial order
Yes there already exists a symbol for that lol. But, they might have chosen a different partial order that does not have a symbol yet.
"Comparable" isn't a property of a set. It's a relationship two sets may have
A and B "can be compared" , or "are comparable"
if A ≤ B, or if B ≤ A
IN THIS CASE, yes
But you can change what the comparison is
That's the abstraction happening here. I can just be like "okay now I'm ordering the sets based on their first element"
So if I choose to order based on first element, then:
{1,2,3} ≤ {2,3}
Because 1 ≤ 2
The point being we can change our mind for what "order" means at any time
Made it cs?
Lol happy you found an angle
Feel free to ask if you have anything else!
Actually wait, I did kind of lie. You can't have a "first element" in a set they're unordered
Maybe we can order them based on "sum of everything in the set" though
strong trench
can someone explain why the answer is c) At?
marsh citrusBOT
can someone explain why the answer is c) At?
crystal turret
Wrong server
marsh citrusBOT
still temple
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
still temple
,rotate
elfin berryBOT
still temple
Help with number 4 pls idk where to start
elfin berryBOT
remote barn
Illustrate it
still temple
I can’t really illustrate it if I don’t have an angle
remote barn
I can’t really illustrate it if I don’t have an angle
there doesn't seem to be angles in the question
it's a shuffleboard
it's on the floor
still temple
Ok well I’m not sure what you mean sorry
Oh
So it’s gliding on the floor
Mb
I thought it was in the air sorry
remote barn
Mb
yeah you could add a block for the mass ._.
and a freebody diagram always helps
force diagram*
still temple
Yes, but again I am sorry as I did not realize it was on the ground
I’m sorry.
Ok like this @remote barn
lofty fulcrum
remote barn
Ok like this <@910426153217581057>
Yeah but it's on the floor
remote barn
Something like what this guy did
lofty fulcrum
So dark what we first have to do is we know its accelerated till 5.8 m/s and then after assuming no more force is imparted on the object the body will be subjected to the force of friction till it stops.
lofty fulcrum
Isn’t that Fa too
Nope. Cus that is like saying we are applying a force throughout the whole time which is non sensical as we had only applied a force till it reaches a speed of 5.8 m/s and then released it.
The sum of Fx represents all of the forces relative to our x direction and in the time frame of our scenario the body is only subjected to the force of friction as mentioned.
You can choose right as negative and left and positive and you can also invert the signs for the y-direction and as along as you do the algebra correctly you'll be fine.
Do you need assistance on all these questions?
lofty fulcrum
I don't mind helping, but I would like for you to put in the work and figure it out. I'll guide you. Only if you really struggle shall I then reveal the answer if you insist, but for your own sake do ur best.
still temple
Okay
lofty fulcrum
Alright so plug in the numbers and tell me whatchu got for number 4
still temple
In order to get the sum for Fx, we need to add all forces in the plane of x
lofty fulcrum
In order to get the sum for Fx, we need to add all forces in the plane of x
Its the sum of all our forces, but remember its relative to our scenario and the scenario we are observing is when the box is only subjected to the frictional force, we don't care about the applied force as we only applied a force till it reached a speed of 5.8 m/s and then released.
The moment we release it we want to know how far it travelled when being subjected to the force of friction
And we know the court is 15.8m, so how far the body travels before coming to a stop must be within this or we know we did something wrong.
I am kinda busy actually, so if u want I'll solve all the questions and send u the answers and steps. Do not look at it until you have attempted the question and reached an answer.
still temple
I am kinda busy actually, so if u want I'll solve all the questions and send u t...
Ok
And to get acceleration real quick is it just change in v over displacement
still temple
Okay
lofty fulcrum
once we obtain acceleration we can plug in our knowns into a kinematic equation that satisfies our variables and solve for displacement,.
still temple
once we obtain acceleration we can plug in our knowns into a kinematic equation ...
By the way I don’t need help with 7 and 8. Thank you for ur help though
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
crystal bone
I need to find the differential of 8.2.2. I used implicit differentiation and I used a different method where you factor out a y on the left side and use the quotient rule. Which one of the two options is correct, seeing as they give very different answers?
marsh citrusBOT
I need to find the differential of 8.2.2. I used implicit differentiation and I ...
crystal bone
If i factor out a Y I get 2, if I use implicit differentiation i get
$\frac{4x-2-y}{x-1}$
elfin berryBOT
SHREK_IS_SENPAI
crystal bone
**SHREK\_IS\_SENPAI**
wolfram agrees with this
sharp bloom
In 8.2.2 I would factor the LHS to y(x-1), then divide both side by (x-1). Use polynomial division for the division, then differentiate .
crystal bone
Yeah I did that as well, but would the implicit differentiation also be correct?
crystal bone
Or should I just stick to the easier method?
crystal bone
We haven't done implicit differentiation in school yet, so I might need to check with my subject head
crystal bone
Less likely to mess up
Thank you, you're right
sharp bloom
We haven't done implicit differentiation in school yet, so I might need to check...
Don’t do it then. Where I live, you can’t really be marked on things you haven’t been taught.
crystal bone
Yeah, where I live it's fine as long as the markers know what you did, but I'm not sure if they're gonna know
Okok I'll use the other method, thx
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marsh citrusBOT
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short wadi
how do they get y(x) from 1/(1+y)=1/(1+x)+c
marsh citrusBOT
how do they get y(x) from 1/(1+y)=1/(1+x)+c
modest adder
u already solved it
devout mauve
do you mean in general or do you mean how they did it so fast. cause they skipped some steps
modest adder
did you understand the integration part?
humble nebula
how do they get y(x) from 1/(1+y)=1/(1+x)+c
they skipped steps
short wadi
yeah i understood the integration
juist not how to get y(x).
cause I assume y(x) is not y
because if I solve for y I dont get the same
copper raven
y(x) and y are the same thing
the unknown function you're trying to solve for
it's not y times x
@short wadi
short wadi
i know......
I just put the right side into common denominator
and then cross multiplied
and I get a different value for y
is it then just an algebra mistake
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marsh citrusBOT
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humble nebula
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neon drum
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humble nebula
you can’t close it because it’s already closed
marsh citrusBOT
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whole sparrow
marsh citrusBOT
whole sparrow
In (A)
I did both (i) and (ii)
There are 11 numbers divisible with 9 between 100 and 200
Thats the (n) of (i)
But in (ii) which asks for how many numbers NOT divisble by 9 comes b/w 100 and 200
The n is 99 for this (ii)
How is this possible
How can there be 99 numbers NOT divisble by 9 b/w 100 and 200
hardy slate
yeah that's not right
whole sparrow
But answer is correct
hardy slate
basically ok
whole sparrow
I verified it everywhere
whole sparrow
Yea
hardy slate
now, to find the sum of all the numbers not divisble by 9
hardy slate
you can sum up all the numbers. just all the numbers. 99 of them
and then subtract all the numbers that are divisible by 9, which you worked out in part i
and that's slightly easier
shortcut
hardy slate
there are 99 numbers between 100 and 200
add them all up
remove the 11 that divide by 9
done
whole sparrow
But the 99 numbers are supposed to be non divisible right?
whole sparrow
From 9
hardy slate
you want the numbers that aren't divisible
you can get this
by taking all the numbers
just all the numbers
and removing the ones that are divisible
whole sparrow
Yea i understand
Ok i got it
Tysm
How do i make this channel unoccupied again?
Ok
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drowsy sky
Hi, recently I just read in a computational physics book that "all ODEs can be rewritten to a standard form", however I am not finding a proof online and also I am a bit suspiscious of the statement, (possibly they only mean linear ODEs), does anyone know whether this is true or not?
marsh citrusBOT
Hi, recently I just read in a computational physics book that "all ODEs can be r...
drowsy sky
and then they basically say you can use rk4 to solve the ODE with a computer after its in that form, but i never knew that every ODE could be rewritten into standard form
copper raven
I mean the basic idea is that you can write a 2nd order scalar (meaning y(t) returns a real number) ODE as a 1st order vectorial (y(t) returns 2D vectors) ODE
the typesetting in that "standard form" indicates that
y is in boldface, so it's a vector now
f also
copper raven
I mean the basic idea is that you can write a 2nd order scalar (meaning y(t) ret...
I can detail the 2nd order scalar to 1st order vectorial transformation on an example if you want
but you can do that for whatever order you have at the beginning
@drowsy sky
willow salmon
marsh citrusBOT
willow salmon
willow salmon
This is the answer
I dont understand how they got the first line
<@&286206848099549185>
still temple
dont ping if 15 minutes havent passed
willow salmon
k.
floral linden
I dont understand how they got the first line
x represents the 2A
so by that double angle formula
it becomes x/2 on the HS
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jagged snow
define a so that the function only gets negative values? I think I should make two cases g(x)=0 and g'(x)=0 so that the functions hill is at zero
marsh citrusBOT
define a so that the function only gets negative values? I think I should make t...
desert socket
well you don't even need derivatives for this one
just make sure discriminant of the numerator is negative and so is the leading coefficient
jagged snow
so what do i do
i know the discriminant is b^2-4ac and it tells how many solutions there are
desert socket
Heres my idea
x^2+1 is positive for all real values of x
So you need to make the numerator negative.
Now for only one sort of values (only negative or only positive), you need the graph to not touch the x-axis and thus the discriminant must be less than zero.
Now the the leading coefficient decides the sign of the value (only negative or only positive)
So, if the leading coefficient is negative and the discriminant of the quadratic is also negative, then it would yield only negative values
The idea is to make the graph somewhat like this
jagged snow
so a has be a negative number?
desert socket
yes
jagged snow
and there has to be no solutions to the function so that it never touches the x-axis
and by having the discriminant be negative this can be achieved
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marsh citrusBOT
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mint smelt
I cant find out CB=?
marsh citrusBOT
I cant find out CB=?
mint smelt
I get CB=2√117
hardy slate
plausible
mint smelt
is that corect?
mint smelt
Can you find AC?
i dont think so
jagged relic
Okay, can you find similar triangles?
mint smelt
maybe AC1D and A1CD
jagged relic
These two look very different on the figure
Look again
Do you know the intercept theorem
aka Thales's theorem or basic proportionality theorem
mint smelt
no
mint smelt
yeah
jagged relic
What does that tell you about the ratios SA/SB, SC/SD, and AC/BD?
mint smelt
idk
jagged relic
Odd that you're on this problem if you don't know one of the most basic theorems in geometry
All these ratios are equal
It works in reverse too: if SA/SB = SC/SD, then AC and BD are parallel
Can you apply that to your problem?
mint smelt
BC1/BA, BA1/BC and C1A1/AC?
mint smelt
thay're parallel
jagged relic
Right
Now, do the same but with D instead of B
This is the same theorem, just with points on either side of S
mint smelt
SB/SD, SC/SA, CA/BD?
jagged relic
No, on this last picture it's the exact same as on the previous one: SA/SB = SC/SD = AC/BD
Do you see where to apply the theorem?
mint smelt
no
jagged relic
Ok can you list all the things you know that are not already on the picture
I have to go so here are the steps you need to take:
- ||BC1/BA = BA1/BC so A1C1 and AC are parallel||
- ||A1C1 and AC are parallel so BC1/BA = A1C1/AC||
- ||A1C1 and AC are parallel so DC1/DC = A1C1/AC||
- ||DC1/DC = A1C1/AC = BC1/BA = 1/2 and DC1 = 4 so DC = 8||
- ||A1C = sqrt(DC^2 + DA1^2) because Pythagoras and BC = 2A1C||
sand sparrow
N^2 / 2 = N?
marsh citrusBOT
N^2 / 2 = N?
zealous ridge
do you mean $n^{\frac{2}{2}}$ or $\frac{n^2}{2}$
elfin berryBOT
ImToxiiq
proud ice
N^2 / 2 = N?
sand sparrow
no
sand sparrow
then what
proud ice
**ImToxiiq**
You were asked for clarification here btw. Please specify
zealous ridge
and what is your question now ?
sand sparrow
(N^2) / 2 = N?
zealous ridge
are you asking which values of n satisfy this equation ?
sand sparrow
no
i am asking if ^2 / 2 = the same as sqrt(x)^2
you know hwat i mean?
oh lol
its not
wait
idk
zealous ridge
consider n=5
then n^2/2=12.5
but sqrt(5)^2=5
so n^2/2 is only in special cases equal to n
sand sparrow
consider n=5
then n^2/2=12.5
but sqrt(5)^2=5
nah im confused now
ok here is original question
you can simplify to n but
idk
zealous ridge
$\frac{2n}{4n} \cdot \frac{18n^2}{4}=n$ do i read that correctly ?
elfin berryBOT
ImToxiiq
sand sparrow
nah its not n its just
nvm so it is = n ye
sand sparrow
**ImToxiiq**
how would you simplify this?
zealous ridge
how would you simplify this?
so you want to simplify this expression ?
sand sparrow
ye
zealous ridge
first notice that 2n/4n is the same as 2/4 since the n's cancel
and 2/4=1/2
then you just multiply the fractions and simplify
sand sparrow
tahnks for wanting to help
offering*
marsh citrusBOT
@sand sparrow Has your question been resolved?
wary bluff
so I should show that f + g in O(h) and f + g in omega(h) right
marsh citrusBOT
so I should show that f + g in O(h) and f + g in omega(h) right
wary bluff
if f + g in O(h) that implies f in O(h) and g in O(h) right?
ik that f in O(g) and g in O(h) for sure
but idk how to get to f in O(h) from that info
f(n) <= c * g(n)
g(n) <= c * h(n)
=> f(n) <= g(n) <= c * h(n) ?
stoic saddle
$\exists n_0, c_1 : \forall n \geq n_0, f(n) \leq c_1g(n) \ \exists n_1, c_2, c_3 : \forall n \geq n_1, c_2 h(n) \leq g(n) \leq c_3 h(n)$
just to write that out formally and fully
and to be careful not to conflate any of the witness constants for any asymptotic notation definition
although
er
backwars
elfin berryBOT
AnnGhost
stoic saddle
there we go
$f(n) \leq c_1 g(n) \leq c_1c_3 h(n)$ thus $f(n)+g(n) \leq (c_1 + c_1c_3)h(n)$, so that's half of it done. if we get to assume $f$ is positive, then we can reuse $c_2$ for our lower bound constant. and the threshold will of course be $\max(n_0, n_1)$.
elfin berryBOT
AnnGhost
wary bluff
wait why do we have 2 constants beside h(n)
if g in O(h) then g(n) <= c_2 * h(n) right
ohhh its coz we know that f <= c_1 g(n)
and g(n) <= c_3 h(n) u just multiplied both sides by c_1 here
my bad
and ye all the functions are positive
N -> N
wait shit im confused about one more thing
u said reuse c_2 but we didnt even use c_2 anywhere
marsh citrusBOT
Available help channel!
slate blaze
what do I do here
marsh citrusBOT
what do I do here
brave marsh
Maybe draw it? I feel like it will help you visualize it.
At the end of the day it's just Pythagoras Theorem, but for a) it should be fairly easy since the x coordinate is the same...
slate blaze
At the end of the day it's just Pythagoras Theorem, but for a) it should be fair...
can I use the distance formula?
slate blaze
The distance formula is Pythagora's Theorem.
so I just simply use the distance formula and I'll get my answer?
brave marsh
Yes.
marsh citrusBOT
@slate blaze Has your question been resolved?
late geode
you're not applying distance formula correctly
pay attention to what you wrote for the value of x_2
fair delta
how do u figure out angle DAB
marsh citrusBOT
how do u figure out angle DAB
late geode
ABCD is a cyclic quadrilateral
an expression for DAB can be obtained from that
late geode
you'll have expressions for all four angles in quadrilateral ABOD,
you can set up an equation/ relation between x and y from that
solving that for y will give you what they want
fair delta
ah ok i went wrong somewhere with the addition, was way easier than i was doing it
thanks for the help
marsh citrusBOT
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ebon shuttle
does this look right?
marsh citrusBOT
does this look right?
vagrant gull
,rccw
elfin berryBOT
marsh citrusBOT
@ebon shuttle Has your question been resolved?
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grizzled stump
marsh citrusBOT
grizzled stump
I'm confused as to why this is wrong
I'm almost sure this answer should be correct
marsh citrusBOT
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oblique geyser
If log10(log10 x) = 2, then log10 x = 10^2 = 100 and so x = 10^100
marsh citrusBOT
If log10(log10 x) = 2, then log10 x = 10^2 = 100 and so x = 10^100
oblique geyser
I don't understand this statement
I get the second half but how does
log_10(log_10 x) = 2 go to
log_10 x = 10^2
nvm
.close
marsh citrusBOT
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mossy kestrel
marsh citrusBOT
mossy kestrel
Hi i need help with this
im not sure what the 2nd statement is and the reasoning behind it.
Any help would be appreciated!
<@&286206848099549185>
what.....
still temple
<@&268886789983436800> user is spamming help channels with this
marsh citrusBOT
@mossy kestrel Has your question been resolved?
mossy kestrel
<@&268886789983436800> user is spamming help channels with this
oh sorry
will close
pls reply <@&286206848099549185>
marsh citrusBOT
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acoustic crown
How would you find the solution to x^2 * (ln(x)-1/2) - 5/2 = 0
marsh citrusBOT
How would you find the solution to x^2 * (ln(x)-1/2) - 5/2 = 0
cunning basin
approximate
acoustic crown
is this as far as you can go with just algebra and rewriting stuff?
u mean to say that there is no "easy" solution?
mossy kestrel
why was my channal closed
stoic saddle
why was my channal closed
you were gone for too long
lucid zenith
u mean to say that there is no "easy" solution?
there is a closed form for the solutions, but they involve the Lambert W function, I suppose
stoic saddle
and didnt press ❌ on the bot prompt
mossy kestrel
oh
acoustic crown
.close
marsh citrusBOT
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shut sleet
Help, in class rn lol. What's x when 8x + 2x = 12x?
marsh citrusBOT
Help, in class rn lol. What's x when 8x + 2x = 12x?
shut sleet
pls explain
hardy knot
Since 10x = 12x, the only possible x is 0
keen pulsar
x can be any no.
shut sleet
Okay ty, had a hard time solving this lmao
shut sleet
So I have to put an explanation that x = 0 cu, 10x = 12x?
hardy knot
8 + 2 = 10
marsh citrusBOT
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tribal raptor
Show that if the number on the LHS of the euclidean theorem is $a$, then the number on the LHS two lines down must be less than $\frac{a}{2}$.
marsh citrusBOT
Show that if the number on the LHS of the euclidean theorem is $a$, then the num...
elfin berryBOT
vin
elfin berryBOT
vin
tribal raptor
have to prove r1 is less than a/2
marsh citrusBOT
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stoic saddle
. @cloud pumice post here
cloud pumice
okay
stoic saddle
now you can post your question(s)
stoic saddle
we can't help you from a single word
give us a picture or screenshot of the problem
cloud pumice
cloud pumice
no i learn in mexico with my abuela
cloud pumice
oh ok
marsh citrusBOT
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marsh citrusBOT
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still temple
The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of
the curve through the point (1, 1) is
marsh citrusBOT
The x-intercept of the tangent to a curve is equal to the ordinate of the point ...
hardy knot
The x-intercept of the tangent to a curve is equal to the ordinate of the point ...
So the x intercept is the same for the tangent and the curve?
still temple
mhm
hardy knot
You mean the equation of the tangent of the curve at 1,1 is, right?
still temple
uh wait
not necessary
1,1 is some point on that curve
basically ik that using differential equation we can get the equation
with constant of integration
and when we put x=1,y=1 we get the integration constant c and hence the equation of the curve
thats what i think
but my answer dont match
i took tangent from some random point which also lies on the curve (x,y)
still temple
So the x intercept is the same for the tangent and the curve?
my bad
x intercept is equal to the y cordinate from which the tangent is drawn
x intercept of the tangent
not of curve
now maybe thats clear ?
hardy knot
So x = y?
hardy knot
I'm sorry if I don't understand
still temple
yeah its fine
you can give it a try
even i dont know the answer
you want options ?
hardy knot
The x intercept is equal to the y corrdinate of which the graphs touch each other?
And yeah sure
still temple
The x intercept is equal to the y corrdinate of which the graphs touch each othe...
yeah
hardy knot
Ohhhhh
still temple
the line and the curve
hardy knot
But wait, where on the curve does that happen?
still temple
question 13
still temple
But wait, where on the curve does that happen?
i am not sure if its 1,1 or
any point on the curve
hardy knot
The distance of a point from the x-axis scaled with the y-axis is called the ordinate or y coordinate of the point. For example, if (x, y) is an ordered pair in the Cartesian plane, then the first coordinate in the plane (x) is called the abscissa and the second coordinate (y) is the ordinate.
Is what I got from Google
So just x = y? which I don't understand since that would just mean it happens at maxima
lucid zenith
the question means that at the point (1,1), the tangent is parallel to the x axis
i.e it's slope = 0
should be enough
still temple
@hardy knot exactly what you told
still temple
should be enough
can you help me a bit more in figuring out the exact equation ?
cloud field
the question means that at the point (1,1), the tangent is parallel to the x axi...
shouldnt it be parallel to the y-axis instead?
marsh citrusBOT
@still temple Has your question been resolved?
cloud field
@still temple ok so i tried this question for a bit, and i reached a point where i need to solve a differential equation
dy/dx = y / x-y
marsh citrusBOT
@still temple Has your question been resolved?
cloud field
@still temple ok i think i got it
you need to use the equation for the tangent line
y - y1 = m(x-x1), where m = f'(x1)
rearrange it into the form y = mx + c
then use the fact that x-intercept is equal to y-value of point of contact
after that, write f'(x) as a function of x and y
then solve the differential equation, the constant of integration and you get your answer
cloud field
and yes i did solve that differential equation
still temple
option matches ?
cloud field
yep
cloud field
it was good
cloud field
ok
still temple
yay
i would like to ask you small doubts
wont annoy you
dont worry bud
anyways lemme close this
someone might need this ticket
bye!
.close
dusky viper
$-\frac{1}{2}±\frac{sqrt{3}}{2}i$
marsh citrusBOT
$-\frac{1}{2}±\frac{sqrt{3}}{2}i$
elfin berryBOT
Galaxy
dusky viper
oh well
vernal forge
\sqrt
dusky viper
anyways, how do i determine the argument for this
vernal forge
$-\frac{1}{2}±\frac{\sqrt{3}}{2}i$
elfin berryBOT
artemetra
vernal forge
anyways, how do i determine the argument for this
divide the imaginary part by the real
dusky viper
$-\sqrt{3}$
elfin berryBOT
Galaxy
dusky viper
-pi/3
vernal forge
oh wait ±
vernal forge
2pi/3 is the same thing as -pi/3
dusky viper
yeah my brain has gone flat, how do i solve for that
vernal forge
because if it's an argument of a complex number, it must lie within $(-\pi; \pi]$
elfin berryBOT
artemetra
vernal forge
yeah my brain has gone flat, how do i solve for that
huh?
you... aren't really supposed to get 2pi/3
but if you insist
look at the unit circle
dusky viper
?
2pi/3 is the answer im meant to get an -pi/3 sits on the bottom right quadrant no?
dusky viper
2pi/3 sits on the top left quadrant?
marsh citrusBOT
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dusky viper
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dusky viper
$w=cos\frac{2\pi}{3}+isin\frac{2\pi}{3}$
marsh citrusBOT
$w=cos\frac{2\pi}{3}+isin\frac{2\pi}{3}$
elfin berryBOT
Galaxy
elfin berryBOT
Galaxy
lucid zenith
!status
marsh citrusBOT
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
idk where to begin, never squared in mod arg form before
lucid zenith
well
night mica
for $w^2$ just double the angle
elfin berryBOT
everg
dusky viper
for $w^2$ just double the angle
does i get squared?
night mica
ye because there is a square in the task
dusky viper
aight well i did something wrong
i ended up with $1-\frac{1}{2}+\frac{\sqrt{3}}{2}i+\frac{1}{2}-\frac{\sqrt{3}}{2}
oops
$1-\frac{1}{2}+\frac{\sqrt{3}}{2}i+\frac{1}{2}-\frac{\sqrt{3}}{2$
elfin berryBOT
Galaxy
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dusky viper
ffs i fucked up again
$1-\frac{1}{2}+\frac{\sqrt{3}}{2}i+\frac{1}{2}-\frac{\sqrt{3}}{2}$
elfin berryBOT
Galaxy
proper zodiac
note that 1 + w + w^2 is a geometric sum
dusky viper
?
sour relic
$\sum_{i=0}^{2} w^{i}$
elfin berryBOT
Fucktalogist
dusky viper
i dont get how this helps me
marsh citrusBOT
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dusky viper
.close
smoky frigate
Could someone elaborate this? I'm unsure about how they got to this final answer.
marsh citrusBOT
Could someone elaborate this? I'm unsure about how they got to this final answer...
carmine sinew
let $z=x+yi$ then $|z| = \sqrt{x^2 + y^2}$
elfin berryBOT
SKELEROY
carmine sinew
so in this case we have $|(x-4) + (y-3)i|$
elfin berryBOT
SKELEROY
carmine sinew
thus we get $\sqrt{(x-4)^2 + (y-3)^2} = 3$
elfin berryBOT
SKELEROY
carmine sinew
which evaluates to $(x-4)^2 + (y-3)^2 = 9$
elfin berryBOT
SKELEROY
smoky frigate
**SKELEROY**
How did you get to this? 
carmine sinew
grouping real and imaginary terms
so rewrite as $x-4+iy -3i$ and then factor the i $x-4 +i(y-3)$
elfin berryBOT
SKELEROY
carmine sinew
Also in general any equation with form $|z-u|=r$ where $u \in \mathbf{C}$ will be a circle centered at $(Re(u),Im(u))$ with radius $r$
elfin berryBOT
SKELEROY
smoky frigate
**SKELEROY**
So you square everything here to get rid of the i?
But why doesn't it give you ... -(y-3)^2 then?
carmine sinew
ahh that's because of how $|z|$ is defined
elfin berryBOT
SKELEROY
smoky frigate
Hmmmm but I don't see any Z in your second step?
Sorry I'm pretty unfamiliar with complex numbers. I find them quit difficult to understand
carmine sinew
No don't stress!
smoky frigate
crappy diagram time
Oh yeah I remember something like that yeah, indeed. But why is that needed in this case?
carmine sinew
So the pythag is used to compute the magnitude (which is the |...|)
To like shift it back a little lets say $z=1+i$ then by pythag $|z|=\sqrt{1^2 + 1^2}$ as $1+i$ is a line segment that has been shifted to the right by 1 unit and up by 1 unit
elfin berryBOT
SKELEROY
carmine sinew
|z| is just the "length" of the complex numbers
smoky frigate
Oh so when you are given something like Z = 2 +2i
Then the magnitude would be |Z| = \sqrt(2)^2 + (2)^ = 2?
Correct?
And with my original question it's just the other way around, right?
carmine sinew
yes exactly! what do you mean the other way around though?
smoky frigate
Yeah you are giving the magnitude |Z|, and you need to find Z?
carmine sinew
in your problem $z=(x-4) + (y-3)i$ right so $|z|=\sqrt{(x-4)^2 + (y-3)^2}$
elfin berryBOT
SKELEROY
carmine sinew
ok so we aren't trying to find z here
smoky frigate
**SKELEROY**
No we were given |Z|???
carmine sinew
we are actually trying to find the equation of the locus of points that satisfy $|z-4-3i|=3$
elfin berryBOT
SKELEROY
smoky frigate
And by locus you mean Z? Sorry, never heard of that.
carmine sinew
ok so a locus is an equation that satisfies a certain condition
so basically say we were given $|z|=3$
elfin berryBOT
SKELEROY
carmine sinew
what this essentially means is that find all the points on the complex plane, such that the magnitude of those numbers are all =3
smoky frigate
Ah yes, check
carmine sinew
so in your problem its the same thing, except we have subtracted 4+3i from z
so now it's saying "What complex numbers z satisfy the equation such that all complex numbers of z subtracted by 4+3i have a magnitude of 3"
so for instance z=-4 satisfies this equation
however we need a bunch more points
so we let $z=x+yi, x,y \in \mathbf{R}$ as a way of denoting that z can be any generic complex number
elfin berryBOT
SKELEROY
carmine sinew
then we substitute z = x+yi into your original equation
Then we get a relation that successfully adheres to the conditions of the locus
which happens to be a circle of radius 3 around 4+3i
smoky frigate
So if I understand correctly, what we have found earlier is the radius. And now we just need to find the X and i and add those together to get the final answer?
carmine sinew
smoky frigate
Wait an equation for the circle or the location of the circle?
carmine sinew
equation for the circle
in cartesian form
you can think of -4-3i like a transformation on z
which shifts it 4 to the right and 3 units up
smoky frigate
Hmmm. Okay. Well I might have to take another look at the book maybe. 😅
Think this is a bit next level for me at the moment.
Thanks for your help. Though I have one more question.
I tried the following approach first. Is that also possible?
If I square both sides of the original equation, I get:
x^2 -y^2 + 16 + 9 = 9
Which results in: x^2-y^2+16 =0
Tho I got stuck there
carmine sinew
nope cause this gets you a conical hyperbola
smoky frigate
So there's no possible way to write it as the final answer?
carmine sinew
nah cause they aren't the same type of graph even
smoky frigate
Hmmm okay
carmine sinew
smoky frigate
Well, I'll take another look at the book then. I really do appreciate your help
I don't want to waste your time even more 
carmine sinew
Nahhhh I ain't busy right now its past midnight anyways
I just do pracitce exams during the day to prep for my VCE exams
smoky frigate
Ah okay. That sounds crazy. I got my first analysis exam next week about this subject.
So if you have some more time, could please elaborate what you do in this step?
carmine sinew
of course!
from the initial equations $|z-4-3i|=3$ we let $z=x+yi, x,y \in \mathbb{R}$
elfin berryBOT
SKELEROY
carmine sinew
why? because z = x+yi can represent any point on the complex plane
smoky frigate
Is that a basic rule? z = x +yi?
carmine sinew
yes! when you are in doubt for a locus problem or a difficult solving problem, z=x+yi works well
cause essentially you are just letting z be an arbitrary complex number
smoky frigate
Thanks will write that down
carmine sinew
ok so after that step we can sub it in to get $|x+yi-4-3i|=3$ which gives $|x-4+(y-3)i|=3$
elfin berryBOT
SKELEROY
carmine sinew
making sense so far?
smoky frigate
Check, got it
carmine sinew
ok! Then by definition $|a+bi|=\sqrt{a^2 + b^2}, \forall a,b \in \mathbb{R}$ thus $\sqrt{(x-4)^2 + (y-3)^2}=3$
elfin berryBOT
SKELEROY
smoky frigate
Ah yes, and that lenght you wrote there = |x+yi-4-3i|
carmine sinew
precisely!!!
smoky frigate
Ah yeah now I finally see how that phytagoras works the other way around
carmine sinew
so what the final rule tells us is the collection of points that are a distance of 3 units away from 4+3i is satisfied by all points on the circle defined by $(x-4)^2+(y-3)^2=9$
elfin berryBOT
SKELEROY
carmine sinew
which should also make some intuitive sense! cause all the points on the circle from its centre has the distance of the radius from the centre
carmine sinew
no problem!!! don't hesitate to ask anything else to me if you'd like 🙂
smoky frigate
Cheers, will first get some more practise in! ;P
carmine sinew
Haha sounds good 👍
smoky frigate
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marsh citrusBOT
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ionic mountain
3x+5y=10 3y+y=5
marsh citrusBOT
3x+5y=10 3y+y=5
round brook
3x+5y=10 3y+y=5
What help do you need with this?
still temple
3x+5y=10 3y+y=5
3y+y=5 second equation no typos?
still temple
go on
ionic mountain
so it be 3x+5(5-3x)=10
right
and i need to slove this
is that all
and is ap math a good ap to take
still temple
so it be 3x+5(5-3x)=10
yh
hard gull
it would be faster if u subtracted first equation from second
ionic mountain
but does that work either way
waxen dust
but does that work either way
Of course.
You went with the substitution method
JustToPro suggested substracting equations which would get rid of x - the elimination method
waxen dust
By substitution?
ionic mountain
yes