i know that i can arrange this in 3! ways
#help-41
fair nest
coral wigeon
write the 6 permutations out. how many times do you count each one?
fair nest
i count 213 and 132 twice
coral wigeon
right
and 312 and 231 once
and 123 and 321 no times
ok letโs try 1234 now. but donโt write them all out
fair nest
and 312 and 231 once
and 123 and 321 no times
wait what? i thought 213 and 312 are the same
since the deck is inverted
coral wigeon
fair nest
coral wigeon
i would not have thought these to be the same since we are talking about ascending orders
fair nest
what did u mean by counting 213 twice
oh wait
sorry
my bad
im braindead
we move the 1 one time and the 2 one time
right
coral wigeon
ok letโs try 1234 now. but donโt write them all out
back to this, how many times will you count
1243?
how about 4123?
coral wigeon
theyre adjacent
ding ding ding
fair nest
yoooo
coral wigeon
yes, those are the types of permutations you count twice
ones that just transpose 2 adjacent numbers
how many of those are there?
coral wigeon
yep
fair nest
so i just subtract 16?
coral wigeon
yea
so i think the answer is either 16^2 or 16^2 + 1
there is one little detail unclear to me in the question though still
fair nest
what is it?
coral wigeon
can change, does that mean changing no cards is an option?
if so we should add one for the permutation that does nothing
fair nest
*can* change, does that mean changing no cards is an option?
no, i dont think it is
this question was given by my friend in casual language
coral wigeon
maybe thereโs an easier explanation for why itโs 16^2
since that is a nice number
coral wigeon
you too
fair nest
.close
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normal dove
can we put [x]=1 here directly
amber waspBOT
can we put [x]=1 here directly
cerulean fossil
can we put [x]=1 here directly
yea that works
strange field
confused since teacher said no putting partial limits
yeah but if putting partial limits doesnt affect the overall function then you can
ivory sorrel
confused since teacher said no putting partial limits
I don't think that would even count as putting a partial limit
stoic locust
what is [x]
normal dove
floor fn
strange field
floor function
stoic locust
ok
split sail
you can use the product rule as long as it makes sense
normal dove
hmm okayyy
ivory sorrel
can we put [x]=1 here directly
Also, this is not even an indeterminate form
So why would it matter
normal dove
hmm'
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sharp rapids
If $x_n$ is a sequence of positive numbers such that $$\lim_{n\to\infty} \frac{x_{n+1}}{x_n} = L > 1$$ show that $x_n$ diverges
weak zinc
letter x 
sharp rapids
Why did that happen?
gloomy tide
dunno you're the one that typed it
weak zinc
If $x_n$ is a sequence of positive numbers such that $$\lim_{n\to\infty} \frac{x...
If $x_n$ is a sequence of positive numbers such that $$\lim_{n\to\infty} \frac{x_{n+1}}{x_n} = L > 1$$ show that $x_n$ diverges
gloomy tide
grizzled pagodaBOT
Halex
solar gust
!occupied
amber waspBOT
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sharp rapids
Fixed thx. So I was trying contradiction but I'm not sure what contradiction should I get
gloomy tide
this is not your channel
solar gust
He is ded
gloomy tide
that will likely depend on the purported limit value of x_n
gloomy tide
you could use X for the limit of x_n
and show that no matter what X is, that can't be the limit
keen topaz
x_n - x >= e
I thought it was less than
amber waspBOT
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surreal scroll
use a limit test
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edgy lion
I think this should be discussed in advanced math but I dont know which one. $\int_{0}^{1}\frac{\mathrm{d}x}{\oint_{|z-\frac{\pi}{2}|=\frac{\pi}{2}}\frac{z\mathrm{d}z}{\sin(z)-z\cos(z)-\pi-2x\sqrt{1-x^2}+2\arccos(x)(2x^2-1)}}$
grizzled pagodaBOT
Gregory
edgy lion
I think it might be real-complex analysis?
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fervent tinsel
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heavy spear
How do I work out question 4.3?
amber waspBOT
How do I work out question 4.3?
haughty token
CT is a radius to point T and y=3x/4 is a tangent at point T
So they would be perpendicular to one another
There's one more bit of information you can use to form the line. Do you know any points that lie on CT?
heavy spear
No I only calculated the first 2 questions and they don't involve CT
mint wraith
How do I work out question 4.3?
use the formula for the distance of point to the line
heavy spear
On the memo it says CTm= -4/3
So I can use that to calculate the equation y=mx+c
But I'm not sure how they figured out the gradient(m)
fathom bramble
How do I work out question 4.3?
I assume that if you've moved onto 4.3 you've gotten 4.2 right?
heavy spear
Yes
fathom bramble
In that case, notice T is the intersection between the line and the circle
Through that, you can just calculate T, having two points you've got all you need to determine the straight line
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hard canopy
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hard canopy
this is an AIME 14 from 2020
I don't get why P(3)+P(4) = 3+a
And I don't get how a=7P(3)+1/8
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hard canopy
<@&286206848099549185>
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@hard canopy Has your question been resolved?
pliant pendant
$x^2yโโ-xyโ+y-xy=0$
amber waspBOT
$x^2yโโ-xyโ+y-xy=0$
grizzled pagodaBOT
ใใธใจใณ
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reaction for more information.
(You may edit your message to recompile.)
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junior jewel
amber waspBOT
junior jewel
I don't understand this problem
Idk how I solved for the cases all I remember is I need piecewise functions for problems like this?
I'm reviewing
alpine flower
that function is modulus or absolute value
basically how the abs value is opened based on the limit
first one is left hand limit and second one is a right hand one
for the first limit x is approaching from the left side, so (x<2) and you would get -(4-x^2)
second limit x is approaching from right side (x>2), so its just (4-x^2)
amber waspBOT
@junior jewel Has your question been resolved?
junior jewel
for the first limit x is approaching from the left side, so (x<2) and you would ...
Ohh so I just flip it
Yeah cuz I got to (x<2 but didn't get the reasoning for flipping it
I don't think I still get the reason
I keep forgetting it
alpine flower
it's just Left and Right hand limits
also remember the property of abs value
how it opens when x>0 and x<0
junior jewel
What about the denominator?
junior jewel
I don't get how I got -4 and 4 tho cuz when I look at what you tell me I cuz think of getting 0 again
alpine flower
@junior jewel you can write |4-x^2| as |x^2 - 4| and then factor it and simplify
for the first limit take (-1) outside of the limit and then multiply with the final value
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ebon lichen
(question 17 only.) i don't understand how -52 dissapeared and became 72
verbal jewel
(question 17 only.) i don't understand how -52 dissapeared and became 72
where does -52 disappear and became 72?
ebon lichen
in no. 17, i transposed 52, to the right side and put the other terms in the left so i can arrange them and i completed the square for both variables and the right side of the equation's result was 14, but when i checked the correct term was actually 72
verbal jewel
you are talking about something which only you can see or only you do have. how should someone help you if you do not provide this?
split sail
provide your work pls
ebon lichen
i think i did it even wrong this time
verbal jewel
there is a 2 outside the bracket:
so you have 8 at the left side, but 4 on the right side.
and it should be +64 instead of -64 on the left, so again the right side changes.
but still i dont understand your question: "i don't understand how -52 dissapeared and became 72" ...
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toxic minnow
Can anyone help me with ii)
amber waspBOT
Can anyone help me with ii)
toxic minnow
I don't understand how do the long division part when there's unknowns
quartz mist
you dont need to do long division
Q(x) is some unknown polynomial of degree 3, so you can write it as Q(x) = tx^3 + ux^2 + vx^x + w and then substitute that into the equation you already have
toxic minnow
so itll look something like x^5 + ax^3 + bx^3 - 3 = (x^2 - 1)(tx^3 + ux^2 + vx + w) - x - 2?
quartz mist
yeah like that
quartz mist
yeah you can expand it and notice that in order for both sides to be equal they have to have the same coefficients for each power of x
like if i had a different equation that looked like ax^2 + bx + c = 5x^2 + 4x + 3 then you can see that a=5, b=4, and c=3, yea ?
toxic minnow
yea I can see that
toxic minnow
so itll look something like x^5 + ax^3 + bx^3 - 3 = (x^2 - 1)(tx^3 + ux^2 + vx +...
alright I expanded it but now I got unknowns on both sides โ ๏ธ
quartz mist
yeah but some of them you can solve for
quartz mist
like when you expand that you'll find that the coefficient for x^5 will be equal to t which you can equate to the coefficient on the left side of the equation
toxic minnow
for x^5 + ax^3 + bx^3 - 3 = (x^2 - 1)(tx^3 + ux^2 + vx + w) - x - 2
can I do -3 = -x - 2
which gives x = 1
but will that help me to find a and b
quartz mist
for x^5 + ax^3 + bx^3 - 3 = (x^2 - 1)(tx^3 + ux^2 + vx + w) - x - 2
can I do -3...
not really, the entire equation has to be true regardless of the value of x
toxic minnow
i see
toxic minnow
like when you expand that you'll find that the coefficient for x^5 will be equal...
x^5 = tx^5
t is 1 yeah
quartz mist
yes
quartz mist
do you see the strategy yet ?
toxic minnow
x^5 + ax^3 + bx^3 - 3 = (x^2 - 1)(tx^3 + ux^2 + vx + w) - x - 2?
can I compare the tx^3 in the above equation with ax^3?
or i cant
quartz mist
you have to expand it out first
toxic minnow
alright
quartz mist
cause when you expand it out there will be another term with a power of x^3
toxic minnow
yeah which are vx^3 and -tx^3
a = v-t
but I still don't understand how I can get the value of a
sorry for having to put up with me im not very good at polynomials ๐
toxic minnow
x^5 + ax^3 + bx^2 -3 = tx^5 + ux^4 + vx^3 + wx^2 - tx^3 - ux^2 - vx - w - x - 2
is what i got
quartz mist
yeah
quartz mist
yeah
you gotta make more equations with the other degrees of x too so you can figure out what t,u,v,w are
if you make an equation for x^5, x^4, x^3, x^2, x^1, and x^0 youll be able to solve all of them
toxic minnow
i see
x^5 + ax^3 + bx^2 -3 = t(x^5) + u(x^4) + v-t(x^3) + w-u(x^2)- v-1(x)- w - 2
t = 1
u = 0
v-1 = 0
v = 1
v-t = a
a = 0
is that correct so far?
toxic minnow
because the marking scheme says a = -2 and b = 1 ๐ฅฒ
i have the answer but cant figure out the working
but it's alright
thank you for trying your best hahaha
appreciate it a lot stilll
quartz mist
the method should be right
i guess it just went wrong somewhere, i didnt check your work too closely
quartz mist
you can use .close
quartz mist
np
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lone pond
how to express this vector if we are working with cylindrical coordinates?
my guess is (0 rho hat, idk , z zhat)
lone pond
vectors in cylindrical coordinates
Rhat, theta hat, zhat
amber waspBOT
@lone pond Has your question been resolved?
thorn lily
what symbol can i use to denote the answer of a problem?
i've been using Ans but i want something more elegant
tepid verge
what symbol can i use to denote the answer of a problem?
i've been using Ans but...
imo it's more elegant to not designate a response as an answer. so you just use full sentences
if you're talking about an exam or otherwise hand-written response for someone to judge, just put a box around it or something
orrr
$\therefore x=1$
grizzled pagodaBOT
Flip
tepid verge
with a box, or two scratch marks
//
to indicate that it's the end of your response
so that one would intuit your answer is the last line
in a paper or something, you wouldn't want to say "answer" because it sounds juvenile
tepid verge
**Flip**
you would be using the three dots symbol if you're under the impression that the preceding work is a chain of logical statements that justify your conclusion
if a question were just like, "state the definition of continuity" you wouldn't preface your definition with "therefore" because it doesn't make sense to assert that you derived or proved a definition
tepid verge
with a box, or two scratch marks
the scratch marks or box would go generally in the bottom right, just after or on the same line as your last line of content
you don't want to write QED because it makes you look pretentious. like, you're in a pre-algebra class and suddenly you know latin? yeah right
amber waspBOT
@thorn lily Has your question been resolved?
thorn lily
I would write in full sentences for exams of course
i had to mention that it was for my notes ;-;
tepid verge
oops lmao
I like to use an arrow to indicate the start of a solution, and scratch marks to indicate the end of a solution if needed
actually no, I don't use an arrow, I think I write "sol" to preface it
dire locust
let me quess this was 3d vectors?
tepid verge
${\rm Sol}^{\underline{{\rm ut}}}$
grizzled pagodaBOT
Flip
thorn lily
I like to use an arrow to indicate the start of a solution, and scratch marks to...
How can I use scratch marks?
tepid verge
let me find an example
I kinda just slap them onto the end vaguely to the right of the page
this was a response I gave for an undergraduate graph theory quiz
just above it, it's a proof of something, so I prefaced with "pf" and haphazardly wrote two scratch marks to the bottom right
I'm also realizing that I don't really put scratch marks at the end of an exercise if the original question wasn't written, and I rarely ever do that, often just calling the whole exercise an example
mild kindle
Can someone explain what this engineering textbook means by this formally?
mild kindle
What does it mean for a_R to "change" with the theta and phi coordinates to the point P
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@mild kindle Has your question been resolved?
hasty rock
amber waspBOT
hasty rock
Just want to see if all the transformations and mapping is correct
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pallid canopy
rosses are red violets are blue math sucks and gemometrey to
Irrelevant comments go in #chill
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thorny terrace
stuck on part a, not too sure what to do, anyone have any tips?
thorny terrace
i only have dS/dt = (salt enter rate) - (salt leave rate)
dS/dt = (0.25 lbs/min) - (salt leave rate)
not too sure how to find the salt leave rate, if it only tells me how much water leaves per minute
restive harness
sir
restive harness
of course
you're right, it does only tell you how much water leaves per minute
if you knew the concentration at time t
then you'd know how much salt leaves per minute
thorny terrace
yep
so concentration at time t
that is amount of salt/amount of water at time t
amount of salt at time t is just S?
restive harness
S(t)
thorny terrace
yea
restive harness
yes
thorny terrace
ok then amount of water hmm
thorny terrace
but it says pure water is added to keep it full
thorny terrace
yes
restive harness
assuming S(t) is amount of salt in pounds
thorny terrace
yea, and so amount of salt at t = amount of water * concentration at t
amount of water = -1/2 gal/min
but wait its added back
restive harness
but the salt isn't
you're finding the rate of salt leaving the tank
it will be 1/2 gal of fluid per minute, but its your job to find out how much salt is in that 1/2 gal
thorny terrace
amnt salt leave / amnt water leave = concentration salt leave
amnt salt leave = amnt water leave * concentration salt leave
amnt salt leave = 1/2 gal/min leave * concentration salt leave
amnt salt leave = 1/2 gal/min leave * (amnt salt/amnt water) leave
amnt salt leave = 1/2 gal/min leave * (S lbs/5 gal) leave
amnt salt leave = 0.5 gal/min * 0.2S lbs * gal^-1 leave
amnt salt leave = 0.1S * lbs/min leave
thorny terrace
oh wait
restive harness
S is in lbs
restive harness
salt tanks go brr
thorny terrace
is this more accurate now
restive harness
sure
thorny terrace
ok yea thank you, this stuff is totally new to me lol
restive harness
np
if you have diffeq doubt
send it to me
dont post here where lustful eyes watch
thorny terrace
๐ appreciate it Sir ๐
restive harness
๐
azure hound
amber waspBOT
azure hound
why dont I evaluate the ln -(lnx) and ln (lnx) in this , like i would for any other absolute value
but for this its just ln(2)
like for example if I was integrating |x^2-1| with bounds -2,0 I would have to split it apart to -(x^2-1) and x^2-1 respectively
and put their respective bounds for each
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left sage
amber waspBOT
pulsar beacon
i just use f(b)-f(a) / b-a
You're right to use that, but maybe you made a mistake in your calculation? Just tried it and it should work
left sage
yeah okay so the google calculator and desmos calculator seemed to give me an error
i did it with my physical calculator and it worked just now
ty
pulsar beacon
Np!!
left sage
.close
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halcyon ridge
how do i graph
amber waspBOT
how do i graph
restive harness
do it a piece at a time
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@halcyon ridge Has your question been resolved?
cold tide
I need help with finding the constant for this equation I am not sure if I am correct or not?
jaunty shale
I need help with finding the constant for this equation I am not sure if I am co...
the working method is correct
but the antiderivative of e^(2y) is wrong
there is no y multiplied by 1/2 e^(2y)
amber waspBOT
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livid bloom
Can someone help me solve this?
amber waspBOT
Can someone help me solve this?
livid bloom
i dont know where to start other than the fact you can easily get the area of the 8x7 rectangle
hollow forum
So you need help finding the area of the whole shape?
livid bloom
mainly the triangle
hollow forum
another obvious rectangle would be 3x5
the triangle uhh
45 degrees
one of these guys
livid bloom
i have never seen that before but lemme take a look and see if i can understand how to do it
visual cradle
hello guys
hollow forum
helloo
hollow forum
isosceles triangle ahh core
hollow forum
undergrads ?
huh
livid bloom
yes, also the 45 degrees is outwards but that has given me an idea of where to start, Since its a triangle we can do 45-60 right?
since all triangles = 180 degrees
hollow forum
livid bloom
oh yea
im kinda slow ig
so two 45 degree angles and a90 degree
and we know the side of the triangle is 5 ft since 3-8 is 5
livid bloom
thank you for making me realize i could just make it a rectangle cuz its just a right triangle
livid bloom
right
hollow forum
thank you for making me realize i could just make it a rectangle cuz its just a ...
alg
livid bloom
So just to make sure im mathing correctly since A=1/2 x base x height
hollow forum
yes
livid bloom
A=1/2(5ft)(5ft)=12.5 ft
hollow forum
area of a triangle is 1/2bh
livid bloom
then the volume would just be 12.5*10
hollow forum
yes
livid bloom
thank god
man i genuinely could not remember how to solve that and started panicking
thank u so much
hollow forum
i would do 17*8 = 136ft and subtract the square and triangle on the outside
hollow forum
thank u so much
npp
so then the full area of this shape would be 98.5ft i think squared yes
x10 = 985 ft so then 7368.31 gallons
x0.02 = 147.3662 dollars to fill the pool
livid bloom
125+280+300 = 705 cu ft?
hollow forum
and then 2(3x5x10)
livid bloom
dont we need to include the part above the triangle
hollow forum
125+280+300 = 705 cu ft?
woahh where's the 280 from
livid bloom
oh yea
hollow forum
hence 2(3x5x10)
livid bloom
ah your right
hollow forum
so 560
livid bloom
idk im tripping i was using calculator i think i put the wrong numb in
lemme check again
livid bloom
idk im in freshman college
hollow forum
o
livid bloom
(7x8x10)+(2(3x5x10))+(12.5x10)
hollow forum
and this is ur hw or smth
livid bloom
is this correct?
livid bloom
and this is ur hw or smth
practice exam
livid bloom
ye
hollow forum
(7x8x10)+(2(3x5x10))+(12.5x10)
yes so 560+300+125
livid bloom
985 cub ft
hollow forum
yup
livid bloom
then i need to find how many gallons per cub ft?
livid bloom
livid bloom
yea
thats what i got too
phew
thanks for your help
ik the next step is just multiple the gallon by 0.02 cents
livid bloom
.close
amber waspBOT
hollow forum
so then the full area of this shape would be 98.5ft i think squared yes
x10 = 98...
the shorter way was here but ok
cool cool
anyways
rapid kestrel
in america yes
haha yes
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Available help channel!
spark iris
Why does y=2z?
amber waspBOT
Why does y=2z?
spiral zealot
Why does y=2z?
who's saying that? (because that isn't true)
surreal fulcrum
no~x=41ยบ y=131ยบ and "ยบ" attach
because 41ยบ+90ยบ= 131ยบ so z=49ยบ
why
whywhy
ใ กใ ก
i'm Korea
spiral zealot
you seem to be randomly bringing in 90ยฐ with no justification
jaunty shale
y=2z only if z was
surreal fulcrum
Assuming it is a right triangle, it must be 90ยบ
surreal fulcrum
However, if you say it is an isosceles triangle, things may be different
spiral zealot
Assuming it is a right triangle, it must be 90ยบ
you shouldn't be assuming things like that, the calculations don't make sense regardless
fresh ocean
Only thing you should 'assume' here is y is the angle at the centre of the circle
surreal fulcrum
So do you know the answer?
surreal fulcrum
Then, we need to know that the correct answer is that the angle of y is the center and calculate it
jaunty shale
according to the incribed angle theorem
final matrix
Why does y=2z?
am I mistaken or is the triangle on the left an isosceles triangle
are those two lines of equal length
fresh ocean
am I mistaken or is the triangle on the left an isosceles triangle
looks equilateral
surreal fulcrum
The center is called an isosceles triangle
final matrix
in that case you would have z=82 given by the inscribed angle theorem given you have angles 49 and 49
surreal fulcrum
If you draw a vertical line with y as the center, it can be considered a vertical isosceles triangle
final matrix
looks equilateral
it's definitely not equilateral if we consider the inscribed angle theorem because the interior angles cannot add up to 180
fresh ocean
it's definitely not equilateral if we consider the inscribed angle theorem becau...
two of the sides are radius of the circle and the third one is marked equal to one of the radius
final matrix
two of the sides are radius of the circle and the third one is marked equal to o...
in the case that two sides of the triangle are of equal length the triangle should be an isosceles
fresh ocean
yes, and equilateral is a very specific case of isosceles triangles
final matrix
if these two sides are equal
final matrix
yes, and equilateral is a very specific case of isosceles triangles
for a triangle to be equilateral then z = 60 but based on information that isn't the case
surreal fulcrum
No, even if the lengths are the same, if the opposite sides are the same and the angles are the same, it can be an isosceles triangle. In other words, it is ASA congruent
fresh ocean
for a triangle to be equilateral then z = 60 but based on information that isn't...
and what information is saying z cant be 60?
final matrix
and what information is saying z cant be 60?
I rescind my earlier statement because inscribed angle theorem doesn't apply
nvm
spark iris
who's saying that? (because that isn't true)
i asked my sister and she said (so sorry i had to go do something)
surreal fulcrum
ok
spark iris
so how would we do it?
surreal fulcrum
m...
People have different opinions, so let's do the math and make a decision with one majority vote
final matrix
Why does y=2z?
to find Z we know that 2 of the sides are equal to the radius and the third side is equal to the same length so all sides of the triangle are of equal length
spiral zealot
apply properties of radii / special triangles
note that x,y are irrelevant when finding z
final matrix
making it an equilateral triangle of all angles 60 degrees
final matrix
so z is just 60?
yep
amber waspBOT
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fiery canopy
amber waspBOT
fiery canopy
anyone can help me w (a)?
idk if i started correctly.
the last step is prob wrong
<@&286206848099549185>
fresh ocean
First off, the information given is not sufficient to draw a unique diagram. As you can see, there are two options, red and blue, that would have the exact same measurements as the information provided, and are totally different (its not to the scale, but it should convey the point)
fiery canopy
First off, the information given is not sufficient to draw a unique diagram. As ...
so the question has problem?
fresh ocean
imo, yes
fiery canopy
alr thanks
fresh ocean
but, from what you have calculated, you have the area of BCD
fiery canopy
but, from what you have calculated, you have the area of BCD
yea i was planning to use it to solve
but i found out that i cant
fiery canopy
:0
fresh ocean
And if you and whoever put those answers did the calculations right, one of the answers should match with theirs
so, in step one, you have sin(CDB), so it can have an acute angle as well as an obtuse angle as the solution. You have used acute solutions, so I'll use it for further stuff. The other would ffollow the same logic, just different numbers
From that you get CD (again, 2 possible solutions here), use it to calculate AC. And, use the area of BCD to calculate the height of BCD from C (height to be used for EDC)
To get AB:
Use cosine rule on ABD, with angle D and the sides AB, 10 and 4 (angle D is known from the previous calculations)
To get EDC area:
Use cosine rule again, to get EB on angle B (known from your work), and get EC = BE - BD. Use area = 0.5*base(ED)*height(from first sentence of this message)
amber waspBOT
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glossy bay
how does dy/dx equate to 2?
amber waspBOT
how does dy/dx equate to 2?
fresh ocean
coz they said specifically that gradient is 2 at P
glossy bay
coz they said specifically that gradient is 2 at P
ohhh ๐ญ i didnt know that that was what equate meant, thx
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amber waspBOT
glossy bay
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amber waspBOT
โ
dull glen
$ f(x) = \frac{x(x-1)}{2} \cot(\pi x) $
glossy bay
how does dy/dx equate to 2?
first part of question is here
paper stone
@fiery canopy Is the problem referring to a right triangle or is it a non right triangle. You need to start with the correct assumptions for the right trig laws I think.
mint shard
Anyone could help me to do this in short
jaunty shale
use the equation that you already showed in (i)
amber waspBOT
fiery canopy
<@1209752184082923533> Is the problem referring to a right triangle or is it a n...
okey
paper stone
@mint shard quadratic
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keen pawn
so I;m trying to prove the product rule for limits
amber waspBOT
so I;m trying to prove the product rule for limits
keen pawn
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amber waspBOT
amber waspBOT
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real basin
Could anyone give a brief explanation of the characteristic function for someone doing their calculus sequence?
real basin
I saw the notation recently, but many of the explanations are motivated by higher courses.
amber waspBOT
@real basin Has your question been resolved?
molten briar
If i have a matrix B and factor out a common constant from the entries so that i have 1/3 * A, where A is the factored matrix, can I find the eigenvalues of A and then multiply that by 1/3 later on to get the eigenvalues of B?
indigo cloud
yes
edgy jackal
Hi, I don't want someone to solve the exercise for me, I just want someone to explain to me how to do it because we haven't had a lesson on it yet, thanks! (exercise 2)
edgy jackal
split sail
All you need to know is that i^2 = -1. Just simplify so that you have the form
Something + something* i
edgy jackal
thanks! finally I succeeded but not the last one I don't know how to develop
amber waspBOT
@edgy jackal Has your question been resolved?
amber waspBOT
@edgy jackal Has your question been resolved?
urban raft
@edgy jackal
t'as besoin d'aide pour la quelle?
jsuis en mpsi 1ere annรฉe jpeux t'aider
edgy jackal
Pour le 4 de l'exercice 2 stp
edgy jackal
jsuis en mpsi 1ere annรฉe jpeux t'aider
Moi aussi je veux, j'espรจre รชtre admis au moment des voeux ๐ค
urban raft
t'as trouvรฉ la 3)?
urban raft
Moi aussi je veux, j'espรจre รชtre admis au moment des voeux ๐ค
trkl tant que tu vises pas h4 รงa devrait etre bon
et si tu veux vrmt faire une prรฉpa tu pourras tjrs
edgy jackal
t'as trouvรฉ la 3)?
pas sur j'ai utilisรฉ a2-b2+2abi
urban raft
t'as trouvรฉ quoi?
edgy jackal
2s je reprends ma feuille
z3=i/2 ?
j'ai pas mon tรฉl, je peux pas t'envoyer l'exo dรฉtaillรฉ
urban raft
de tete j'ai plutot z3= i
edgy jackal
de tete j'ai plutot z3= i
de tรชte๐ญ alors que j'ai mis 15min ร le faire
urban raft
รงa viendra tkt
mais dcp t'as un truc du genre 1/2 + 2*(2i/4) - 1/2
= i
essaie de le refaire et si t'y arrives pas je te le detaille proprement
edgy jackal
de tete j'ai plutot z3= i
ok ok je vais essayer ducoup je re dans 5-10min
urban raft
ok
edgy jackal
Oui ducoup c'est bien z3 = i ๐ญ
edgy jackal
Attends 2 secondes je rรฉflรฉchis j'ai peut-รชtre zappรฉ un truc tout bรชte
Ah bah oui je suis dรฉbile
Z4 = (Z3)ยฒ
Donc z4 = -1
C'est รงa ?
edgy jackal
Ok ok merci beaucoup !
urban raft
pas de soucis si t'as d'autres questions n'hรฉsite pas
edgy jackal
D'accord ducoup j'ai oublie, je dois faire comment pour fermer le salon?
urban raft
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chilly jackal
amber waspBOT
chilly jackal
AM-GM apparently
amber waspBOT
@chilly jackal Has your question been resolved?
patent raptor
AM-GM apparently
yea I think so
I would brin 1/a + 1/b + 1/c together as one fraction
Then in the numerator you might apply AM-GM
chilly jackal
Then in the numerator you might apply AM-GM
hmm lemme try
what how does that help 
i get $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \geq (abc)^{\frac{-1}{3}}$
grizzled pagodaBOT
rakยณen
patent raptor
,, \frac{bc+ac+ab}{abc} \leq \frac{\left ( \frac{b+c}{2} \right )^2 + \left ( \frac{a+c}{2} \right )^2 + \left ( \frac{a+b}{2} \right )^2}{abc}
grizzled pagodaBOT
bacc
chilly jackal
am-gm applied on bc, ac, ab 3 times
yeah i got it
patent raptor
i am also trying to figure it out currently...
chilly jackal
i actually did subtraction
u add and subtract 2(cyclic sum ab)
then split
and ur done
patent raptor
can you show
chilly jackal
and ur done
from here u basically get
$$ \sum_{cyc}^{} \frac{1}{a} \leq \frac{a^2+b^2+c^2 - ab - bc - ca + 2ab + 2bc + 2ac}{2abc} $$
patent raptor
yea i got that
chilly jackal
$$ \sum_{cyc}^{} \frac{2}{a} \leq \frac{a^3+b^3+c^3+ 2ab + 2bc + 2ac}{abc} $$
patent raptor
oh
patent raptor
from where does this come a^3+b^3+c^3?
chilly jackal
from where does this come a^3+b^3+c^3?
its an identity
a^3 + b^3 + c^3-
OH
SHIT
NEVERMIND
AM STUPIDDDD
thanks
grizzled pagodaBOT
Requested by adoniszgks
patent raptor
me either
chilly jackal
,w a^3+b^3+c^3 = a^2+b^2+c^2-ab-bc-ca
i missed a -3abc
thats what happened
a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)
patent raptor
that was your plan
chilly jackal
yes
patent raptor
a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)
you can estimate up anyway by leaving out the -3abc term since it'S negative
chilly jackal
I think i got it
o send the son pls
chilly jackal
you can estimate up anyway by leaving out the -3abc term since it'S negative
wat
hows the inequality true?
patent raptor
I noticed a little nuance
in my solution
I have gotten to $$ 2 \cdot \frac{(a^3+b^3+c^3)}{abc} + \frac{1}{2} \left ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right )$$
grizzled pagodaBOT
bacc
chilly jackal
for real this time?
grizzled pagodaBOT
bacc
patent raptor
I hope it works ๐
patent raptor
chilly jackal
i was almost there eh
patent raptor
I dont get it too LMAO
chilly jackal
and this
chilly jackal
I dont get it too LMAO
๐ญ
patent raptor
I always disliked such tasks
felt too dumb
but i tried it now lol
with your help
chilly jackal
hope mine will be much shorter
?
grizzled pagodaBOT
bacc
patent raptor
no
icy solar
a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)
use a + b + c = 1 to simplify this to
$$3abc = a^3+b^3+c^3-(a^2+b^2+c^2-ab-bc-ca)$$
also multiply both sides of the given inequality by abc to get rid of the denominator
grizzled pagodaBOT
vin100
patent raptor
and this
,, m^2+n^2+p^2+3+3+3 \geq \sqrt[3]{12}\sqrt[6]{m} \cdot \sqrt[3]{12}\sqrt[6]{n} \cdot \sqrt[3]{12}\sqrt[6]{p} \Rightarrow x^2 + 3 \geq \sqrt[3]{12}\sqrt[6]{x}
chilly jackal
,, m^2+n^2+p^2+3+3+3 \geq \sqrt[3]{12}\sqrt[6]{m} \cdot \sqrt[3]{12}\sqrt[6]{n} ...
got this thx
grizzled pagodaBOT
bacc
grizzled pagodaBOT
patent raptor
oh bruh
chilly jackal
the given ineq shld b equiv to
*bc* + *ca* + *ab* โค 3*abc* + 2(*a*ยณ + *b*ยณ + *c*...
mhm i got we need tp
a^2+b^2+c^2
<=
3(a^3+b^3+c^3)
chilly jackal
wat?
icy solar
on a โค b โค c and aยฒ โค bยฒ โค cยฒ
after multiplying a + b + c = 1 on LHS
โบ (a + b + c)(aยฒ + bยฒ + cยฒ) = โฏ โค 3aยณ + 3bยณ + 3cยณ
cancel out aยณ + bยณ + cยณ on both sides
grizzled pagodaBOT
vin100
patent raptor
**vin100**
What does sum_cyc even mean
amber waspBOT
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Available help channel!
icy solar
What does sum_cyc even mean
cyclic sum
that's used on APoS
amber waspBOT
cyclic sum
that's used on APoS
icy solar
wat
random sum smaller than or equal to direct sum
when I first encountered this as a F.4 student, my MO tutor claimed that this is intuitive to a small kid
.close
amber waspBOT
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Available help channel!
oak kayak
when they say reciprocal r they just asking for the equation of the graph?
oak kayak
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wraith oriole
amber waspBOT
wraith oriole
What is the function?
crisp stratus
we need to see the whole table for that
wraith oriole
๐ญ
crisp stratus
we need to see the whole table for that
but i assume it's both (?)
since the number of elements in the domain and range is the same
crisp stratus
,rccw
grizzled pagodaBOT
wraith oriole
it was not both๐ญ
i don't even know what the functions mean
tried lookin it up and it was not simple
fr
it's hard
day 1 of homework and this is it
im already lost, im cooked for the whole class
i have to lock in
need a 4.0 this year
crisp stratus
<@&268886789983436800>
pale thunder
Muted for spam
wraith oriole
๐๐
alright so like back to the math at hand
What even is the difference between a one to one and an onto function?
amber waspBOT
@wraith oriole Has your question been resolved?
severe scroll
What even is the difference between a one to one and an onto function?
โone to oneโ is when you can distinguish points based on the output values, and โontoโ just means every point is hit at least once. onto is probably an easier one to get your head around at first
woven slate
how to calculate average with negatives in php ? let's say i have -5, -2, -3, 2 and i wanna get -3 in php hmm
woven slate
but i get -2 as result
gloomy tide
,calc -5-2-3+2
grizzled pagodaBOT
Result:
-8
I kinda feel like you should get -2
woven slate
when i do -5 + -2 + -3 + 2 / 4
gloomy tide
why do you think you should get -3?
violet gust
Just add and divide them like normally, but with integers
woven slate
because 5 + 2 + 3 + 2 / 4 is 3
violet gust
Answer is -2
gloomy tide
okay... but that's not what you have
you have -5, -2, -3, and +2
with different signs
woven slate
so average with theese numbers are -2 ?
gloomy tide
yes
gloomy tide
the same as an average of -2 and +2 would be 0
woven slate
thats crazy i was thinking needs to be -3 ๐
gloomy tide
i have no idea why you thought that 
woven slate
ok i'm brainless thx
violet gust
And then divide them by four like normal. PS you're actually smarter than most.
violet gust
Then divide them by 100
woven slate
does it matter which i count as first ?
woven slate
should i count from highest number to lowest ?
or it does not matter how i count them together ?
i have lot of negatives and positives
mixed
violet gust
Just add all the numbers then divide them by 100
A positive and a negative added to each other equals less
Just add them like normally
woven slate
ok
woven slate
1 ?
violet gust
Correct
woven slate
ok thx bro
violet gust
No problem
amber waspBOT
@woven slate Has your question been resolved?
icy solar
I hope it works ๐
sorry for tagging but the above AM-GM is wrong somewhere in the middle. Consider the equality case when a = b = c = 1/3
icy solar
sum of reciprocals is 9
in the target/given inequality, a = b = c gives equality
but in your 1st paragraph and at the end of the second paragraph, it's clear that you're not getting equality
patent raptor
at which step?
,w 1/(1/3)+1/(1/3)+1/(1/3) <= 3+2*((1/3)^3+(1/3)^3+(1/3)^3)/(1/31/31/3)
grizzled pagodaBOT
icy solar
i looked at it for a while and found that the 2nd '=' is wrong
patent raptor
can you circle it?
icy solar
can you circle it?
when an inequality has to be proved, a complete solution should contains the equality case
patent raptor
wdym?
patent raptor
it's an inequality here
icy solar
your solution is based on AM-GM, so the equality case should be a = b = c
icy solar
Why should I consider this?
That's part of a complete solution
patent raptor
they can be arbitrary
which means both cases are involved
Also you didnt show me where a=b=c=1/3 gives a wrong solution
icy solar
Also you didnt show me where a=b=c=1/3 gives a wrong solution
For your question, that's the end of the 1st paragraph
patent raptor
be a bit more specific
icy solar
Try substituting the values for the equality case
patent raptor
it's not equal and greater
icy solar
be a bit more specific
It's already very specific
patent raptor
it's equal or greater
grizzled pagodaBOT
bacc
patent raptor
less or equal or both
icy solar
it's equal or greater
Try input the values into the end of your 1st paragraph
patent raptor
i cant tell what you mean
icy solar
patent raptor
You are reading this step wrong
icy solar
i cant tell what you mean
Normal MO inequalities problem's solution shld contain a line "equality holds iff ..."
patent raptor
,, \frac{1}{a} + \frac{1}{b} +\frac{1}{c} \leq \frac{(a^3+b^3+c^3)}{abc} + \frac{1}{2} \left ( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right )
grizzled pagodaBOT
bacc
icy solar
,, \frac{1}{a} + \frac{1}{b} +\frac{1}{c} \leq \frac{(a^3+b^3+c^3)}{abc} + \fra...
substitute the equality case into this
And you'll see that the LHS gives 9
RHS gives 3 + 9/2 = 7.5
patent raptor
,w 1/(1/3) + 1/(1/3) + 1/(1/3) <= ((1/(1/3))^3+(1/(1/3))^3+(1/(1/3))^3)/((1/3)(1/3)(1/3)) + 1/2(1/(1/3) + 1/(1/3) + 1/(1/3))
I see I forgot the 4
icy solar
This explains (perhaps) why there's a gap "+3" in the last paragraph
icy solar
Why should I consider this?
That's a common practice in MO inequalities
It's also a way for error detection
Sometimes even though not explicitly rewritten, the equal case should be very clear (from the classic inequality applied in the solution)
Please feel free to ask if you've any questions.
icy solar
ITS RIGHT
Sorry for tagging. You may see the above discussion (around the equality case) to see what's wrong
icy solar
You're welcome ๐
swift shore
How do I do this (question 7)
amber waspBOT
How do I do this (question 7)
red knot
Apply product rule
shadow stump
you can distribute the multiplication and use exponent rules to simplify first
swift shore
๐ฐ๐ฐ
red knot
,tex .diff rules