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#help-33
marsh citrusBOT
stone dirge
I am confused, when I do p/q I have +-1, and 3/ +-1, +-5 so what should I do?
stone dirge
What like x^3(5x+9) -x(19x+3)?
stone dirge
x
dry prawn
better
now it's just a matter of plugging your potential roots in until one of them works
stone dirge
wait so it sohuld be x(5x^3+9x^2-19x-3)?
dry prawn
you'll have an easier time computing stuff with a cubic
stone dirge
now it's just a matter of plugging your potential roots in until one of them wor...
Thats what i am confused about how do I start using p/q
dry prawn
you've generated a list of potential roots
now you need to start plugging them in to see if any of them actually are roots
stone dirge
so I have +-1, and 3/ +-1, +-5 and I need to plug em all in
I dont do like +-3/+- 5 for example
dry prawn
start with the smaller integers for easier computing
+-1, then +-3, then get frustrated if none of those work
stone dirge
So basically I took the stuff from p and put it over -+1 q right
dry prawn
i'm not sure what that means
stone dirge
like I was watching the organc chemistry tutor
and he said to divide the top with the bottom
and then plug in with what you get
dry prawn
indeed
stone dirge
so when I plug in do I have to do both versions of 1 or an I just do positive 1
dry prawn
one at a time
stone dirge
okay so if it has a remainder it dont work right?
I did it with 1 and had a remainder of -8
so does that automatically mean -1 wont work too
dry prawn
it doesn't mean that, no
that's why you have to check them all
(or at least check until one works)
stone dirge
okay
I got -3 to work
I'm also gonna assume 0 works as well right because each number in there has an x
so I know its 0, -3
but now I gotta use 1/5 and 3/5 right?
stone dirge
indeed you do
can you clarify which this is for
dry prawn
"so i know..."
dry prawn
well not necessarily
since you know -3 is a root, you can factor your original expression and reduce it to a quadratic
well that will just give 0
stone dirge
Yeah I just realized hahah
dry prawn
smh deleting on me
stone dirge
since you know -3 is a root, you can factor your original expression and reduce ...
How do I start this process?
dry prawn
(x+3) is a factor of the expression
so you know (5x^3+9x^2-19x-3)/(x+3) will have no remainder
stone dirge
yes
dry prawn
now compute (5x^3+9x^2-19x-3)/(x+3)
stone dirge
ngl I forgot how do to divide these
oh nvm
its either long division or synthetic right
dry prawn
either works
stone dirge
Which one do you prefer?
dry prawn
neither
stone dirge
Is there another way?
stone dirge
okay we already have that answer
5, -6, -1, and 0 but Idk what to do
so does it become 5x^4-6x^3-x^2
or smt?
stone dirge
wait sorry I have to go
Thank you for the help so far
Sorry
have a nice night\
.close
marsh citrusBOT
marsh citrusBOT
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buoyant jetty
Let ( L: \mathbf{X} = \lambda(2, 0, 1) + (0, 2, 5) ), \
Plane ( \Pi_1 : x + 3y + 2z = 8 ), \quad Plane ( \Pi_2 : -3x - y + 3z = 4 ). \
Find two lines ( L_1 ) and ( L_2 ) that satisfy the following conditions simultaneously:
\begin{itemize}
\item ( L_1 \subset \Pi_1 ) and ( L_2 \subset \Pi_2 )
\item ( L_1 \parallel L_2 )
\item ( L_1 \cap L \neq \emptyset ) and ( L_2 \cap L \neq \emptyset )
\end{itemize}
marsh citrusBOT
Let \( L: \mathbf{X} = \lambda(2, 0, 1) + (0, 2, 5) \), \\
Plane \( \Pi_1 : x + ...
elfin berryBOT
ඞඞඞ
sand kindle
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
sand kindle
write out the general form for two lines
and go through each of the conditions one by one
marsh citrusBOT
@buoyant jetty Has your question been resolved?
buoyant jetty
and go through each of the conditions one by one
Explain
buoyant jetty
write out the general form for two lines
I don't got the direction nor a point
Unless I'm tripping
sand kindle
points 1 and 3 tell you the lines are in a plane and intersect with another line
can you get a point from those?
buoyant jetty
How do I do tthat
sand kindle
How do I do tthat
L1 intersects L and is in Pi1
so if L intersects Pi_1 at a single point, then you have a point for L1
marsh citrusBOT
@buoyant jetty Has your question been resolved?
marsh citrusBOT
@buoyant jetty Has your question been resolved?
sand kindle
I mean it's a line and Pi1 is a plane
maybe L is in Pi1
or parallel (making the question impossible to answer)
but usually a line will intersect a plane at a point
buoyant jetty
there could exist infinite amount of points for which the line satisfies the equation of the plane no?
i.e. the whole line is contained in the plain
@sand kindle
sand kindle
does there?
it could be, in which case you're spoiled for choice
but it's worth checking
buoyant jetty
anyways how would you tackle this type of exercise?
can you provide an outline of the general steps
carmine surge
@buoyant jetty how long do you sleep
marsh citrusBOT
@buoyant jetty Has your question been resolved?
carmine surge
wdym?
6AM awake, 9:30 AM still awake
or where do you live
or do you wake up at 5AM or something
elfin berryBOT
The current time for 938c2cc0dcc05f2b68c4287040cfcf71 is 09:53 AM (-03) on Wed, 18/09/2024.
buoyant jetty
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unborn adder
I got kinda stuck in this question that indirectly says in arabic "simplify this funcion to look like the previous one (the one in the top).
marsh citrusBOT
I got kinda stuck in this question that indirectly says in arabic "simplify this...
unborn adder
I tried to simplify it but got almost nowhere near the right one
marsh citrusBOT
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marsh citrusBOT
@unborn adder Has your question been resolved?
loud idol
1/(2*(2x²- 2x+1)) * (2x³ - 2x² + x + 2x²- 2x + 1 + 1 - 3x)
=1/2 * (2x³ - 4x + 2) / (2x²- 2x + 1)
= (x³ - 2x + 1)/(2x²- 2x + 1)
You wrote -1 in the denominator instead of +1
marsh citrusBOT
@unborn adder Has your question been resolved?
unborn adder
You wrote -1 in the denominator instead of +1
just saw it, thank you
wheat rover
umm close the other one
.close
on the other one
yeah now post the question
post anyway
,rotate
elfin berryBOT
wheat rover
as for q8, find 1.9% of 120000 that is the increasing factor
now that number of people add to the current population every year
now you can find the population after 10 years (i.e. in 2020)
marsh citrusBOT
@green granite Has your question been resolved?
marsh citrusBOT
@green granite Has your question been resolved?
wheat rover
yeah kinda
marsh citrusBOT
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@green granite Has your question been resolved?
tender steppe
marsh citrusBOT
lucid trellis
Hello I cant seem to be able to find the particular equation
seems to me like you could use U(x) = e^integral{{cosx}dx}
tender steppe
You mean the integrating factor?
lucid trellis
yeah
tender steppe
Does the integrating factor gets me directly y=(integrating factor)?
lucid trellis
y' + P(x)y = Q(x)
e^integral{P(x)dx}
after you solve do
multiply both sides by integrating factor, basically you get
{U(x)y}' = Q(x)U(x)
then you integrate both sides to get
(U(x)y) = integral{Q(x)U(x)dx}
tender steppe
Okay thank you ill give it a shot
lucid trellis
Okay thank you ill give it a shot
i wrote this ugly lil picture for u
marsh citrusBOT
@tender steppe Has your question been resolved?
marsh citrusBOT
@tender steppe Has your question been resolved?
lucid trellis
?
tender steppe
Oops
tender steppe
Yee
lucid trellis
alright!
marsh citrusBOT
@tender steppe Has your question been resolved?
slender dirge
marsh citrusBOT
slender dirge
anyone can help me with this
timber imp
if (x-1) and x-2 are factors of x4+mx2+nx-16 find mn, I got told x-1=0 and x-2=0 but why do they equal 0?
marsh citrusBOT
if (x-1) and x-2 are factors of x4+mx2+nx-16 find mn, I got told x-1=0 and x-2=0...
red nimbus
if (x-1) and x-2 are factors of x4+mx2+nx-16 find mn, I got told x-1=0 and x-2=0...
If they are factors of the polynomial of 4th degree you can rewrite it as
f(x) = (x-1)(x-2)(x^2+...)
Now if you were to analyze the x-intercepts of f(x) you would do
(x-1)(x-2)(x^2+...) = 0
and due to the zero product theorem you deduce
x-1=0 and x-2=0
timber imp
If they are factors of the polynomial of 4th degree you can rewrite it as
f(x) =...
wdym analyze roots?
timber imp
x-intercepts
im not rlly sure what u mean cause idrk what a x^4 graph would look like and its maybe a bit too advanced of an explaination rn? idk tho cause the main thing is the second step
red nimbus
You don't to know how it looks
timber imp
You don't to know how it looks
isnt that abt the x intercepts tho?
red nimbus
When you have linear factors, then you can read off the x-intercepts
And I stated the reason why above
timber imp
When you have linear factors, then you can read off the x-intercepts
wdym by that? srry im a bit dumb
red nimbus
wdym by that? srry im a bit dumb
(x-1) and (x-2) are called linear factors
They have the cool property that you can tell instantly the x-intercepts just by looking
(x-1) * bla bla bla
now if x = 1
you get 0 * bla bla bla = 0
that's an x-intercept
same with (x-2)
red nimbus
if (x-1) and x-2 are factors of x4+mx2+nx-16 find mn, I got told x-1=0 and x-2=0...
So this is the reason why you got told
I got told x-1=0 and x-2=0
timber imp
They have the cool property that you can tell instantly the x-intercepts just by...
so in the graph y=x-1 the x intercept is 1 but how does this relate to the main thing?
ike the x4 thingy
red nimbus
so in the graph y=x-1 the x intercept is 1 but how does this relate to the main ...
Let f(x) = that "x4 thingy"
Now you deduced x = 1 and x = 2 are x-intercepts
So you know
f(1) = 0 and f(2) = 0
And to me
that looks like you can determine m and n when you solve that system
elfin berryBOT
bacc
timber imp
that looks like you can determine m and n when you solve that system
Hi so sorry my dad called me to do smt
timber imp
Now you deduced x = 1 and x = 2 are x-intercepts
how do we know that if its only a factor of it?
red nimbus
how do we know that if its only a factor of it?
I don't understand this question
timber imp
I don't understand this question
how do we know that x4+mx2+nx-16 has x intercepts 1 and 2 based on the factors?
red nimbus
That is given from the task
If it has more
isn't really of interest for us
because the information provided is enough to deduce m and n
I will try to show one last time
ax²+bx+c is the addition quadratic factor that can be calculated with polynomial division but there is no need to
elfin berryBOT
bacc
timber imp
ax²+bx+c is the addition quadratic factor that can be calculated with polynomial...
but why does finding x intercept help with this question?
red nimbus
It's an information about the function
That way you can set up equations
find such m and n that satisfy these constraints
timber imp
That way you can set up equations
but wont different x values give different results
red nimbus
but wont different x values give different results
i dont know what to say to this
timber imp
i dont know what to say to this
is it like a really dumb question
red nimbus
i just dont understand
it
We just work with f(1) = 0 and f(2) = 0 the rest we don't know much and we dont care
If you plug in an x value into your function f(x) you get your y value
But you don't know what y value
it all depends on m and n
only x = 1 and x = 2 are an exception, here we know they are x-intercepts and so the y-value is 0
we don't know more
with these information you can create two equations and find such m and n that satisfy the constraint that (x-1) and (x-2) are factors aka x-intercepts
and then you can calculate the product of m and n
timber imp
so we are finding the y value of x=0 and plugging that in to the equation with m and n to get y? im a bit confused
red nimbus
why x = 0
how are you coming up with that
you wanna find m and n
did you read the task?
red nimbus
you are finding m and n based on the fact that x = 1 and x = 2 yield both y = 0
this also what f(1) = 0 and f(2) = 0 mean
notation wise
marsh citrusBOT
@timber imp Has your question been resolved?
timber imp
mb im just thinking abt it rn
marsh citrusBOT
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timber imp
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jolly elbow
marsh citrusBOT
jolly elbow
anyone?
bitter terrace
marsh citrusBOT
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small stream
marsh citrusBOT
small stream
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rigid kelp
marsh citrusBOT
rigid kelp
This is a 2 part question.. i solved the first part i just have a question abt the second part.
do we consider the initial velocity the balloon is already falling? or is the water accelerating from 0 at the distance it breaks when the dart hits it
marsh citrusBOT
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rigid kelp
<@&286206848099549185>
marsh citrusBOT
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main idol
do we consider the initial velocity the balloon is already falling? or is the wa...
the will be a positive initial velocity yes
rigid kelp
the will be a positive initial velocity yes
ok
marsh citrusBOT
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marsh citrusBOT
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feral nova
I need help with B and C
marsh citrusBOT
I need help with B and C
dim mantle
I need help with B and C
so to find the price where the revenue is maxed out (before it starts decreasing) you need to find the vertex of the parabola
Do you know how?
feral nova
No
dim mantle
do you know what the vertex is
dim mantle
If it's upside down yes, if it's upright it'll be the lowest
well I don't know what you've learned but the vertex can be found with x = -b/2a
where b and a are the co-efficients of the standard form of your parabola
dim mantle
what is b in this situation again?
so the equation you have is in factored form
you need to break appart these brackets
as in expand your equation
feral nova
as in expand your equation
how?
dim mantle
how?
you need to take the terms in the parenthases and distribute it to each term in the other parenthases
marsh citrusBOT
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marsh citrusBOT
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elfin wedge
im a bit confused on why its d and not c
marsh citrusBOT
im a bit confused on why its d and not c
marsh citrusBOT
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mellow frigate
How can speed even be negative??
marsh citrusBOT
How can speed even be negative??
tired raft
How can speed even be negative??
means its going down
mellow frigate
Wouldn’t that be velocity??
I thought speed has no direction
And the ground is basically x2 right?
tired raft
i would say yeah it isnt necessary to add the negative sign if it already mentions it going downward, but its just referring to the height
mellow frigate
And the ground is basically x2 right?
Like in a parabola
mellow frigate
i would say yeah it isnt necessary to add the negative sign if it already mentio...
Ohh I see
So I just solve for the x intercepts and take the most right one? X2?
Oh no wait it asks for how long
How do I know here if to take one or two derivatives
This makes no sense now that acceleration is added too
Because in this question it doesn’t get taken into consideration but the ball obviously accelerates in a fall
But if I calculate it based on constant speed then it’d make no sense since it has no constant speed until it hits maximum velocity
marsh citrusBOT
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snow estuary
@livid lance
marsh citrusBOT
<@729899348506181763>
livid lance
<@729899348506181763>
yes.
snow estuary
i dont have a problem currently on me
but could you explain how i can convert measurements to differenet ones
snow estuary
yea
livid lance
To solve a unit conversion, identify the units you want to convert between and find the conversion factor that relates them. Multiply the quantity you have by this conversion factor to get the value in said unit.
If you have any specific problems you would like to discuss, please don't hesitate.
snow estuary
maybe 30 kilometers to miles
snow estuary
1.61
livid lance
Okay great
so you always are going to have the similar units on the bottom of the fraction like so:
30km = ?/1.61km
Because we are using miles it's going to be 30 Kilometers = 1 Mile/1.61
livid lance
cause you should get less than 30 miles
no shit
amber birch
so that means 30 * 1.61 miles is wrong
amber birch
then you can just try the other one, 30/1.61
livid lance
idiot
livid lance
then you can just try the other one, 30/1.61
thats what im saying
30 x 1/1.61 = 18.63
livid lance
no need for the language
I am the teacher here, not you
cyan lodge
Hello, just here for the first time.
livid lance
Hello, just here for the first time.
yello how may I help u
glossy flint
Hello, just here for the first time.
! occupied
marsh citrusBOT
Hello, just here for the first time.
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).
amber birch
<@&268886789983436800> this user lucas is being rude
livid lance
<@&268886789983436800> this user lucas is being rude
I was helping this guy until u came in
and ruined everything
now ur making a scene 🤦
good job, you sure know how to wreck everything
glossy flint
now ur making a scene 🤦
You are making it a scene
peak fiber
you were being corrected and made a fuss over it
livid lance
you were being corrected and made a fuss over it
I wasnt
i was correct
he was being a jerk by saying I was wrong when I clearly wasnt
amber birch
you were being corrected and made a fuss over it
I wasn't trying to correct them
late geode
30km = ?/1.61km
implies
? = 30km * 1.61km
units would be incorrect
amber birch
I was simply telling Lonely Tree (the question asker) a neat strategy
livid lance
> 30km = ?/1.61km
implies
? = 30km * 1.61km
units would be incorrect
nah I am using the ? as the top unit in this case, miles
livid lance
I was simply telling Lonely Tree (the question asker) a neat strategy
I guess but the way its taught in school is the other way
late geode
yes. and that equation your wrote implies something like
some miles = some km^2
fickle slate
snow estuary
not the mods 😭
livid lance
not the mods 😭
do u understand
livid lance
okay any other problems
peak fiber
ur names alberto shut up
irregardless of who's correct, saying "no shit idiot" or this ^ is uncalled for
so consider this a warning
snow estuary
okay any other problems
nope ty for helping me
livid lance
nope ty for helping me
okay also try watching some youtube vids on it, it helps
livid lance
nope ty for helping me
I said no shit then called him an idiot for fighting back, i never said all of that
snow estuary
how do i close out this channel
peak fiber
yes, .close
livid lance
ok bye
snow estuary
.close
marsh citrusBOT
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marsh citrusBOT
fast bramble
Which X do I minus
glossy flint
What do you mean?
fast bramble
Is it -5X or -7x
glossy flint
|A| = |B| means A = ±B
glossy flint
Is it -5X or -7x
I don't get what the technique you're saying is
fast bramble
Ahhh so it’s 5X-2 and 7x+2
And 5X-2=-7x+2
glossy flint
No
fast bramble
Why not
glossy flint
You need parentheses
fast bramble
(5X-2)=(7x+2)
(5X-2)=(-7x+2)
glossy flint
5x - 2 = 7x + 2
or
5x - 2 = -**(**7x + 2**)**
.
glossy flint
Well now they are just two first degree equations, which you should know how to solve
glossy flint
And +7X for both on bottom
Yes
fast bramble
And then after that +2?
glossy flint
Yes
glossy flint
Nope
glossy flint
5x - 2 = 7x + 2
or
5x - 2 = -**(**7x + 2**)**
The bottom one becomes:
5x - 2 = -7x - 2
==> 12x = 0 ==> x = 0
The -2 cancel each other out
fast bramble
The bottom one becomes:
5x - 2 = -7x - 2
==> 12x = 0 ==> x = 0
Where did you get this from
It’s positive 2
Not negative
glossy flint
Yes
fast bramble
And the other side
Is positive 2
7x+2
Or when we do the negative
Does it make the 2 negative
glossy flint
Does it make the 2 negative
Of course!!
You should know first degree equations well, before doing exercises with abs values...
fast bramble
It's -(7x + 2), which is -7x - 2
Ahhh
Thanks
So the whole equation is negative
Always
glossy flint
Wdym?
glossy flint
I don't understand what you are saying, sorry
What does it mean for an equation to be negative? 🤔
marsh citrusBOT
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untold wyvern
marsh citrusBOT
untold wyvern
The very last line 1241^1103 is congruent to …
how would i go about computing this?
devout mauve
the algorithm is called square and multiply
it could in principle be done by hand
but obviously for these numbers it would suck a bit
untold wyvern
i’m abit confused, wdym
or actually, part of my hw is to find the 1030^29 mod 2623
but i’m not sure how either can be done by hand
devout mauve
well, stupid way: 29 steps
a bit smarter: 1030^29=1030*1030^28. so if you can find 1030^28 mod 2623 then you only need to multiply by 1030 again to get it
so far, nothing gained
the trick is in computing 1030^28 mod 2623
because 1030^28=(1030^14)^2
so if you find 1030^14 mod 2623, then you only need to square it to find 1030^28 mod 2623
untold wyvern
2623=43x61 is the prime factorisation but i’m not sure if this would help either
untold wyvern
because 1030^28=(1030^14)^2
ohh
marsh citrusBOT
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tiny nebula
could you help me where did I go wrong?
marsh citrusBOT
could you help me where did I go wrong?
tiny nebula
chilly spoke
https://www.wolframalpha.com/input?i=%28sqrt%2817%29-3%2F2%29%5E%282009%29*%28sq...
you just forgot to put the parenthesis on wolfram alpha
it's doing sqrt(17) - (3/2)
tiny nebula
you just forgot to put the parenthesis on wolfram alpha
it's doing sqrt(17) - (3...
oh thanks man
chilly spoke
yea np
tiny nebula
.close
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haughty token
hi
haughty token
granite knot
what have you done thus far
haughty token
something along the lines of
on the top i put (x+1)(x-1) because i cubic rooted to remove the power 3
haughty token
just like how you square root to the remove the power of 2
granite knot
the cube root would apply to (x^3-1), not just x^3
and that doesnt help with this question anyways
haughty token
the cubic root of 1 is still 1
granite knot
no, (x^3-1)^(1/3) is not equal to x - 1
for example, (a+b)^2 is not equal to a^2+b^2
haughty token
oh ok
so only square roots?
cause i did a square root here w 25 and it worked
do i only use the root tactic when i have a power 2?
granite knot
no, there is no root tactic when finding limits - the only reason you might have gotten the right answer is because x^2-25 = (x+5)(x-5)
haughty token
well its not a root tactic to solve limits its a root tactic for factorization
and then AFTER the factorization i solve the limit
granite knot
thats not exactly how factorisation works as well: $\sqrt{x^2-25}\neq x-5$
elfin berryBOT
Aman
haughty token
yea well its just to factorize not solve
because when i get (x-5)(x+5)
i can the solve the limit by cancelling the top with the bottom in the division
then plug the limit number instead of the x
glossy flint
That's the idea, exactly
For the exercise the idea is the similar, just use another identity
Hint: difference of cubes
granite knot
yeah thats fine, so with the current equation, just factorise x^3-1 and cancel out the denominator to find the limit
haughty token
ok let me think
a3 – b3 = (a – b)(a2 + ab + b2)
isnt this the difference of cubes?
it would work since 1 is not cubed
granite knot
1=1^3
haughty token
so because its a 1 it can be whatever power i want it to be
granite knot
yes basically
haughty token
alright let me attempt this then
alright so the answer is 3
thank you guys for your help
.close
fathom ridge
I'm trying to find restrictions on $p$ and $q$ such that $\displaystyle \sum_n \f{(\ln n)^p}{x^q}$ converges where $p, q > 0$
marsh citrusBOT
I'm trying to find restrictions on $p$ and $q$ such that $\displaystyle \sum_n \...
fathom ridge
this was what I got with the integral test
so is it just p > 0 and q > 1 or am I missing something
.close
deft goblet
I need help figuring out how the 100 gor their in question 12 and why the t is multiplied instead of divided in question 11
marsh citrusBOT
I need help figuring out how the 100 gor their in question 12 and why the t is m...
smoky parrot
Do you know the log rules?
sinful skiff
the 100 comes from the 2
cloud field
I need help figuring out how the 100 gor their in question 12 and why the t is m...
log₁₀(100) = 2
sinful skiff
the plus 2 is inverted into log
deft goblet
I'm just wondering how did it even get up their. I though the 2 would be near the bottom with the b^6. At what step did we take the log of 2
deft goblet
Do you know the log rules?
I do know the rules but I'm still confused on how and when to apply them
smoky parrot
We're not taking the log of 2
Can you think of a number which, if I took the log of that, would give me 2?
deft goblet
100
smoky parrot
Right, substitute 2 = log(100) in there and apply the rules. What do you get?
marsh citrusBOT
@deft goblet Has your question been resolved?
deft goblet
Log a^1/3 - logb^6 + log 100. Wouldn't the 100 need to be near the a to appear in the numerator. Or dose the order of operations not matter hear?
smoky parrot
No, the minus sign only applies to -1/6 logb because there's no parentheses around 1/6 log b + 2
deft goblet
Ooo think I understand so this would be equivalent to the awnser. But it's only 1 step away from solution
Thank you
smoky parrot
Yes
marsh citrusBOT
@deft goblet Has your question been resolved?
quasi sierra
i literally have no clue how to do this
marsh citrusBOT
i literally have no clue how to do this
true parcel
i literally have no clue how to do this
try proving a simpler case
for two variables, 2(ab+1) > (1+a)(1+b)
similarily for c and d
quasi sierra
but then
we get
ohhh damn
ill try thanks
:)
@true parcel i still don't get 8(abcd+1) though anywhere
marsh citrusBOT
@quasi sierra Has your question been resolved?
mellow crag
just an idea
but what happens if we express ur inequality in terms of the elementary symmetric polynomials?
oh wait nvm i've got it
quasi sierra
No clue what you just said but kindly explain
mellow crag
expand out (1+a)(1+b)etc.
quasi sierra
And then?
mellow crag
quasi sierra
ye fine
mellow crag
but then 1 < d
so my idea was could we pair them off and prove i.e.
abcd + 1 > abc + d
which is true by rearranging
quasi sierra
how do we prove it though like mathematically this all makes sense
mellow crag
abcd + 1 > abc + d
rearrange that
(abcd + 1) - abc - d = (abc - 1)(d - 1) > 0
so then just write up how u paired them off basically
cunning jackal
whats the significance of letting delta = infimum of 1 and 2/15 epsilon
cunning jackal
i can just let delta = 2/15 epsilon and the proof should be done?
why involve 1
and why 1 specifically
mellow crag
and why 1 specifically
i glanced over the thing so idk if this is what they've done
but i suspect it's because then you can say i.e.
$\delta^2 \leq \delta$
elfin berryBOT
LY
mellow crag
often it's helpful to assume delta < 1 so then you can make everything a linear multiple of delta
that's what i suspect it's there for
glass silo
In particular, see this part: 1 < x < 3 is equivalent to |x - 2| < 1
That's how you get to bound this thing, but that bound is only when you have the |x - 2| < 1
marsh citrusBOT
@cunning jackal Has your question been resolved?
idle slate
$(x^2-1)y''+x^2*y' + cot(x)y = 0$ I just want to make sure I am determining the singular points of this equation correctly. Is it just $x=1,-1,n\pi$ for $n \in \mathbb{Z}$?
marsh citrusBOT
$(x^2-1)y''+x^2*y' + cot(x)*y = 0$ I just want to make sure I am determining the...
elfin berryBOT
Secret
grave dove
$(x^2-1)y''+x^2*y' + cot(x)*y = 0$ I just want to make sure I am determining the...
yes thats it
idle slate
yes thats it
ok would all those points be regular singular too?
idle slate
wait but regular singularities aren't always removable
grave dove
regular singularities is another name for removable singularities
but the ones above are not regular
true singularities!
idle slate
no when i say regular singular point I mean this
grave dove
oh nvm me then, i didnt study like this
so just perform that test
and deduce whether they are regular or not :p
idle slate
ok makes sense and one more thing, do you know if the frobenius method gives the same indicial equation for all regular singular points?
grave dove
ive heard of the Frobenius method, but i didnt dive too much into this to answer you :d
marsh citrusBOT
marsh citrusBOT
Available help channel!
exotic orbit
The channel i was posting my question in before was timed out since I went to sleep, but here is the last part of my question about arithmetic sequences I'm struggling with
marsh citrusBOT
The channel i was posting my question in before was timed out since I went to sl...
exotic orbit
This is what I've done so far:
At this point I see the telescoping series the sum makes, leaving only $1/a_1 - 1/a_k$
elfin berryBOT
night night
exotic orbit
But I'm not sure how this shows that the sum will always be less than 2
red nimbus
oh nvm
exotic orbit
i just watched a tutorial on the partial sum decomposition for that part so im pretty sure its correct
elfin berryBOT
bacc
red nimbus
So we have to prove that a_k > 0
elfin berryBOT
bacc
elfin berryBOT
bacc
red nimbus
The lowest value is 1/2
mellow crag
aren't you basically done?
you've shown that 1/(a1 + 1) + ... + 1/(ak + 1) = 2 - 1/a_k
and a_k > 0 obviously so we're done?
exotic orbit
The lowest value is 1/2
Ohh thank you, this makes sense! tyvm for the help
exotic orbit
you've shown that 1/(a1 + 1) + ... + 1/(ak + 1) = 2 - 1/a_k
Sorry, I just wasn't paying attention before and didn't see that
exotic orbit
Thank you!! i really appreciate it
I'll close the channel now, because I just need to write it out from here. Thank you for the help again!
.close
marsh citrusBOT
red nimbus
and a_k > 0 obviously so we're done?
I am thinking of whether one should prove this with induction
Since we are only given a start value
mellow crag
I am thinking of whether one should prove this with induction
if u were to prove it formally, then yeah u'd use induction
but tbh it's kinda just obvious
mellow crag
Sorry, I just wasn't paying attention before and didn't see that
yeah sometimes we miss off stuff we've done
marsh citrusBOT
Available help channel!
velvet yarrow
how do I find stationary points after implicit diff
marsh citrusBOT
how do I find stationary points after implicit diff
velvet yarrow
say my function was x^2 + xy + y^2 = 3
so when i diff and simplify
$i get \frac{dy}{dx} = -\frac{2x + y}{x + 2y}$
elfin berryBOT
Big Chicken
raw hawk
i get $\frac{dy}{dx}$ = $-\frac{2x + y}{x + 2y}$
elfin berryBOT
David
raw hawk
Put the "$" on frac
velvet yarrow
ok
elfin berryBOT
raw hawk
Swooped
spark otter
$i get \frac{dy}{dx} = -\frac{2x + y}{x + 2y}$
you have the value of dy/dx
when it's = 0
then you will get y = ...
raw hawk
**<:happy:908558103992225822>David**
For this to equal zero what must happen
spark otter
say my function was x^2 + xy + y^2 = 3
and you can plug it in this equation
raw hawk
velvet yarrow
ok yeah
u solve for y in teh dy/dx = 0
and sub it back in
ez
thanks
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
distant chasm
In a large workplace, there is a pool of 8 printers. Suddenly, one of the printers fails. In how many ways can the 19 print jobs that were in its queue be distributed among the remaining 7 functioning printers, if no more than 4 print jobs go to each printer
gritty hawk
a and b (both natural numbers) gives different uneven remainders after being divided by 5. what is the remainder equal to if you divide the product of a and b by 5?
marsh citrusBOT
a and b (both natural numbers) gives different uneven remainders after being di...
gritty hawk
I did something like this but I don't know how to continue
I simplified it further
divided it by 5
raw hawk
I did something like this but I don't know how to continue
Just $r_1 \cdot r_2$ mod 5
Probably
gritty hawk
🤣 man mods make it so easy
elfin berryBOT
David
gritty hawk
wait
raw hawk
That should be all
gritty hawk
is there a property or something?
raw hawk
This step is not necessary
gritty hawk
I cant
raw hawk
This step is not necessary
Just take the mod5 of the terms here
gritty hawk
every term?
gritty hawk
so I just mod5 the entire thing
raw hawk
so I just mod5 the entire thing
Yup
elfin berryBOT
David
raw hawk
how do you get remainder 3 from r1 * r2 mod5
I don't think you can simplify beyond $r_1 \cdot r_2$ mod5
elfin berryBOT
David
raw hawk
That's the final answer
gritty hawk
that's odd
raw hawk
😃
raw hawk
that's odd
Lol
raw hawk
Remember the two rs were never assigned with any numerical value
raw hawk
thanks yet again for the help 👍
No problem
You can verify with any two numbers
Like 7 and 6
gritty hawk
yea i'll try and substitute
see what happens
I mean
it is given that
they're uneven
if that helps
raw hawk
And see if the remainder is r1*r2mod5
gritty hawk
uneven * uneven = uneven right
I'll try and substitute uneven numbers and see what happens
thanks 👍
raw hawk
I'll try and substitute uneven numbers and see what happens
Yes
If there's anything tell me or ping helpers
marsh citrusBOT
marsh citrusBOT
Available help channel!
limber linden
can anyone help me solve this class is functions and modeling, got to solve using a ti-84
marsh citrusBOT
can anyone help me solve this class is functions and modeling, got to solve usin...
sick walrus
can anyone help me solve this class is functions and modeling, got to solve usin...
What do you need help with? How to use the calculator to find the x values or how to interpret the graph
limber linden
i guess both? Im kinda confused on how to find the largest value and the middle value (not sure if its the middle but the one question in the middle)
sick walrus
i guess both? Im kinda confused on how to find the largest value and the middle ...
You can see that 0 will be the middle value right?
Without even graphing it
limber linden
how so?
sick walrus
Because plugging in 0 will produce 0=0
Both terms have a variable and the other side is 0
limber linden
that makes sense but im still kind of confused on how you knew the middle would be 0? is that a rule, when i found the smallest value i did the equation and graphed it then trace zero
sick walrus
that makes sense but im still kind of confused on how you knew the middle would ...
No, I only noticed both terms have a variable so I thought to test 0 in my head and it ended up being a solution. I know it is the middle solution because I know there is a positive 3rd solution
limber linden
oh i see
that makes sense
for the largest value though what 2nd trace should i use?
sick walrus
How did you find the smallest value
limber linden
2nd-trace-zero
sick walrus
I can’t think of how that looks off the top of my head but, you should be picking the lower bound to the left of the rightmost 0 you see and the upper bound to the right of the rightmost 0
If you have it graphed as y=0.3x-0.2x^3
You should see three points where it crosses the x axis
limber linden
sinful hinge
graphed it on my TI, it doesn't look the same for some reason?
limber linden
what are your window settings?
sinful hinge
xmin = -5 xmax = 4 ymin = -1 ymax = 1
limber linden
xmin=-100 xmax=100 then i zoomed 0 to find y values
sinful hinge
i'll install discord on my phone and send you a pic of how it should look like, cause the graph i got has 3 intersections with the 0 line on x whihc should give you the right answer
sick walrus
Try zooming in perhaps? I graphed it on desmos and it looks different
limber linden
had did you find the intersections on your calculator?
limber linden
xmin = -5 xmax = 4 ymin = -1 ymax = 1
i just used switched to these
sinful hinge
sick walrus
That looks right
sinful hinge
check your mode perhaps?
limber linden
mine looks like that now
sinful hinge
i once used the wrong mode and got all the wrong graphs on a TI84
sick walrus
Try tracing from a point right after 0 and a point at the right end of the graph
sinful hinge
mine looks like that now
if it looks like that now, try getting all the zero values again and it should bring you to the rigth answer
limber linden
if it looks like that now, try getting all the zero values again and it should b...
wym by this? Sorry this is my first math class in like 2 years im a bit dense
sinful hinge
i just used switched to these
oooo i just read this sorry
sinful hinge
wym by this? Sorry this is my first math class in like 2 years im a bit dense
nooo i thought your TI mightve been in degrees instead of radians. i remember that messing up some graphs of mine in the past but yours was just a window problem
ur good
if its working now theres nothing needed to change 😌
limber linden
it doesnt give me any more trys on the problem but the answer was 1.22
sinful hinge
yees
limber linden
i didnt get that though, i used trace maxium and got 0.707
so how did you get 1.22?
sinful hinge
you use zero to find the zero point of the very last intersection with x
so your smallest will be the very left intersection of the graph with x
middle will be the middle one
and largest will be the very right one
limber linden
yes i jsut got that
limber linden
kinda, so do i only use zero once and dont use mini or maxium?
sinful hinge
yes, only use zero !!
limber linden
ah i see
sinful hinge
you can also plot a line y2 = 0 and use intersect to get the values
same results, depends on what you find easier
limber linden
but im confused on how i got a negative for the smallest value
sinful hinge
if we look at the graph, the furthest left intersection of the plotted graph that intersects with x is negative
sinful hinge
the zero point is quite literally just x = -1.22 and y = 0. is that your question??
limber linden
i think im just over complicating the problem ngl im sorry😂
sinful hinge
so are you just moving the keys over to the intersect?
yes? idk what u mean by that compltetely but
for every intersection of the graph with x, you use either zero or intersect to kind of lock the exact point you want coordinates of out to get the location of it
limber linden
i guess what im getting confused about is not using a trace method to find the different values i see where the intersect is on the graph but i thought we had to use some sort of trace method to find the exact answer?
sinful hinge
trace method ?
limber linden
does that make sense or no? if not i understand it enough and apperaciate your help!
2nd trace
like value zero mini max intersect
sinful hinge
yes. if you press 2nd trace and then press 2 again you get the option zero
limber linden
yes i know that part
sinful hinge
after pressing zero, you get the option to choose a left and right bound
do you get that part too?
sinful hinge
np!!
limber linden
.close
analog orchid
when i finished synthetic divisioin i was left w 2x^2-10 so idk if i factored wrong or sm but i got the zeros right so its prolly mostly right
marsh citrusBOT
when i finished synthetic divisioin i was left w 2x^2-10 so idk if i factored wr...
digital robin
when i finished synthetic divisioin i was left w 2x^2-10 so idk if i factored wr...
pretty sure this gives you a remainder of 0
analog orchid
pretty sure this gives you a remainder of 0
yea so that was the verify part
thats not the part that i got wrong
but the quotien was 2x^2-10
digital robin
mb entered the wrong thing while thinking
analog orchid
no thats mb i said the wrong thing
digital robin
anyways factors should have been (x-rad5)(x+rad5) other than the existing 2x-1
analog orchid
anyways factors should have been (x-rad5)(x+rad5) other than the existing 2x-1
ohhh did i not factor completely is that why
next raft
c has an extra 2
digital robin
im also not entirely sure how you got a 2 there
analog orchid
im also not entirely sure how you got a 2 there
factored the 2 out of 2x^2-10
digital robin
anyways for c its just (2x-1)(x-rad5)(x+rad5)
digital robin
its just asking for the factors
analog orchid
oh ok got it
analog orchid
its just asking for the factors
so exclude the 2 from b as well?
digital robin
ye
analog orchid
ok tysm
next raft
2 disappeared when u divided by 2x-1
marsh citrusBOT
marsh citrusBOT
Available help channel!
acoustic plume
how to differentiate this ?
marsh citrusBOT
how to differentiate this ?
copper raven
fervent rampart
chain rule applied several times
acoustic plume
i got e^tan-1(sqrt(2+x)) . (1/2(2+x)^-1/2) / 3+ x
then when i sub x=1 i get the same asnwer as above
does it mean it's equal or was it js coincidence
wait
ffs
they mean the same thing
nvm
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
humble river
marsh citrusBOT
humble river
waht am i doing wrong plz and thnx
i think i dont understadn cm^3 part maybe?
i mean the numbers seem similar to titanium but ik i did somethign wrong surely
wet oriole
Please explain why y is /5, not /10
marsh citrusBOT
Please explain why y is /5, not /10
marsh citrusBOT
@wet oriole Has your question been resolved?
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
wet oriole
Because chatGPT has brain damage
Yes it is, I know, so is it wrong?
I beat the robot yeah?
main idol
,tex .exp rules
elfin berryBOT
riemann
wet oriole
,tex \.exp rules
This is not what I'm asking 😭
wet oriole
Please explain why y is /5, not /10
I got down to this as well, but I be doing /10 here, I checked my answer via the robot n it said /5 here, so I wanna know which is correct
main idol
I got down to this as well, but I be doing /10 here, I checked my answer via the...
Don't use chat gpt for math
Just show your work
wet oriole
Don't use chat gpt for math
I'm just double checking my answers
Can you guys just tell me if my thinking with /10 is correct?
marsh citrusBOT
@wet oriole Has your question been resolved?
main idol
Can you guys just tell me if my thinking with /10 is correct?
Show your work like I said above
marsh citrusBOT
marsh citrusBOT
Available help channel!
gloomy minnow
marsh citrusBOT
gloomy minnow
Hello, can someone point out wheres the mistake that i went wrong ?
The ans given is √(10+2√5) / 4
late geode
can you state what substitution you performed near the end?
gloomy minnow
can you state what substitution you performed near the end?
i just let sin θ = x
late geode
and what do they want the value of?
gloomy minnow
and what do they want the value of?
cos 18 deg
late geode
yes
gloomy minnow
so im in the right way ?
late geode
yes. you're just not done yet