how do i factor this
#help-26
tardy vapor
topaz sinewBOT
how do i factor this
tardy vapor
this is my work so far
don’t get how to factor {-8a^3+24a^2}
like when i do it it gives me 8a^2(-a+3)
which doesn’t cancel out with anything unless i take out a -1
but idk how to do that in this instance
tardy vapor
yeah i tried that but it doesnt give me the right answer
it’s supposed to be
-a+5 / 4(a+2)
polar pewter
looks like the negative sign was moved to the numerator
what you have written down is equivalent
just needs one more step of simplification
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tardy vapor
?
tardy vapor
<@&286206848099549185>
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cedar kindle
how do i factor this
do you still need help w this
tardy vapor
do you still need help w this
yea
tardy vapor
div
cedar kindle
uhh okay sorry for taking a while
but i think i have it
im not 100% but like
let me rewrite it rq so its like legible
ok jk ignore the last part of that
i think u just leave it as (a-5) / -4(a+2)
i like defaulted to setting it equal to 0 for some reason
tardy vapor
i like defaulted to setting it equal to 0 for some reason
yeah thats what i got too but the key says its (-a+5)/4(a+2)
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ivory sorrel
$\lim_{\omega\rightarrow\infty}\left(\frac{e^{kw^2x^2}}{\int_a^be^{kw^2x^2}dx}\right)$
topaz sinewBOT
$\lim_{\omega\rightarrow\infty}\left(\frac{e^{kw^2x^2}}{\int_a^be^{kw^2x^2}dx}\r...
thorny flameBOT
Why am. I here
ivory sorrel
prove that this is 0 if x<b
and $\infty$ if x=b
thorny flameBOT
Why am. I here
thorny flameBOT
Why am. I here
gleaming thunder
approximate the integral intelligently, using the fact exponentials grow crazily
Feels intuitive, try to make a proof out of it
ivory sorrel
approximate the integral intelligently, using the fact exponentials grow crazily...
hmm, OK. Thanks!
gleaming thunder
x < b and x > b should be fairly simple
x = b is where things get trickier
ivory sorrel
hmm, let me try x<b first
to find the limit do I actually have to evaluvate the integrals?
ivory sorrel
hmm I'd probably use the fact that the denominator tends to $\infty$ no matter the values of a and b , if b>a; to prove that the limit is 0?
thorny flameBOT
Why am. I here
gleaming thunder
the numerator and denominator have similar behavior
since denominator / (b-a) is between e^(kw²a²) and e^(kw²b²)
so it's all about the value of x
ivory sorrel
isn't it about the value of $\omega$ here, as that's tending to $\infty$
thorny flameBOT
Why am. I here
ivory sorrel
yeah, so if b>a, the denominator will tend to $\infty$ won't it? That leaves the question of what to do with the numerator
thorny flameBOT
Why am. I here
gleaming thunder
yeah, so if b>a, the denominator will tend to $\infty$ won't it? That leaves th...
why is that a question
ivory sorrel
Because I'm not too sure of what to do beyond this
gleaming thunder
solve it for x = (a+b)/2
See how that method can be generalized for a < x < b
gleaming thunder
there is no x in the denominator
ivory sorrel
there is in the power of the integrand, isn't there?
gleaming thunder
yes there is because you clumsily create an ambiguity by having two coexisting x's in the same expression
so fix that and make it t
gleaming thunder
there is no x in the denominator
now this holds
gleaming thunder
so I fix x?
x is fixed anyways
I'm just hoping this helps you visualize it, since it implies we solve this problem at fixed x
as opposed to some other methods
ivory sorrel
hmm, so when a<x<b, the numerator would be less than the denominator, with the numerator tending to a larger infinity
if that makes sense
gleaming thunder
no it doesn't
Not to me
the numerator is between the min and max of the integrand
so you need to study the integrand
ivory sorrel
ah, OK
gleaming thunder
this is an exponential for a reason
ivory sorrel
I'm still not sure I get it
gleaming thunder
what did you draw ?
ivory sorrel
$\frac{e^{kw^2t^2}}{e^{kw^2a^2}}\le\frac{e^{kw^2\left(t\right)^2}}{\int_a^be^{kw^2x^2}}\ \le\frac{e^{kw^2t^2}}{e^{kw^2b^2}}$
thorny flameBOT
Why am. I here
gleaming thunder
that's not what I meant with x and t thing but whatever
ivory sorrel
oh, is this an application of the sandwhich theorm
gleaming thunder
**Why am. I here**
also this is wrong on quite a few levels
gleaming thunder
since denominator / (b-a) is between e^(kw²a²) and e^(kw²b²)
however stating the obvious won't quite suffice
ivory sorrel
**Why am. I here**
oh, is the LHS of the inequality right though?
$\frac{e^{kw^2t^2}}{e^{kw^2a^2}}\le\frac{e^{kw^2\left(t\right)^2}}{\int_a^be^{kw^2x^2}}\ \le\frac{e^{kw^2t^2}}{e^{kw^2b^2-e^{kw^2a^2}}}$
thorny flameBOT
Why am. I here
ivory sorrel
would this be right?
gleaming thunder
part of me thinks this is worse
Part of me is confused
There's hardly a part of me that sees this as an improvement
Mainly confusion
topaz sinewBOT
ivory sorrel
.reopen
topaz sinewBOT
✅
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gleaming thunder
ok, so what exactly did I do wrong here?
feel free to ping me when you reopen
topaz sinewBOT
✅
ivory sorrel
feel free to ping me when you reopen
Thanks, where did I go wrong?
gleaming thunder
$\frac{e^{kw^2t^2}}{e^{kw^2a^2}}\le\frac{e^{kw^2\left(t\right)^2}}{\int_a^be^{kw...
here
I disagree with all 3 stated inequalities
ivory sorrel
hmm,OK. thanks
$e^{kw^2a^2}<\int_a^be^{kw^2x^2}<e^{kw^2b^2}$
this is true, right?
gleaming thunder
no
thorny flameBOT
Why am. I here
ivory sorrel
now?
gleaming thunder
did you just remove the dx ?
ivory sorrel
yeah
gleaming thunder
wtf
gleaming thunder
$e^{kw^2a^2}<\int_a^be^{kw^2x^2}<e^{kw^2b^2}$
would this hold for a constant function ?
ivory sorrel
hmm, if $a<x<b$ then yes
thorny flameBOT
Why am. I here
gleaming thunder
explain
thorny flameBOT
Why am. I here
gleaming thunder
hence ?
ivory sorrel
tbh, I'm not too sure of what to do from here
gleaming thunder
$e^{kw^2a^2}<\int_a^be^{kw^2x^2}<e^{kw^2b^2}$
You forgot the b-a !
gleaming thunder
$\frac{e^{kw^2t^2}}{e^{kw^2a^2}}\le\frac{e^{kw^2\left(t\right)^2}}{\int_a^be^{kw...
you forgot it here too !
you forgot it all this time
and it's gonna matter for x=b, so you better not forget it
gleaming thunder
$\frac{e^{kw^2t^2}}{e^{kw^2a^2}}\le\frac{e^{kw^2\left(t\right)^2}}{\int_a^be^{kw...
and then you also forgot that taking the inverse inverses the comparisons
ivory sorrel
why do I divide by (b-a)?
ah, ok
got it
so. $e^{kw^2a^2<\left(b-a\right)e^{kw^2c^2}<e^{kw^2b^2}}$?
thorny flameBOT
Why am. I here
ivory sorrel
nvm, just realised there's a hint. I apparently sub z=$kw^2x^2$, and then L'hopital it( How that would work with finite limits is beyond me)
thorny flameBOT
Why am. I here
pulsar sun
Btw b and a both approach 0
Reasoning: as omega approaches infinity, the function basically tends towards a straight line lieing on the y axis. So it's gonna have a very small domain near 0
ivory sorrel
Reasoning: as omega approaches infinity, the function basically tends towards a ...
ah, OK. Thanks!
pulsar sun
U can see this on a graph in geogebra/desmos
Set a parameter a and plot e^(a^2 * x^2)
At a = 100 itself the domain of the function does not go beyond 2
gleaming thunder
Reasoning: as omega approaches infinity, the function basically tends towards a ...
it's just a substitution
pulsar sun
The function diverges beyond 2
pulsar sun
it's just a substitution
Huh?
gleaming thunder
u = t/w²
gleaming thunder
Reasoning: as omega approaches infinity, the function basically tends towards a ...
how big the function gets does not change its domain
pulsar sun
how big the function gets does not change its domain
Why does it diverge near x=2 then
gleaming thunder
At a = 100 itself the domain of the function does not go beyond 2
it does
gleaming thunder
f(3) = e^(90000) is well defined for instance
pulsar sun
Hmm but the graph of the function shows quite a different story
gleaming thunder
how big the function gets does not change its domain
it's just your inability to plot it
gleaming thunder
Hmm but the graph of the function shows quite a different story
plot its log then
pulsar sun
That's just a parabola
gleaming thunder
defined everywhere
pulsar sun
True
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patent light
How many bits are needed to encode a choice from 18 possible ones
values?
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How many bits are needed to encode a choice from 18 possible ones
values?
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outer ledge
How many bits are needed to encode a choice from 18 possible ones
values?
32 bits, right ?
@patent light
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rough crescent
can anyone help me understand how $\vec{r}\cdot d\vec{l}= r\cdot dr$ ?
thorny flameBOT
Sora
rough crescent
do i have to think about it as $r dl \cos{\theta}$ so that $dl\cos{\theta}=dr$?
thorny flameBOT
Sora
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still vortex
A mass weighting 40 lbs stretches a spring 4 inches. The mass is in a medium that exerts a viscous resistance of 94 lbs when the mass has a velocity of 4 ft/sec.
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A mass weighting 40 lbs stretches a spring 4 inches. The mass is in a medium tha...
still vortex
I need help with this problem. The way I setup is 40y''+94y'+120y=0 and y(0) = 5/12 ft, y'(0) = 4 ft/s. Is that wrong? Im missing the answer. Thank you
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willow helm
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willow helm
is this correct so far
brisk terrace
Is it k times 2 or k squared?
brisk terrace
Understood.
Do you know the formula for exponential growth?
willow helm
Understood.
Do you know the formula for exponential growth?
y0 e^kt
what i did in the picture is finding k using the information about how many there were after 3 hours and after 5 hours
brisk terrace
Correct so
10000 = y0 × e^4800k ... 4800 is the number of seconds in three hours.
40000 = y0 × e^18000k...
So you'll need to solve for k first.
willow helm
Correct so
10000 = y0 × e^4800k ... 4800 is the number of seconds in three hour...
why does it need to be in terms of seconds
and also with 2 unknown values how would you solve for k
y0 and k being unknown in both of those cases
brisk terrace
You use seconds to make your answer more accurate. You can do milliseconds if you want to get an even more accurate answer.
But you can solve k by setting up a ratio...
40000/10000 = (y0 × e^18000k) / (y0 × e^4800k)
What happens to y0 here?
willow helm
cancel
brisk terrace
Correct so now you can solve for k 🙂
Just remember your properties of exponents...
e^a / e^b = e^(a-b)
So 18000k - 4800k = 13200k
willow helm
k = ln4/13200
brisk terrace
Remember when we said:
10000 = y0 × e^4800k?
Now that we have k, you plug that in to solve for y0.
brisk terrace
No worries 🙂
shadow hare
Can someone help me with this
brisk terrace
@shadow hare
This room is occupied. Please open your own help room 🙂
willow helm
wait no i'm confused again
brisk terrace
How so?
You said yourself that that the formula was
y = y0 × e^kt
willow helm
brisk terrace
So you're going to use 3 hours instead of 4800 seconds? I mean, that's fine but it'll give you a less accurate answer.
willow helm
ofc i can convert it if i need to
i just want to know moreso the process to getting the answer
willow helm
does this look good?
brisk terrace
Yes, your answer is correct, albeit less accurate 🙂
y0 should be around 6000 or so
Which makes sense because it's less than 10000 at 3 hours.
brisk terrace
Okay actually since you used seconds before, try doing 4800 instead of 3
willow helm
brisk terrace
I think because you used seconds before to solve for k, you should probably use seconds again.
willow helm
okay tysm for the help
brisk terrace
You're welcome 😊
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golden sky
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golden sky
Did I make a calc error
vernal matrix
How did you go from tan^2[(x)] + 2tan(x) - 5 = 0 to tan(x) = -6.3785 and 1.0452?
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vast garden
question is to find lambda
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question is to find lambda
vast garden
idek where to start
bitter hemlock
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crisp kelp
gy n9gg
slim echo
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dim kindle
I came here two days ago with the third exercise, and someone gave me a hint about supposing that c and d are a product of a rational and irational part
storm hearth
Ye i did
storm hearth
Any luck with that?
dim kindle
,rotate
thorny flameBOT
dim kindle
I get to this
But the system of equations that I get don't seems to have a "easy" solution
I am an engineer and I know some numerical methods for this kind of stuff but seems a bit complicated to get it raw algebraically
Some hint to continue?
storm hearth
I have been observing for a bit, cant see a clean way to solve
Feel free to ping other helpers as 15 mins has passed
dim kindle
Are there any ways of solving this not in a clean way?, I think I ll leave this exercise for now but it's good to know if there is some methodology
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<@&286206848099549185>
kindred spade
Are there any ways of solving this not in a clean way?, I think I ll leave this ...
Follow the laws of algebra. You can't use distributive laws on multiplication like that.
Let me see if I can write a solution with explanation.
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kindred spade
Yeah I am trying to solve it. But I can't find my algebra notebook. And I am getting a very morbid mathematical answer.
you can ask for help from others.
Meanwhile I'll trying to find my notebook with laws and stuff.
dim kindle
Okeyy
But what's the problem with the laws?
I have just applied the newtons binomial and then split the equation to a system of equations in rational and irational part
kindred spade
But what's the problem with the laws?
I think I misread your first step.
dim kindle
I think I misread your first step.
I was thinking you did hahaha
No problem
<@&286206848099549185>
dim kindle
The third exercise I don't know how to get the c and d terms
dim kindle
Someone pointed that I may suppose c and d a product of a rational and a irrational part and then split that into a system of eq
But that system isn't easy to solve either
Hahahahahaha
Okey
Thanks
<@&286206848099549185>
solar tiger
STOP PINGING EVERY 2 SECONDS
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ember elbow
Wat
thorny flameBOT
dim kindle
This one
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carmine star
!help
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uneven sandal
A 2 kilo piece of ham costs 48 dollars.
A 150 gram portion of this ham will cost?
topaz sinewBOT
A 2 kilo piece of ham costs 48 dollars.
A 150 gram portion of this ham will cost...
neon iron
how many grams are there in one kilo?
uneven sandal
Anyone knows an easier way to do this without 3 rule?
granite hull
let 45 cook
neon iron
thank you
uneven sandal
how many grams are there in one kilo?
I know the answer, it's very easy but do you know an easier and faster way to do this?
neon iron
that is the easy and fast way
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hallow shuttle
not a question but whats this property called
topaz sinewBOT
not a question but whats this property called
thorny flameBOT
45
neon iron
$(ab)^n = ababab\hdots ab$, $n$ times. Since multiplication of real numbers is commutative this reduces to $a^n b^n$
thorny flameBOT
45
topaz sinewBOT
outer salmon
not a question but whats this property called
Product property of square roots is the most specific term
Basically an extension of the other property mentioned, but still has its own name
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fickle shoal
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fickle shoal
in this graph there is the function f(x) in domain 0<= x <= π
x= π and x = π/2 and x=0 are all assymptotes to the function
to function f(x) f'(x) and f''(x) they have all the same domain
let the line x= π/4 pass through the minimum point of f(x) and the line π/8 intersect the f(x) at a point where its y is (18.4776).
the area between f'(x) x axis and the line x π/8 is 4.335
what is the y value of the minimum point in f(x)
i began drawing the function f'(x) for us to work better with the integral
that would represent f'(x)
crude anchor
the area between f'(x) x axis and the line x π/8 is 4.335
Is it between x=0, x=pi/8 y=f’(x) and y=0?
fickle shoal
im not sure about x=0
crude anchor
Or between pi/8 and pi/4?
fickle shoal
it said between graph of f'(x), the x axis and the line x = π/8
crude anchor
Ok but that doesn’t make sense
That would be an infinitesimally thin line
Which has no area
crude anchor
Yeah but that doesn’t change anything about what area is being represented
fickle shoal
i think we could somehow draw it to make sense
crude anchor
Well we know the area is positive so I guess it must actually be between pi/8 and pi/2
crude anchor
What?
crude anchor
Well that line wouldn’t go through 0,0 either
crude anchor
It’s just a. Vertical line
fickle shoal
yeah
crude anchor
Halfway between pi/4 and 0
fickle shoal
wouldnt that make the area negative?
crude anchor
That’s my point is we don’t know what the 4th boundary is
Do you see my issue now?
With only 3 lines there is no area enclosed
We need to know what the fourth line it
Is it x= pi/2 is it x=1?
crude anchor
It can’t be x=pi/4 because then the area is negative
And it can’t be 0 for the same reason
I guess maybe it’s pi/2
It could be pi though as well
Or any value between pi/2 and pi
I don’t get why the question wouldn’t have that information
fickle shoal
maybe they meant the area above x axis where it stops whenever the π/8 line touches f(x)
but then they would also say area between f(x)
and all the other stuff
crude anchor
Was the original in English? Did you copy it verbatim or translate?
Or maybe paraphrase
fickle shoal
the original isnt in english
it is well translated by me 🙂
jk i dont think i have made any mistakes tho
crude anchor
What language
fickle shoal
it is german
crude anchor
Maybe someone else speaks it, I only speak English myself
I’m sure someone here speaks German
So at least send it
fickle shoal
100% i wrote every single detail
what would u assume if that was written in your test
crude anchor
I would think the prof was trolling me tbh
fickle shoal
ignore the fact u could ask a supervisor
crude anchor
Lmao
fickle shoal
hahahah
crude anchor
There’s not enough information I don’t think
I guess I might choose pi/2 as the upper bound on the integral
And go from there
Just try
fickle shoal
lets try and maybe get the answer from the answer key lol
crude anchor
So I guess you can deduce that the integral of f’(x) from pi/8 to pi/2 = 4.335
But this is an improper integral so I guess we would have to do a limit technically on the pi/2 upper bound
fickle shoal
nope the value i got isnt it
wierd
thats a wierd question tho
thanks for trying to help
.close
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junior spade
Hello!
I am actively playing a game that recently released and I was trying to dig a little bit deeper into the calculation of certain stats, since they don't publicly reveal any formulas about these.
I gathered a bunch of data points for this purpose, but I need some advice on how I can attempt to derive a formula or just a very good estimate from this (if possible)
{
"1": [10, 16.4, 20.8, 24.0, 26.5, 28.4, 30, 30, 31.3],
"7": [1.8, 3.4, 4.9, 6.3, 7.6, 8.8, 10.0, 11.1, 12.1],
"13": [1.0, 1.9, 2.8, 3.6, 4.4, 5.2, 6.0, 6.7, 7.4],
"18": [0.7, 1.4, 2.0, 2.7, 3.3, 3.9],
"21": [0.6, 1.2, 1.8, 2.3, 2.9, 3.4],
"22": [0.6, 1.1, 1.7, 2.2, 2.7, 3.3],
"23": [0.5, 1.1, 1.6, 2.1, 2.6, 3.1],
"24": [0.5, 1.0, 1.5, 2.0, 2.5, 3.0],
"25": [0.5, 1.0, 1.5, 2.0, 2.4, 2.9],
"26": [0.5, 1.0, 1.4, 1.9, 2.3, 2.8],
"27": [0.5, 0.9, 1.4, 1.8, 2.3, 2.7],
"28": [0.4, 0.9, 1.3, 1.8, 2.2, 2.6],
"30": [0.4, 0.8, 1.3, 1.6, 2.0, 2.4],
"31": [0.4, 0.8, 1.2, 1.6, 2.0, 2.3]
}
To explain the format I saved these datapoints in:
The leftmost number followed by a colon indicates the current level the player has.
The values in the array/list following after display how much crit chance % the player has with increasing amounts of the precision stat (from 1 to 6)
Example: "18": [0.7, 1.4, 2.0, 2.7, 3.3, 3.9]
At Level 18, the player has 0.7% Crit with 1 Precision and 2.7% Crit with 4 Precision
Edit: Closed for now, since I don't wanna take up the channel much longer.
If anyone is interested in helping out, feel free to dm me!
topaz sinewBOT
Hello!
I am actively playing a game that recently released and I was trying to ...
@junior spade Has your question been resolved?
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wraith night
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wraith night
I need help solvving this
oh on which line?
OHH
It says this ones wrong did i mess up the equation?
it says this ones also wrong
neon iron
💀
neon iron
wouldnt you solve for f'(x) then plug in (5,0)
neon iron
wraith night
I always do my math under the assumption im doing the completely wrong thing and then I mess up simple things because i think im going down the wrong path
anyways CLOSO SESAME
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fallow igloo
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neon iron
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neon iron
not sure what they mean
weary crystal
not sure what they mean
it just means to state which x values f is differentiable on
domain is x values
neon iron
what does differentiable mean
weary crystal
the derivative exists at that point
weary crystal
yep
neon iron
and that's because you can't take the derivative of that point right
weary crystal
correcto
neon iron
hmm okay, are sharp points like that the only instance of indifferentiability?
or what exactly is the criteria I suppose is the better question
weary crystal
those and points where the function is undefined yeah
well more than just that
the derivative at $x_0$ is defined by
$f'(x_0) = \lim_{x \rightarrow x_0} \frac{f(x)-f(x_0)}{x-x_0}$
thorny flameBOT
doaby
worthy storm
places with "vertical" (infinite) slope would be another situation, for example x^(1/3) at x=0
weary crystal
so you need the limit to exist from the left and the right
neon iron
i mean in this case -2 is the limit
weary crystal
of f yes
but if you look at what the slope is approaching from the left of -2, that's different than the slope to the right
so the limit is undefined, meaning so is the derivative
that's why sharp points are no bueno
neon iron
the limit should be defined though I don't understand
they're both approaching a common point
from LS and RS
weary crystal
yes, but we're not talking about the function, we're talking about the slope
neon iron
yeah pos/neg slope
weary crystal
look at what the slope of the tangent line is approaching from the left of -2. that's different from the right
so the derivative doesn't exist there
neon iron
hmmm okay that's a good way to think about it
so basically if the slopes are approaching a common point then it is defined at all values
but if not it isn't
an example of this would be the graph of y=x
and the opposite of that would be the graph of y=x^2
weary crystal
an example of what?
weary crystal
y=x^2 is also differentiable everywhere
neon iron
,w plot y=x^2
thorny flameBOT
neon iron
but how come?
from the left side the slope is negative
and from the right it's positive
weary crystal
yes, but you can't just look at one point on each side. this is a limit, so you need to consider slopes super super close to (0,0)
are slopes approaching the same value on each side as you get infinitely close to 0?
thorny flameBOT
weary crystal
here, no matter how close you get to 0 on either side, the slopes on either side don't ever approach a common value
but for x^2, the slopes on either side both get closer and closer to 0
you could do this with concrete numbers if it helps
neon iron
the difference is in the steepness of the curve, which means that for y=x^2 it's easier to approximate is what I think your argument is
weary crystal
lemme show with actual values. the derivative of x^2 is 2x. we are looking at x = 0 to determine if it is differentiable there
so, we should check the limit of the slopes on both sides. when x =0.01, f'(x) = 0.02. When x = -0.01, f'(x) = -0.02
as x gets closer and closer on each side, the derivative gets closer and closer to 0.
however, in the case of |x|, the derivative is -1 everywhere to the left of 0 and positive 1 everywhere to the right. so using the same method as before, if x = 0.01, f'(x) = 1, and if x = -0.01, f'(x) = -1. no matter how small x is, the slopes are different on both sides, and they don't approach a common value
neon iron
I think I get what you mean now
also I had no idea the derivative of |x| was -1
pretty cool
weary crystal
if x < 0 it is
neon iron
oh right
weary crystal
but at 0 the derivative is undefined by the logic I gave above
neon iron
ok I just read the first part of that statement then lol
weary crystal
lol
neon iron
thanks, I think I understand it now
weary crystal
no problemo
neon iron
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help
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
3
restive inlet
lets break this down
because you're not differentiating f,g properly
what rules are you applying in your attempt to differentiate
$$e^{-8x}$$
thorny flameBOT
ℝαμΩℕωⅤ
glossy hollow
Lesson is continuity how to solve for if it is continuous it was never taught to us
topaz sinewBOT
Lesson is continuity how to solve for if it is continuous it was never taught to...
wooden osprey
Lesson is continuity how to solve for if it is continuous it was never taught to...
continuous on what
im assuming R
or only on its domain?
topaz sinewBOT
@glossy hollow Has your question been resolved?
outer ledge
Check the domain if the fundtion, right.
Since $x+5>0$, x>-5. And the function is imaginary for x<-5. And undefined for x=-5. That way, the function is continuous for its domain.
thorny flameBOT
Solomaniac
outer ledge
@glossy hollow
cosmic bloom
does anyone have good study tips for math revision?
topaz sinewBOT
does anyone have good study tips for math revision?
formal cairn
cosmic bloom
ok thanks, I'm new to studing and getting grades on tests and I want to do the best this year so with maths is there a way to set your notes a certain layout or idk
<@&286206848099549185>
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/stop
how i end this
slim ermine
how i end this
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high flame
Hi
high flame
A particle moves with uniform acceleration 0.5m/s² in a horizontal line ABC.The speed of the particle at C is 80m/s and the times taken from A to B and from B to C are 40 and 30s respectively.Calculate velocity at A
Displacement BC
This is the solution I didn't understand.Can anyone help?
@pseudo bear
crystal goblet
,w (80^2-65^2)
crystal goblet
Looks good, but idk why you wrote ans:-6. Velocity at A is 45m/s and displacement BC is 2175m
sweet shard
thorny flameBOT
Result:
2175
No, I didn't want to flood the channel, so I deleted the message afterwards
crystal goblet
Understood the solution
Which part
high flame
A-C one
crystal goblet
Ok, what is the time taken in going from a to c?
crystal goblet
Yes
high flame
Why did subject the u tho
crystal goblet
Because we are trying to find the velocity at A, which is u
U is the initial velocity in the formula v=u+at
high flame
Yea
crystal goblet
And the initial velocity is the velocity at A
Which is what we are trying to find
So we made u the subject
crystal goblet
It just means that the acceleration does not change in that time interval(it stays constant)
The formula v=u+at can only be applied when the object is experiencing uniform acceleration
crystal goblet
What do you mean by "time is constant"
The "t" in v=u+at stands for the "time taken to reach velocity v"
In our case, "t" would stand for "the time taken to reach velocity 80m/s", which is 70s like you had said
crystal goblet
The acceleration does not change
In this case, the acceleration was 0.5m/s^2 for the whole time
high flame
Yea so it is constant
crystal goblet
Yes
crystal goblet
What?
crystal goblet
Yes
crystal goblet
Because it takes 40s to go from A to B
We are using the velocity at B as the initial velocity to calculate the displacement from B to C
high flame
Because it takes 40s to go from A to B
Ohh yea
high flame
We are using the velocity at B as the initial velocity to calculate the displace...
How
Didn't got it
crystal goblet
Because when you are going from B to C, you start at B, and the velocity at the starting point is called the initial velocity
And the velocity at B is the final velocity when you go from A to B
high flame
And the velocity at B is the final velocity when you go from A to B
Yea
And B-C seems the most confusing part to me
crystal goblet
When going from B to C, your initial velocity is 65m/s, do you agree?
high flame
How?65 was the final velocity
crystal goblet
We got to know the velocity at B from the A-B part
In the A-B part, velocity at B was the final velocity
In the B-C part, the velocity at B will be the initial velocity
crystal goblet
Ok, so you agree that the initial velocity when going from B to C is 65 m/s?
What is the velocity at C(final velocity)?
high flame
And there two initial velocities 80 and 65.I understood 65 but 80??
crystal goblet
Look at what is written under v^2
They rearranged the equation to find s
v is 80 and u is 65
So 80^2=65^2+2(0.5)s
high flame
And under V² there is written s but why.And 2×0.5.The thing is I also have problem in subjecting part.Here it is done without the steps
thorny flameBOT
smidgin
high flame
So 80^2=65^2+2(0.5)s
Sorry I don't understand typing ones
thorny flameBOT
smidgin
crystal goblet
I put v=80 and u=65
high flame
Yea
thorny flameBOT
smidgin
crystal goblet
I subtracted 65^2 from both sides
crystal goblet
65 squared
high flame
Ohh
crystal goblet
**smidgin**
Do you agree with this?
high flame
Umm
crystal goblet
**smidgin**
You just agreed with this
I just moved 65 squared to the other side
I am trying to make s the subject
high flame
**smidgin**
Which formula is this
crystal goblet
v^2=u^2+2as
high flame
high flame
**smidgin**
It's the same?
thorny flameBOT
smidgin
crystal goblet
@high flame
crystal goblet
To find velocity at A
high flame
And cuz C has 30s?
crystal goblet
It took 70s to go from A to C
high flame
Yea so it was the total time
crystal goblet
Yes
high flame
And initial velocity of A-C is 45
high flame
Yea
crystal goblet
So we made u the subject
high flame
And 45 is initial velocity in A-B
crystal goblet
Yes
high flame
As it is from the beginning
crystal goblet
Yes
high flame
Ohh now I got it
Can u wait for me.Imma try 6 on my own and then move to next problems and I would tell u if I have any problems
crystal goblet
Can u wait for me.Imma try 6 on my own and then move to next problems and I woul...
Till then you should close this channel, i have to go now
You can ask the other helpers
high flame
Till then you should close this channel, i have to go now
U can't wait?
crystal goblet
No
crystal goblet
And also since it's a new problem, it is always good to open a new channel
crystal goblet
Like can I pin you in other channel
👍🏻
high flame
Btw which country u from
crystal goblet
I prefer not saying, also keep such discussions away from help channels
high flame
Nah I was just asking
crystal goblet
And also since it's a new problem, it is always good to open a new channel
@high flame
high flame
Okay
topaz sinewBOT
daring venture
Hello
high flame
.reopen
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high flame
Wassup
daring venture
What help do u need
high flame
No for now I am trying
daring venture
Alright
high flame
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alpine jetty
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alpine jetty
for b does anyone know why they used the perimeter?
when i was originally solving this i assumed that they wanted the total area of the 2 squares, so A = x^2 + y^2
restive inlet
remember what x and y represent
alpine jetty
the shape right
restive inlet
no
x and y don't represent the shape itself
they represent the perimeter of each square
squaring the perimeter of a square doesn't give its area
alpine jetty
oohhh so x is like the total perimeter
same with y
and they find one side by dividing by 4
restive inlet
yes
topaz sinewBOT
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plush dew
my question is when we consider doing an integral over any interval (considering basic conditions for a function to be integrable beforehand), don't you think that even in that finite interval it is impossible to take all real numbers there and integrate(density property of real numbers)?and from this point of view i think integral will blow up,but nevertheless it gives the precise value of that bounded area. so using math itself(or any other intutive way) can you please redefine things for me such that there is no contradiction like this
i know there has to be a problem in my thought process but i m unable to comprehend it myself
topaz sinewBOT
my question is when we consider doing an integral over any interval (considering...
noble laurel
my question is when we consider doing an integral over any interval (considering...
the integral is not about counting the number of real numbers in some interval of the real line
It seems like that is your confusion
The definition of the Riemann integral is too complex for someone to define for you in a help channel, but you can find many videos and resources defining it online
plush dew
the integral is not about counting the number of real numbers in some interval o...
(i said nothing)
noble laurel
What?
plush dew
u mean infinimumu supremum sums
alpine jetty
💀
noble laurel
Darboux sums can be used to define the integral yes
plush dew
will that solve my prob
noble laurel
Your problem is not well-communicated
plush dew
i think u dont beleive in my problem
noble laurel
No I can't tell what it is
plush dew
can u disprove my statement
plush dew
my question is when we consider doing an integral over any interval (considering...
this
noble laurel
Your statement is not clear
plush dew
if u cant then this means integral has to count them all
then i think integral cant give bounded area
noble laurel
The integral does not count the number of real numbers over a finite interval
as I said earlier
noble laurel
You need to go learn a formal definition of the integral and then you will not have this question
there is no point discussing it here until you've done that
plush dew
<:this:489575168314966026>
i just think it does because in fundamental theorem on integral calculus we take those infinitesimal limts so it has to
noble laurel
You are confused because you do not know the formal definition of an integral
plush dew
which is?
noble laurel
As I said earlier,
noble laurel
Either find your own resource, or you can use this
Read the chapter on integrability, it will have the definition of the Riemann integral there
But unless you have a different question you should close this channel
plush dew
Either find your own resource, or you can use this
ok
plush dew
isnt that definition of sigma changing to integral
isnt this the thing u want me to read
?
noble laurel
No
topaz sinewBOT
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indigo sedge
If the integral of 1/(3-x) is -ln(3-x) why if I multiply by -1/-1 the integral is -1/(x-3) and it equals -ln(x-3) which isn't equal
topaz sinewBOT
If the integral of 1/(3-x) is -ln(3-x) why if I multiply by -1/-1 the integral i...
junior acorn
If the integral of 1/(3-x) is -ln(3-x) why if I multiply by -1/-1 the integral i...
technically it is ln |3-x| and ln |x-3| which are equal
indigo sedge
If ln|3-x| = ln|x-3| what happens when I e both sides cancelling the ln?
|3-x| = |x-3|?
indigo sedge
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wet heron
what is the answer to lim (x+1)/(x^2secx) as x approaches infinity
sonic turret
I asked first fam.
neon iron
what is the answer to lim (x+1)/(x^2secx) as x approaches infinity
Read #❓how-to-get-help . This channel is used for resolving another problem currently.
outer ledge
what is the answer to lim (x+1)/(x^2secx) as x approaches infinity
!occupied
topaz sinewBOT
what is the answer to lim (x+1)/(x^2secx) as x approaches infinity
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
outer ledge
What's your doubt in this ?
@sonic turret
It's a simle conversion of $cos(2x) = 2cos^2(x)-1$
thorny flameBOT
Solomaniac
topaz sinewBOT
@sonic turret Has your question been resolved?
thorny flameBOT
alen8934
neon iron
Ah, I messed upon the typesettting, let me fix it
To expand if it's not obvious, look at the formulas for trig:
$$ \cos{2x} = \cos ^2 {x} - \sin ^2{x}$$
$$ 1 = \sin ^2{x} + \cos ^2{x} \rightarrow \sin ^2{x} = 1 - \cos ^2{x} $$
We just plug it in and get
$$ \cos{2x} = \cos ^2 {x} + \cos ^2{x} -1 $$
thorny flameBOT
alen8934
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atomic kestrel
How do I solve a general linear system of equations with three equations, using pivoting?
topaz sinewBOT
How do I solve a general linear system of equations with three equations, using ...
small nymph
$ X^2
woeful stone
How do I solve a general linear system of equations with three equations, using ...
Gaussian Elimination. A key consideration is what type pivoting you want
topaz sinewBOT
@atomic kestrel Has your question been resolved?
atomic kestrel
Gaussian Elimination. A key consideration is what type pivoting you want
It’s a general system and I’m asked to find the solutionspace and the different conditions there would be on the coefficients for the different solutions
Ie, intersection being a point, line, plane
woeful stone
Yes so Gaussian Elimination. It is a standard algorithm. You will find it in any textbook or course on linear algebra
atomic kestrel
I started on it for a system of 2 linear equations, don’t feel like it makes any more sense like that?
topaz sinewBOT
atomic kestrel
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woeful stone
For your particular case you will have free variable. Any variables that are not pivot-variable or base variables are free variables
What you could do is express the pivot variables using the free variables. So you would have as an answer X = [f(x3), g(x3), x3]
where x3 is the free variable
It is bit hard to explain. Maybe reading a textbook on linear algebra is better
topaz sinewBOT
@atomic kestrel Has your question been resolved?
neon iron
topaz sinewBOT
outer ledge
Use Diophantine.
neon iron
Use Diophantine.
Use what?
outer ledge
Basically putting values into the equation.
ab = -12 right ? How is this possible ?
A= 3 b=-4 and vice versa.
A= 6 and b=-2 and vice versa.
A=12 b=-1 and vice versa.
neon iron
Yeah I've tried that
I got uh
11 as the answer I think
But it's wrong
Wait oh my god
12 - (-1) is 13
I keep making dumb mistakes
Thank you for the help
.close
queen hornet
i know the limit is e but I dont know how to prove it
topaz sinewBOT
i know the limit is e but I dont know how to prove it
chilly walrus
i know the limit is e but I dont know how to prove it
square the sum and take a square root of it
queen hornet
square the sum and take a square root of it
its just 1?
neon iron
No, it's 1+ sin2/n
chilly walrus
a bit more work
chilly walrus
No, it's 1+ sin2/n
yes
queen hornet
No, it's 1+ sin2/n
which sum did he meen?
crystal goblet
The thing in the bracket
neon iron
(sin x + cos x)^2 = sin^2 x + cos^2 x + 2sin x cos x = 1+sin 2x
queen hornet
ok ill try to write it down and see what im doing wrong
wait but its 1/x so I just substetute x for 1/x?
topaz sinewBOT
@queen hornet Has your question been resolved?
queen hornet
yhe idk its not fully working
i see the definition of e in there inside the sqare root sqrt(sin(2/x)+1)
but idk i cant seem to reorgenize it
neon iron
wait but its 1/x so I just substetute x for 1/x?
x=1/n
queen hornet
yhe i got it but i cant simplefy after the sqare root
neon iron
(1+sin 2/n)^(n/2) -> e^(n/2 sin 2/n) -> e^1
queen hornet
(1+sin 2/n)^(n/2) -> e^(n/2 sin 2/n) -> e^1
can you explain how you got here just a little furthur? i understand that the nth power cancelles out with the square root
got it
.close
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fleet turtle
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subtle frigate
Hi. I’m struggling to figure out the answer to this.
topaz sinewBOT
Hi. I’m struggling to figure out the answer to this.
dapper lantern
Remember the definition of sin cos and tan based on sides of triangle
Find the one that fits with the data and solve the equation
subtle frigate
Tan30=h/20?
subtle frigate
Tan=opposite side/adjacent side?
dapper lantern
Is the hypotenuse
subtle frigate
Oh I see so if 20 is the hypotenuse and I don’t have any other value besides 30 what do I do?
dapper lantern
That's literally the problem you have
dapper lantern
Remember the definition of sin cos and tan based on sides of triangle
.
dapper lantern
Find the one that fits with the data and solve the equation
.
subtle frigate
I’m so confused rn
subtle frigate
Omdsss thank you so much!! That was my problem! I was doing the wrong equitation thank you so much!!
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dusky tartan
Hello, I am trying to reverse a result obtained with a function:
f(a, b, c, d) -> s
And I am expecting f(s) -> a, b, c, d
Now, I know that this is may not be possible because let's say you have a + b + c + d = s, you cannot know which numbers were used if you only have s, however I would like to give it a try.
This is the formula to retrieve s by a, b, c, d:
And yes, please excuse that this is java but I do not know how to express it otherwise (it is just math so it shouldn't be too hard to translate.)
public double getResult(double a, double b, double c, double d) {
double aP = clamp(Math.log10(a) / 15, 0, 1000000);
double bP = clamp(Math.pow(b, 0.1) / 500, 0, Double.POSITIVE_INFINITY);
double cP = clamp(Math.pow(c, 0.2) / 1000, 0, Double.POSITIVE_INFINITY);
double dP = clamp(Math.pow(d/ 20, 0.45), 0, Double.POSITIVE_INFINITY);
double wp = aP * bP * cP * dP;
return Math.floor(Math.pow((wp / 1000), 0.4));
}
And I am looking for the inverse of this, which returns AN APPROXIMATE of those 4 (a, b, c, d) based on one value retrieved by top code block.
topaz sinewBOT
Hello, I am trying to reverse a result obtained with a function:
``f(a, b, c, d)...
@dusky tartan Has your question been resolved?
topaz sinewBOT
@dusky tartan Has your question been resolved?
topaz sinewBOT
@dusky tartan Has your question been resolved?
dusky tartan
<@&286206848099549185>
bright hazel
idk
steady quarry
Hello, I am trying to reverse a result obtained with a function:
``f(a, b, c, d)...
Whether or not this is even possible is going to depend heavily on the function; in general, this is only going to work with very specially constructed functions. (Any linear functions, for instance, will not work here.) This is because, intuitively speaking, when you map from 4 numbers to 1 number you lose a lot of information when it comes to most functions, since many different points in R^4 will map to a single point in R under the vast majority of transformations.
I recommend you read up on injective, surjective, and bijective functions.
If a function is not injective it will have multiple points (a,b,c,d) that map to some s, if it is not surjective, some s will have no points that map to it. Bijective functions are ones with both injectivity and surjectivity and they are the only ones with proper inverses. Very few functions are truly bijective between different-dimensional spaces, since unless you carefully store information, you’re either losing information by going to a smaller dimension or you don’t have enough information to fully map to a larger dimension.
topaz sinewBOT
@dusky tartan Has your question been resolved?
neon iron
topaz sinewBOT
neon iron
Im currently using De Moirves theorm but im stuck haha
my first step was to use pythagoreans theorm to find r, which gives me sqrt(13)
but im not sure how to find the exact value of the angle
vernal vale
shouldnt it just be $\theta(a+bi) = \arctan \qty(\frac ba)$?
thorny flameBOT
jan Niku
vernal vale
,w arctan(-2/3)
thorny flameBOT
