Yeah i can't claim i entirely understand this formula
#help-23
old ibex
but i am beggining to grasp this
ok thank you so much i have to go to bed
have a good night
.close
safe radishBOT
light shoal
you too, cheers
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Available help channel!
neat swallow
help
inner flare
safe radishBOT
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@inner flare Has your question been resolved?
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@inner flare Has your question been resolved?
safe radishBOT
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modern pond
How would I compute the minimum point of the following equation? Where q is a sequence of length c of which the contents fall within the range [0,1] and as such does x
safe radishBOT
How would I compute the minimum point of the following equation? Where **q** is ...
modern pond
Alternative form:
obtuse jackal
I guess a is qn ?
safe radishBOT
@modern pond Has your question been resolved?
modern pond
<@&286206848099549185>
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@modern pond Has your question been resolved?
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viral current
how do i solve this?
safe radishBOT
how do i solve this?
plucky elk
how do i solve this?
Find the closed form of each function first
Then multiply the functions and then calculate its power series
viral current
Find the closed form of each function first
what does closed form mean?
viral current
how do i find the other series closed form?
lean otter
g(x)=x+2x^2+3x^3...
x.g(x)= x^2+2x^3...
g(x)(1-x)=x+x^2+x^3...
plucky elk
how do i find the other series closed form?
arkos basically did the whole work for you
but another idea is to differentiate f(x) and multiply by x to get g
safe radishBOT
@viral current Has your question been resolved?
viral current
arkos basically did the whole work for you
so its x^(n) then?
plucky elk
so its x^(n) then?
i don't know what you're referring to. show some work.
safe radishBOT
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timber snow
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timber snow
Am I breaking up my terms correctly with ln?
safe radishBOT
@timber snow Has your question been resolved?
bright crow
$\ln(a+b)\neq \ln(a)+\ln(b)$
flat frigateBOT
Euclid31415
timber snow
Oh so can I not use ln on that at all?
bright crow
You can but it won't distribute that much
bright crow
It would just be ln(numerator)-ln(denominator)
lean otter
$\ln{\frac {a}{b}}=\ln {a} - \ln {b}$
flat frigateBOT
Frustrated Cat
lean otter
This right
bright crow
A thing you could do is divide 8^x from both numerator and denominator
bright crow
So yeah, limit as x approaches infinity of this expression is indeed 0
bright crow
So yeah, limit as x approaches infinity of this expression is indeed 0
I said if x approached positive infinity limit is 0.
timber snow
I know but like
bright crow
This we can evaluate directly
timber snow
I don't understand how 5^x approaches 0
bright crow
Just replace k=-x so that k can be taken to approach +infinity
It will clear things up
timber snow
I don't have negative x anywhere
bright crow
$\lim_{x\to -\infty}5^x=\lim_{k\to \infty}5^{-k}$
flat frigateBOT
Euclid31415
timber snow
So really small numbers as the exponent of a positive constant will make them approach zero?
bright crow
Which can be written as 1/(5^k)
verbal pulsar
safe radishBOT
verbal pulsar
I need explanation of this step
tame charm
holy christ
looks like they distributed 1/o_p^2, and then factored that difference of r's
safe radishBOT
@verbal pulsar Has your question been resolved?
verbal pulsar
I figured out the first one
Just left this step which idk
<@&286206848099549185>
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@verbal pulsar Has your question been resolved?
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@verbal pulsar Has your question been resolved?
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@verbal pulsar Has your question been resolved?
verbal pulsar
<@&286206848099549185>
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@verbal pulsar Has your question been resolved?
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@verbal pulsar Has your question been resolved?
verbal pulsar
<@&286206848099549185>
golden flower
<@&286206848099549185>
verbal pulsar
<@&286206848099549185> im in pain
raw wharf
it simply isn't true, unless you know some things about the variables that we don't.
safe radishBOT
@verbal pulsar Has your question been resolved?
sharp sage
plucky elk
.close
lean otter
x^2 - x = 100
x = ?
safe radishBOT
x^2 - x = 100
x = ?
worthy hemlock
Move the 100 over, solve quadratic
lean otter
x^2 - x + 100 = 0 ?
sonic spruce
no
lean otter
x^2 - x = 100
- x = 10 ?
lean otter
x is negative right?
worthy hemlock
If you have x + 123 = 456, how would you solve for x?
lean otter
456 - 123 = x
worthy hemlock
Good
In your problem, x^2 - x = 100, you want to set that equal to 0
Meaning "stuff = 0"
How would you do that?
lean otter
first i do the square root of x^2 ?
worthy hemlock
No
You want to set that equation equal 0
Meaning you need to get all the terms on one side
How do you do that?
lean otter
x^2 - x - 100 = 0
worthy hemlock
Have you never factored quadratics before?
lean otter
no never, I have just started the equations, I am French, I live in France
sonic spruce
have you learnt any other ways of solving quadratics?
opaque oak
Mr. or Mrs. dldh06, i think this equation is easier to solve with the quadratic formula
lean otter
I'll look at that later, thanks for your help, I'm going
worthy hemlock
Mr. or Mrs. dldh06, i think this equation is easier to solve with the quadratic ...
Yes, true.
safe radishBOT
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flat crow
lets say you have a circle with a radius of 1, if I were to draw a line from the center point to the edge of the circle (45 degrees), what would the X and Y coordinate be? and what about 22.5 degrees? and how would I know how to do it with other degrees?
safe radishBOT
lets say you have a circle with a radius of 1, if I were to draw a line from the...
final halo
x = cos(angle), y = sin(angle)
stable igloo
{z ∈ C : Re(z) ∈ Z}
safe radishBOT
{z ∈ C : Re(z) ∈ Z}
lean otter
Will the answer of 8 (a) be 15,120?
safe radishBOT
Will the answer of 8 (a) be 15,120?
lean otter
9 ! / 4!
no 9c5
choose 5 then put them in order
No, list is an alphabetic order.
Shouldn't we use permutation formula? 😀
@lean otter
then u would have permutations like BACGH
I see.
Thank you 🙂
.close
stable igloo
z ∈ C : π 2 ≤ arg (z) ≤ π how do I graph this?
safe radishBOT
z ∈ C : π 2 ≤ arg (z) ≤ π how do I graph this?
stable igloo
something like this?
plucky elk
It's a sector
plucky elk
but how do I represent it
Sector has a very specific meaning in math
Specifically circles
final halo
It's a sector
?
final halo
It is the whole quadrant
karmic zenith
safe radishBOT
karmic zenith
dont really know where to start
plucky elk
dont really know where to start
you just want the slope at 3
The derivative of a function at a point represents the slope of the function at that point
languid quartz
thats graph of g(x) tho
karmic zenith
yah
languid quartz
I think he needs to use fundamental theorem of calculus
plucky elk
Ah yes. I missed the g
languid quartz
karmic zenith
i understand it to be some sort of composition by i dont know like does the derivative and integral just cancel or something
languid quartz
Do you recall this equation?
languid quartz
since we want the value of f'(3)
we need to find the derivative of the integral
since f(x) is an integral
languid quartz
languid quartz
The problem is, it is not x, it is x squared
languid quartz
yes, since that is the derivative of x^2
karmic zenith
so f'(3) = g(3) * 2x?
karmic zenith
g(9) is like 3.5 or seomthing weird
unless its 4
its 4
alright so 24 thank you
I do have some other questions if u dont mind?
languid quartz
I would really want to help, but I gotta have dinner rn 😦 sry
You can DM me if you really need my help
glass dock
safe radishBOT
glass dock
how are we going from the first step to the second?
am i blind to some sort of basic manipulation of complex numbers haha
humble venture
how are we going from the first step to the second?
If z*w = some real number, what can you say about arg(z) and arg(w)
Or like you can use some tricks of the arg function too
glass dock
complex conjugates of each other so arguements are opposite?
humble venture
Yea
glass dock
right so arg(z) = -arg(z conjugate)
humble venture
Pretty much
glass dock
but if z = (a/ ... ) how is its conjugate just the denominator
humble venture
a is a real number right, then just multiply by the denominator
And it's in the same form as earlier
hearty wraith
I need the answer pls
hearty wraith
safe radishBOT
nova roost
for this question do i simplify (x-2) and put -3 in front of x or do i do it a different way?
safe radishBOT
for this question do i simplify (x-2) and put -3 in front of x or do i do it a d...
cosmic moth
you have to square the (x-2) and then u can distribute the 3
nova roost
do i distribute the 3 to the whole equation or just the (x-2)
safe radishBOT
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lilac patio
do i distribute the 3 to the whole equation or just the (x-2)
Just (x-2)^2
(x-2)^2 is x^2-4x+4
Multiply by 3 then add 13
Then factor or quadratic formula whichever one you want
graceful siren
Can I have help on 31?
safe radishBOT
Can I have help on 31?
graceful siren
I know the series is convergent and I am using the limit comparison test, I choose my bn to be 2/n^2 which is convergent but I do not know where to go from here
safe radishBOT
@graceful siren Has your question been resolved?
light shoal
I know the series is convergent and I am using the limit comparison test, I choo...
you can use |x+y| <= |x| + |y| in the numerator, which will give you |2 + sin(n)| <= |2| + |sin(n)| = 2 + |sin(n)| <= 2 + 1 = 3
toxic junco
toxic junco
Hi
May someone please explain on how to get the correct answer to this please?
I have no idea what it is
safe radishBOT
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toxic junco
.close
sturdy cobalt
safe radishBOT
sturdy cobalt
Question no 2
old moat
@sturdy cobalt Which set of numbers in the interval (0,1) is closer to 0 than 0.38?
old moat
Yep
old moat
Exactly
sturdy cobalt
Alright, thanks
old moat
You can complete Q3 in the same way
sturdy cobalt
Do the [] brackets make a difference ??
old moat
In the case of probabilities, no
The probability of landing in the interval (a,b) is exactly the same as landing in the interval [a,b]
Since landing on either a or b is a probability 0 event
safe radishBOT
old moat
👍🏻
tame charm
The probability of landing in the interval (a,b) is exactly the same as landing ...
Interesting
old moat
Interesting
Disagree?
old moat
Ok haha
old moat
Mhm yes
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old moat
Sigma-additivity gives $\mathbb P(a \leq X < b) = \mathbb P(X=a) + \mathbb P(a < X < b) = \mathbb P(a < X < b)$
safe radishBOT
Sigma-additivity gives $\mathbb P(a \leq X < b) = \mathbb P(X=a) + \mathbb P(a <...
flat frigateBOT
jckynaston
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lean otter
What is the smallest real number a so that the equation x|x-a|=3 has exactly one real solution?
safe radishBOT
What is the smallest real number a so that the equation x|x-a|=3 has exactly one...
lean otter
no calculators allowed 
upper badge
take the cases for which x ≥ a and x < a
open the mod
you'll get a quadratic
equate D = 0 and find all possible real values of a in each scenario
lean otter
for x>a, D=0 when a has no real values and for x<a a= sqrt 12 or - sqrt 12
I thought -sqrt 12 but the answer sheet says that a has no smallest value
flat frigateBOT
The following error occured while calculating:
Error: Syntax error in part "√3(1 + √2)" (char 2)
upper badge
for x>a, D=0 when a has no real values and for x<a a= sqrt 12 or - sqrt 12
for a = -√12, x does have one solution less than -√12 but the other solution is greater...
we should have gotten a common smallest value for both x ≥ a and x < a ig
safe radishBOT
@lean otter Has your question been resolved?
lean otter
its very tricky
lean otter
yes coz i am still confused lol
potent bay
i didnt use a calculator either, just wanted to show you that the "bump" from the x^2 goes down
these looked like this, if you remember
and the reflection is at the value 'a'
so for negative it becomes like this
again, its just a transformed parabola
lean otter
ok then, graphing wins
lean otter
What is the smallest real number a so that the equation x|x-a|=3 has exactly one...
x|x-a|=3
xsqrt((x-a)^2)=3
x^2(x-a)^2=9
x^2(x-a)^2-9=0
(x(x-a)+3)(x(x-a)-3)=0 x>0
x(x-a)+3=0
x^2-ax+3=0
D=a^2-4 * 3=a^2-12
x1=(a+sqrt(a^2-12))/2>0 a>=sqrt(12)
x2=(a-sqrt(a^2-12))/2>0 a>=sqrt(12)
x(x-a)-3=0
x^2-ax-3=0
D=a^2-4 * (-3) =a^2+12
x1=(a+sqrt(a^2+12))/2>0 a(-infinity;+infinity)
x2=(a-sqrt(a^2+12))/2>0 no solution
so it has one solution when a(-infinity;sqrt(12))
safe radishBOT
@lean otter Has your question been resolved?
acoustic violet
the 3rd line turned the problem into a quartic equation. squaring might include unnecessary solutions, say $x = -\sqrt{a}$.
flat frigateBOT
vin100
acoustic violet
why x > 0?
lean otter
if x<=0 it has no solution
acoustic violet
yes i got that
sorry for bothering
that's much quicker than fatman's way of dividing into x>a and x<a.
lean otter
if x<=0 it has no solution
how?
lean otter
how?
when x=0 left side is 0 right is 3, when x<0 left side is negative right is positive
lean otter
when x=0 left side is 0 right is 3, when x<0 left side is negative right is posi...
oh so intuitely the absolute value is always positive thats the idea right?
nvmd
thanks tho
how can i reward you?
lean otter
$(a+sqrt(a^2-12))/2>0
safe radishBOT
$(a+sqrt(a^2-12))/2>0
woven anchor
$(a+sqrt(a^2-12))/2>0$
flat frigateBOT
R31_
woven anchor
$\frac{a+\sqrt{a^2-12}}{2}>0$
flat frigateBOT
R31_
lean otter
what do you need
what do i do here?
lets simply ok? a+ sqrt (a^2-12)>0
then sqrt (a^2-12)>-a
if you then square both sides,
a^2 -12>a^2
but the a values cancel!!!!
woven anchor
you can't square both sides here
lean otter
why not 😭
woven anchor
you can only square both sides when the signs are the same
(you have to reverse the sign as well if they're both negative)
since x^2 is increasing when x>0 and decreasing when x<0
lean otter
so how to solve this?
woven anchor
if a>0 then the inequality always hold when the value inside the square root isn't negative
and if a<0 you can square both sides
woven anchor
the equation has no solutions
hushed mirage
i think a is positive
a+sqrt(a^2-12)>0
multiply by sqrt(a^2-12)
a*sqrt(a^2-12)+a^2>12
a(a+sqrt(a^2-12))>12
but in the parens is the original thing multiplied by a
tall bough
google distance formula
did u read the rules
read it
read it
wont say it third time
<@&268886789983436800>
adios
wild cape
astral ivy
please can someone help me with binomial expansion
safe radishBOT
please can someone help me with binomial expansion
plucky elk
you're missing 3x+4
astral ivy
you're missing 3x+4
are you saying it'd be easier doing (3x+4)(1+x)^-1(x+2)^-2
astral ivy
the partial fraction I formed
astral ivy
in the first part
astral ivy
yeah
flat frigateBOT
astral ivy
ah yes, thank you
crimson spear
Umm?
lean otter
$1$ The opposite angles in a cyclic quadrilateral are supplementary.
flat frigateBOT
Jester
remote shadow
is this taylor series
safe radishBOT
is this taylor series
remote shadow
oh
how do i determine if it converges or diverges
its not geometric right
(for #1)
final halo
why have you been given questions on whether sequences converge if you dont know any way to tell if sequences converge?
remote shadow
well i know how im just not sure how itd fit in here
converges if -1 <= r <= 1
diverges if r> 1 or r<=-1
is it safe to ping someone
remote shadow
calc 2
flat frigateBOT
kaynsu
remote shadow
uh
lean otter
$\lim_{n\rightarrow \infty} 5 - \frac{2}{e^n}$
flat frigateBOT
kaynsu
remote shadow
it looks like it gets bigger
flat frigateBOT
kaynsu
lean otter
as n goes to infinity, 2/3^n will go to 0
lean otter
do you see why?
remote shadow
yes bc the denominator is getting bigger
lean otter
yes
remote shadow
numerator stays the same
lean otter
yes
remote shadow
ic
lean otter
you can rigorously prove it too, but you're not there yet
remote shadow
so for the others i just have to see where the function goes
as n approaches infinity
lean otter
as n goes to infinity yes
lean otter
np
.close to close the channel if you want to
only the last sequence does not converge
remote shadow
ok ik the answer to this one
safe radishBOT
ok ik the answer to this one
thin bridge
divide numerator and denominator by n^2
thin bridge
for infinite limits of rational functions it is sufficient to consider the leading terms of the numerator and denominator
remote shadow
thank you
safe radishBOT
@remote shadow Has your question been resolved?
stable igloo
safe radishBOT
safe radishBOT
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stable igloo
.close
hollow hound
Take the parabola P: y^2 -2x = 0, find the values of k for which L: x + 2y + k = 0
- intersect
Pin two different points - are tangent to
P - don't intersect
Pin any point
safe radishBOT
Take the parabola `P: y^2 -2x = 0`, find the values of `k` for which `L: x + 2y ...
hollow hound
how can I approach this?
safe radishBOT
@hollow hound Has your question been resolved?
eager ravine
there’s a nicer way to do this than what I first thought using just algebra and not calculus
so first write the second equation should be rewritten to isolate y, so -2y = x + k. now square it to get 4y^2 = (x + k)^2
also rewrite first equation as y^2 = 2x
this means that 4y^2 = 4(2x) = 8x
thus 8x = (x + k)^2
this can be rewritten as x^2 + 2kx + k^2 - 8x = 0 or x^2 + 2(k - 4)x + k^2 = 0
the determinant of a quadratic is b^2 - 4ac. if D < 0, there’s 0 solutions. If D = 0, there’s 1 solution. If D > 0, there’s 2 solutions
in this case a = 1, b = 2(k - 4), and c = k^2
therefore D = 4(k - 4)^2 - 4k^2
@hollow hound I will let you solve for k here such that
D < 0 (doesn’t intersect P)
D = 0 (tangent to P)
D > 0 (intersects P at two different points)
covert kestrel
I had a Linear Algebra Question. When solving for eigenvalues, does it matter between using det(A - I lamda) or det(I lamda - A)
safe radishBOT
I had a Linear Algebra Question. When solving for eigenvalues, does it matter be...
final halo
It does not
The polynomials will be negatives of eschother and thus have the same roots
grim pumice
$\det(I\lambda - A) = \det(-(A-I\lambda)) = (-1)^n\det(A-I\lambda) = 0$ where n is the number of columns
flat frigateBOT
Crescendo PiaNo
grim pumice
this does not change the value of lambda since it is the root of polynomials
safe radishBOT
@covert kestrel Has your question been resolved?
viral current
quick question
safe radishBOT
quick question
viral current
for this, why isnt the bottom correct
(tried both positive and negative btw)
i did arctan of -4/3
light shoal
with arctan you need to be careful about quadrants
which quadrant is the point (-3,4) in?
viral current
2?
light shoal
yes and what quadrant is theta = 0.927295218 in?
viral current
i believe the first?
light shoal
right
so that can't be the answer
you probably did something like arctan(-4/3) on a calculator
viral current
yea
light shoal
which gives you the same answer for (3,-4) and (-3,4)
btw
even if you did arctan(-4/3) wouldn't the result be minus 0.927295218, not plus?
viral current
yea ik like i said i tried + and -
light shoal
yeah neither one is right actually
but arctan(-4/3) would give you -0.927295218
then you see that's in the 4th quadrant
whereas your point is in the 2nd
so you add pi
viral current
oh thats it?
light shoal
yep
that just says, i don't want the point in that quadrant, i want the corresponding point in the opposite quadrant
viral current
i see
light shoal
like in this case you don't want the angle for (-3,4), you want the one for (3,-4)
and those angles differ by pi
viral current
what do u use for one in quad 3?
light shoal
usually arctan (like a button on a calculator or whatever) is constrained to give an answer in quadrant 1 or 4
(so it assumes positive x)
if you're using software there might be a function like atan2
which allows you to specify both x and y, not just their ratio
and it can then work out the quadrant for you and give the right answer
lean otter
hello
worthy hemlock
Yes
worthy hemlock
What trig ratio would you use to find the height?
shadow glade
Just tell your teacher this problem cannot be answered with the information given, it doesn’t specify the tree is vertical…
lean otter
do i use cah
worthy hemlock
Just tell your teacher this problem cannot be answered with the information give...
Yeah.... No, the assumption is it's vertical
What side is the height?
lean otter
the right
worthy hemlock
And that side is what, in relation to the angle?
lean otter
opposite
worthy hemlock
So would it be correct to use CAH to find the height, when you just said the side was opposite the angle?
shadow glade
And how do you know the tree isn’t growing like this?
lean otter
So would it be correct to use CAH to find the height, when you just said the sid...
yea
worthy hemlock
CAH?
worthy hemlock
And how do you know the tree isn’t growing like this?
No one cares, so stop
worthy hemlock
So what ratio should you use to find the height?
lean otter
OH TAN
worthy hemlock
What is the ratio for tan?
shadow glade
No one cares, so stop
…good teachers appreciate students pointing out flawed problems and showing actual critical thinking, so I stand by my suggestion as valid, relax 🙂
lean otter
its opposite / adjacent
worthy hemlock
…good teachers appreciate students pointing out flawed problems and showing actu...
It's not a flawed problem if the lesson is about right triangles and trig
So stop, no one cares
worthy hemlock
its opposite / adjacent
Can you write the proper equation now?
With the information you have
worthy hemlock
If you're good now, feel free to close the channel using
.close
safe radishBOT
safe radishBOT
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fading raft
When the positive ends of two batteries are connected like below. How will it work? Will the charges be collecting the sum of the emfs as they pass through both batteries? (7.6+14)
safe radishBOT
When the positive ends of two batteries are connected like below. How will it wo...
fading raft
safe radishBOT
@fading raft Has your question been resolved?
glad flower
@fading raft no, higher voltage battery determines how current flow in circuit. lower voltage battery will be a consumer.
fading raft
<@872024354572103731> no, higher voltage battery determines how current flow in...
So does the lower voltage battery act as a resistor. I.e. taking energy away from the charges?
glad flower
So does the lower voltage battery act as a resistor. I.e. taking energy away fro...
yeah, 14v battery will charge 7.6v battery.
total emf = 14-7.6
fading raft
yeah, 14v battery will charge 7.6v battery.
what do u mean by charge
glad flower
what do u mean by charge
you consider 14v as a charger and 7.6v as battery of phone.
safe radishBOT
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kind pollen
safe radishBOT
kind pollen
<@&286206848099549185>
bleak pendant
So do you know what x intercept means
kind pollen
no
bleak pendant
x-intercept is when the graph crosses x- axis
to find it
you put y = 0
and solve the equation for x
kind pollen
so c
bleak pendant
no
put y = 0
and solve the quadratic eqaution
you have the find values of x when y is 0
kind pollen
i jsut got help from a collage student and they said it was c
kind pollen
did you solv it yourself
bleak pendant
oh wait
it is c
solve the quadratic equation
lol
BUT you should know how to solve it
vocal gazelle
Hello, I don’t really know what question d) is asking me to do? Any help would be appreciated!
safe radishBOT
Hello, I don’t really know what question d) is asking me to do? Any help would b...
plucky elk
Hello, I don’t really know what question d) is asking me to do? Any help would b...
Take the limit as t goes to infinity
cerulean edge
In the figure there's a graph showing the function y = c-x^2 for a certain value c > 0.
a) Write the expression for the area of the shaded area, and calculate the exact value when c = 3.
b) Determine c such that the area of the shaded area is 4 area units.
safe radishBOT
In the figure there's a graph showing the function y = c-x^2 for a certain value...
cerulean edge
Would this be correct for a) $\int^{}_{} c-x^{2}dx$
flat frigateBOT
AuHasard
tall bough
your boundaries
cerulean edge
What are they?
tall bough
what do u think
cerulean edge
c-x^2 = 0
√c = x
$\int^{\sqrt{c} }_{-\sqrt{c} } c-x^{2}dx$
Like this?
@tall bough
flat frigateBOT
AuHasard
flat frigateBOT
AuHasard
tall bough
yes
tall bough
wdym
tall bough
yes
cerulean edge
or you can just tell me if i did this correctly
tall bough
its dx
cerulean edge
alright
$[3-\frac{x^{3}}{3} ]^{\sqrt{3} }_{-\sqrt{3} }=(3-\frac{\sqrt{3}^{3} }{3} )-(3-\frac{(-\sqrt{3}^{3} )}{3} )$
flat frigateBOT
AuHasard
cerulean edge
good?
tall bough
ye u should become 6,9
cerulean edge
,w integrate 3-x^2 from -√3 to √3
flat frigateBOT
cerulean edge
Nice.
@tall bough Can you help me with b)?
$$\int^{\sqrt{c} }_{-\sqrt{c} } c-x^{2}dx=4$$
tall bough
its like solving for an unknown variable
cerulean edge
This is my guess on how to start…
Or hmm
The upper and lower bounds are the same
flat frigateBOT
AuHasard
tall bough
yes
cerulean edge
$$\int^{\sqrt{c} }{-\sqrt{c} } c-x^{2}dx=[\frac{c^{2}}{2} -\frac{x^{3}}{3} ]^{{}^{\sqrt{c} }}{-\sqrt{c} }=4$$
flat frigateBOT
AuHasard
cerulean edge
Good start?
$$[\frac{c^{2}}{2} -\frac{x^{3}}{3} ]^{{}^{\sqrt{c} }}_{-\sqrt{c} }=(\frac{\sqrt{c}^{2} }{2} -\frac{\sqrt{c}^{3} }{3} )-(\frac{(-\sqrt{c}^{2} )}{2} -\frac{(-\sqrt{c}^{3} }{3} )=4$$
flat frigateBOT
AuHasard
tall bough
**AuHasard**
btw the integral is 3x-(x^3)/3
cerulean edge
oh true
$$\int^{\sqrt{c} }{-\sqrt{c} } c-x^{2}dx=[cx-\frac{x^{3}}{3} ]^{\sqrt{c} }{-\sqrt{c} }$$
$$=(c(\sqrt{c} ){-\frac{(\sqrt{c} )^{3}}{3} )-(c(-\sqrt{c} )-\frac{(-\sqrt{c}^{3} )}{3} )} =4$$
flat frigateBOT
AuHasard
cerulean edge
@tall bough
is this good?
,w simplify [(c(\sqrt{c} ){-\frac{(\sqrt{c} )^{3}}{3})]-(c(-\sqrt{c} )-\frac{(-\sqrt{c}^{3} )}{3} )}
flat frigateBOT
tall bough
,w integral of c-(x^2) from -sqrt(c) to sqrt(c)
tall bough
oops
cerulean edge
so third root of 12?
tall bough
mann
flat frigateBOT
tall bough
that qual to 4
flat frigateBOT
Result:
4
tall bough
,w (4c^(3/2))/3=4 solve for c
flat frigateBOT
cerulean edge
man I give up on this question lol
tall bough
why
cerulean edge
I don't want to occupy more of your time and it seems like we are not getting anywhere
tall bough
,w (4c^(3/2))/3=4 solve for c
thats the aanswer
since its symmetrical u could just do integral of the function from 0 to sqrt(c) then multiply by two
tall bough
parentheses are missplaced
cerulean edge
,w simplify [(c(\sqrt{c} ){-\frac{(\sqrt{c} )^{3}}{3})]-(c(-\sqrt{c} )-\frac{(-\sqrt{c}^{3} )}{3} )}
flat frigateBOT
cerulean edge
come the fuck on
tall bough
u can just do the definite integral lol
tall bough
yes
safe radishBOT
lean otter
Question d.
I think i correctly got the |a-b| term in the end, but i cant get the other terms to cancel. What was i supposed to do/doing wrong?
Btw ignore the very very end
I’ll also be trying some more. Thanks for responses in advance
safe radishBOT
@lean otter Has your question been resolved?
lean otter
$sqrt3 sinx - cosx = sqrt3$
safe radishBOT
$sqrt3 sinx - cosx = sqrt3$
flat frigateBOT
EndTimes
winter pivot
I don't think this is a simple equation
We might have to bust out the exponential defns
lean otter
i took cos x to the other side, squared both sides and got: 3 sin^2 (x) - 3 - 2sqrt3 cos(x) - cos^2 (x) = 0
divide by two
sqrt(3)sin(x)/2-cos(x)/2=sqrt(3)/2
sqrt(3)/2 * sin(x) - cos(x) * 1/2 = sqrt(3)/2
sin(pi/3) * sin(x) - cos(x) * cos(pi/3) = sqrt(3)/2
-(cos(x) * cos(pi/3) - sin(pi/3) * sin(x)) = sqrt(3)/2
-cos(pi/3 + x) = sqrt(3)/2
oh its some sort of reverse trig and reverse addition rule
safe radishBOT
@lean otter Has your question been resolved?
safe radishBOT
@lean otter Has your question been resolved?
lean otter
.close
urban gale
safe radishBOT
plucky elk
rewrite your eqn in hyperbola standard format
urban gale
i did
using completing the square, i got
(x+2)^2/ 36 - (y-2)^2/16 =1
did i graph wrong?
plucky elk
,w expand (x+2)^2/ 36 - (y-2)^2/16 - 1 = 0
flat frigateBOT
urban gale
is this the same thing?
plucky elk
,w expand 16 * 36 *((x+2)^2/ 36 - (y-2)^2/16 - 1) = 0
flat frigateBOT
urban gale
so it looks like i got it right
for the center = (-2,2)
Asymptote = 4/6 = 2/3
<@&286206848099549185>
safe radishBOT
@urban gale Has your question been resolved?
crude geyser
Hi. So we were asked to determine the m of the angles using the following trig ratios, and show our solutions. The only method that I know, and I believe it is by far the only method that we've been taught, is to put it in an inverse trig function and let the calculator do the work. If this is the case, then, how do u think can I "show my solution?"
safe radishBOT
Hi. So we were asked to determine the m of the angles using the following trig r...
obtuse jackal
Don't forget periodicity. The calculator only gives one answer
crude geyser
I'm not sure what periodicity is, sorry. Could you give an example, say sin ∅ = 1/2.
obtuse jackal
theta could be π/3, or 2π/3. Or one of these offset by any multiple of 2π because sin is 2π periodic: the values offset by 2π are the same
safe radishBOT
safe radishBOT
Available help channel!
fiery fiber
Hi
fiery fiber
What are some very beginners Conjecture on number theory ?
fiery fiber
What are some very beginners Conjecture on number theory ?
Except goldbach and fermat last
hearty egret
every Conjecture on number theory isn't for beginners
hearty egret
fiery fiber
.close
safe radishBOT
fiery fiber
.close
potent bay
3n+1 is interesting too
safe radishBOT
Available help channel!
fleet salmon
WHAT DID I DO WRONG 😭😭
safe radishBOT
WHAT DID I DO WRONG 😭😭
shy temple
,rotate
flat frigateBOT
safe radishBOT
@fleet salmon Has your question been resolved?
sudden cargo
hey i need some help
safe radishBOT
hey i need some help
safe radishBOT
fleet salmon
oh man, thank you so much
sudden cargo
.reopen
safe radishBOT
✅
fiery fiber
whats the matter
safe radishBOT
safe radishBOT
Available help channel!
lean plank
let P(S) be the powerset of some set S where |S| = n, so that |P(S)| = 2^n.
What is the probability that the symmetric difference of three randomly chosen elements in P(S) is the empty set? Repetition (choosing the same element multiple times) IS ALLOWED!!!
My thought is: if it is asking whether the symmetric difference of three elements will INCLUDE the empty set, it would be 100% since all sets include the empty set. But if the question is asking if the symmetric difference is ONLY the empty set, I would think it only be when all the elements selected include elements that others contain as well. Anyone have a guess as to which is being asked for?
stoic dune
Definitely the second interpretation
lean plank
Okay, do you have any suggestions on how to get started on finding the prob? What I have noticed so far is every element of the 3 sets selected must be present in one of the other sets selected, but I am not sure how to show that mathematically. Additionally, each set selected has a (#ofElements)^2 of possible sets it can be paired with, so I think I could figure it out for 2 sets but not sure about 3
Edit: actually each selected set has 2^(#OfElements) possible sets it can be paired with
safe radishBOT
@lean plank Has your question been resolved?
lean plank
.close
jade vessel
safe radishBOT
jade vessel
<@&286206848099549185>
wet girder
i can help u
jade vessel
Am I right?
jade vessel
so just square the x
worthy hemlock
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
wet girder
u can close this channel now
jade vessel
thanks my boi
wet girder
is it right?
jade vessel
idek yet
wet girder
but if u have a side to side transformation (x axis) make sure they're included inside the bracket to square them
y axis is outside
lean otter
6(3) - (4-(3)^2)
safe radishBOT
6(3) - (4-(3)^2)
lean otter
Yes,
im confused on why it would be
6(3) - 4 - 3²
i keep getting
6(3) - 4 + 3^2
worthy hemlock
6(3) - 4 + 3^2
Like what happened to the negative sign?
lean otter
Like what happened to the negative sign?
ye
worthy hemlock
You typed it, I'm questioning it
shadow glade
6(3) - 4 + 3^2
That’s correct
worthy hemlock
That’s correct
How?
lean otter
maybe i typed it wrong
hold up
(g - f) = 6x - (4 - 2x²)
= 6x - 4 - 2x²
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
worthy hemlock
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
f(x) = 4 – x^2?
worthy hemlock
(g - f) = 6x - (4 - 2x²)
= 6x - 4 - 2x²
Because so, then this is wrong
Because you have that extra 2 for some reason
That's the mistake
worthy hemlock
Can you just post a screenshot of the question?
lean otter
6(3) - (4 - 3^2)
worthy hemlock
And you have the solution too?
lean otter
And you have the solution too?
ye