@heavy frigate Has your question been resolved?
#help-28
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spice orchid
this is just your usual u substitution
but with the letter y
find dy in terms of dx
if y = f^(-1)(x) then x = ?
which is...?
u?
right
so x = f(y)
should be clear to you now
good job, no worries
,w int arctan(x)
seems so yes
spice orchid
er wait i think you need more in the tan int
yeah you need to times by the derivative of arctan(x)
well it doesnt
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granite marlin
so I don't have work, i just want to know the first 5 digits of pie
shrewd hamlet
glossy valveBOT
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hoary nacelle
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hoary nacelle
been stuck for way too long
chrome idol
,rotate
glossy valveBOT
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@hoary nacelle Has your question been resolved?
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torn prairie
Here is my problem or question...
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Here is my problem or question...
torn prairie
how tall is the great pyramid?
The height of the Great Pyramid of Giza, also known as the Pyramid of Khufu, is 146.7 meters (481 feet).
is the a meaning to the number 481
The height of the Great Pyramid of Giza being 481 feet is just a measurement and doesn't have any symbolic meaning as far as we know. It was built thousands of years ago, and the exact method used to determine its height is not known. However, it's likely that the ancient Egyptians used a simple measuring system based on their own body parts, such as cubits, to determine the dimensions of the pyramid.
what is 481 feet in cubits?
A cubit is an ancient unit of length that was used in many civilizations, including ancient Egypt. It is estimated to have been about 44.5 cm (17.5 inches) in length, but there is some variation in the length of cubits used in different periods and locations.
To convert 481 feet to cubits, we need to know the exact length of the cubit used in ancient Egypt, which is not known with certainty. However, using the estimated length of 44.5 cm per cubit, we can calculate that 481 feet is approximately 755 cubits. Please note that this is just an estimate and the actual length in cubits may have varied.
44.5 times 755
If we multiply 44.5 (the estimated length of one cubit in centimeters) by 755 (the estimated number of cubits that make up the height of the Great Pyramid), we get approximately 33,497.5 cm, or 335 meters.
335 meters converted to feet?
To convert 335 meters to feet, we can use the conversion factor of 1 meter = 3.2808 feet. Multiplying 335 by 3.2808, we get approximately 1096.47 feet.
481 minus 335
If we subtract 335 (meters) from 481 (meters), we get 146 (meters), which is the height of the Great Pyramid of Giza.
Is this possibly how the Egyptians measured with cubits?
normal tree
is that written by chatgpt
torn prairie
Me and chat gpt yes
torn prairie
Is that accurate or just nonsense?
normal tree
Is that accurate or just nonsense?
it contains a ridiculous amount of non-essential information, blabbers a lot, and doesn't really have anything cohesive to say
hence why I asked whether it was chatgpt
torn prairie
Is it accurate?
torn prairie
IDK, I think I just figured out how ancient egyptians measured using cubits
normal tree
is that your question?
torn prairie
are the calculations correct?
torn prairie
Are the calculations from the long message correct?
normal tree
which one
torn prairie
All the calculations..
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@torn prairie Has your question been resolved?
austere rose
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primal yoke
Anyone Good at maths phy and checm
austere rose
I have tried to work out the answer, but I am stuck on one of the final steps
primal yoke
deemedEpic are u good in maths phy and chem?
austere rose
decent
primal yoke
<#488120190538743810>
ok ok sorry
torn jolt
I have tried to work out the answer, but I am stuck on one of the final steps
what did you do so far?
austere rose
hi
torn jolt
have you converted all the terms to log base 4 yet?
austere rose
Yeah
What I did was:
log_2(a) = 2log_4(a)
Not sure how I got there I just used some logic
Im not sure how to proceed from this step
<@&286206848099549185>
@torn jolt
.close
twin wolf
How do I find the velocity in here? I know it’s displacement/time so v1-v0/t but how do I find the displacement using what I have here
meager dew
$\bar{v}=\frac{\Delta x}{\Delta t}$
glossy valveBOT
a disappointing son
twin wolf
**a disappointing son**
I only have one speed here in the table for each row so how would I find the change in x
For example like 6.25m/s - 0m/s or something?
meager dew
x is not speed
meager dew
$\Delta x$ represents displacement
glossy valveBOT
a disappointing son
glossy valveBOT
a disappointing son
twin wolf
Change in distance?
meager dew
correct
twin wolf
So for example the first row the change in distance would be 10m and 0m because the initial distance is 0?
meager dew
er -- position, rather
no
you start at O, move to A, then move back to O
so your final position is at O and so is your initial position
meaning you have a displacement of ...?
meager dew
oh shoot i was looking at the 2nd row lol
twin wolf
Okay
meager dew
sorry, was looking at the wrong one
you are correct for the first one
displacement would be 10
twin wolf
So 10/1.6 for the first one then
meager dew
yes
twin wolf
Oh so the average speed and velocity would be the same
meager dew
correct
meager dew
yep
twin wolf
Oh I think I found the pattern. So for any column in the table where you return to the original position, the average speed and velocity would be 0 and anything that doesn’t return would be the same as your average speed correct?
meager dew
that's correct, but i would recommend knowing the logic behind that rather than seeing the pattern
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gentle glacier
Vertex of parabola is (-1, 16), equation of graph written as -ax^2+ bx + c find highest possible value of b
torn jolt
given the vertex, give me the equation of the function
torn jolt
no
gentle glacier
oh
torn jolt
just give me
torn jolt
sure
gentle glacier
what i first did was = -a(x+1)^2+16
torn jolt
yes
gentle glacier
= -a(x^2 + 2x + 1) + 16
so then
= -a (x^2 + 2x + 17)
so far so good?
and then I replaced values
torn jolt
yeah
torn jolt
huh?
torn jolt
what value you replaced?
gentle glacier
16 = -a (-1)
torn jolt
why
gentle glacier
plugged in the vertex
gentle glacier
so what should i do
torn jolt
what i first did was = -a(x+1)^2+16
this formula by definition gives you the vertex (-1, 16)
torn jolt
so you got -ax^2 + -2ax + 16-a right
gentle glacier
yeah
torn jolt
so b = -2a
since a can be anything in R
b doesnt have a maximum value
you can get any number for b also
gentle glacier
wait but would it be 17a or 17?
torn jolt
but assuming how it wrote -a i think a is (constrained) to be a positive number
gentle glacier
ok
gentle glacier
To be honest Idk
it was a quesiton I remembered i dont have the ms
in any case If they give you a vertex
to find b I should just do these same steps?
torn jolt
wait but would it be 17a or 17?
actually 16 - a
torn jolt
to find b I should just do these same steps?
yeah
gentle glacier
so b = -2a
ok and this formula is for the axis of symmetry right?
and then you equal
ok
i got it
thanks
.close
bronze magnet
y = x^2 + 7x Point : (-3,-12)
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y = x^2 + 7x Point : (-3,-12)
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VulcanOne
bronze magnet
what is the importance of the f? the equation is y = x^2 +7x
short siren
y = f(x)
bronze magnet
oh
so what happens next
i think you meant to put negative sign on top of fraction right ?
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warm vale
can someone help explain how to turn 2-2i into it's polar form
torn jolt
find the norm
warm vale
i am not sure how the - changes it
torn jolt
the minus?
warm vale
changes the end result that is
torn jolt
like just do 2-2i = (2) + (-2)i
warm vale
but when working out the θ, I get a different value for cos(θ) and sin(θ), is that ok?
I got the one in the cos bracket as being positive
and i think it comes down to me getting confused over having a negative length value
sharp vine
but when working out the θ, I get a different value for cos(θ) and sin(θ), is th...
what did you get
cos(-x) = cos(x)
so if you have
cos(pi/4) it's fine
torn jolt
sin(x) = -sin(-x)
warm vale
ohh ok, so would work out both cos(θ) and sin(θ) and then use cos(-θ) = cos(θ) to make sure they are the same
to make sure the θ values are consistent in both i mean
torn jolt
but i mean me personally i would just do z=a+bi => a = |z|arccos(a/|z|), b = |z|arcsin(b/|z|)
no matter if its positive or negative
warm vale
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dire flame
can some explain what i put the bounds for this integral
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can some explain what i put the bounds for this integral
short siren
Okay
dire flame
short siren
Oh this is an enclosed integral
dire flame
yeah for like closed surface area
but idk what the bounds should be or if there should be any
short siren
Hmm unfortunately I haven't dealt with enclosed integrals before
So I can't help with that
Lemme look it up and see if I can explain it
dire flame
okayy ty
dire flame
Have you taken like a course on electricity?
short siren
I have but all I have done for these types of integrals is basically find the areas of recognizable shapes like rectangles, circles, sphere surfaces, etc...
restive hawk
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ivory cairn
your set up is wrong
restive hawk
):
ivory cairn
the x^2/(y^2-8) just moves to the other side of the equals, it should be flipped
restive hawk
ho rigg
no
i flipped my divisions
and multiplicatins
yeah
whoops
does this look better
ivory cairn
yes
restive hawk
and x side is an easy integratin
assuming i need u sub for y side
gotten up to here but kind of stuck for isolation
i think i may have to use my initial condition y(1)=sqrt9 to drop the sign
ivory cairn
exponential functions are always positive, so you don't need the absolute values
restive hawk
oh thats true
ivory cairn
i think anyway....
restive hawk
well that makes sense
plus in my initial cond
i have a positive
so a negative sign would never work
on a positive exp
at least from looking ahead
sand belfry
you made some mistakes
sand belfry
your second line should look like that
sand belfry
your second line should look like that
the left side should look as the follows:
just replace the 'x' here with y for the 1st picture
sand belfry
the left side should look as the follows:
just replace the 'x' here with y for ...
then the left side as follows:
and finally equate them together to get the answer @restive hawk
ionic gate
How would I do this?
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How would I do this?
rocky vale
Do you know what is meant by stationary points?
ionic gate
When the gradient is 0
rocky vale
right so you want dy/dx = 0
ionic gate
Yess
rocky vale
So how can we get dy/dx from these parametric equations? 🤔
ionic gate
I tried doing it implicitly like x=y^3/2 -8y^1/2
But when I Don't know if that's right
rocky vale
You could probably do something along those lines
but
it's much simpler to just do
dy/dx = (dy/dt) / (dx/dt)
ionic gate
Yea
but how whould I do that
rocky vale
which means dy/dx = ?
ionic gate
2t/(3t^2-8)
ionic gate
2t/(3t^2-8)=0
And solve it?
ionic gate
I got t=0
rocky vale
yep
ionic gate
Okay I didn't make any mistakes right
rocky vale
Nope, that's all good 👍
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deep crag
Can someone please explain why this has a limit? I was told that jumps meant a limit did not exist.
deep crag
hollow sable
Can someone please explain why this has a limit? I was told that jumps meant a ...
This is not a “jump”, it’s just a discontinuity. A jump would be like from -1 to 3.
Like (0.99,-1) and (1.01, 3) would be a jump
But (0.99,2) and (1.01, 2) would be a discontinuity
deep crag
ahhh so a significant change to the y axis is the only thing that qualifies it as a jump?
simple totem
But (0.99,2) and (1.01, 2) would be a discontinuity
this is considered a discontinuity if the y value at x = 1 is not 2
hollow sable
this is considered a discontinuity if the y value at x = 1 is not 2
But the limit as x approaches 1 would be 2 right?
simple totem
in the image yes
deep crag
so is this not a discontinuity?
simple totem
this is a discontinuity because the value at x=2 is not defined
deep crag
ahhhh gotcha. thanks!
brisk obsidian
Your basic test for continuity.
If f(a) does not exist, then it is discontinuous.
fathom cairn
One of the two dice was rolled a thousand times, scoring four 324 times. Which one do you think it was? Justify
simple totem
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1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
simple totem
do you know about probability?
simple totem
if we have a coin and we flip it 1000 times, about how many times should we get heads?
fathom cairn
you cant know, because it can be like for example 100times head then 50 times number and go on
simple totem
im talking about what you would expect
not what would actually happen
would you expect to get 1000 heads?
fathom cairn
No
fathom cairn
500
simple totem
exactly
now if we have a dice
where half the squares are labeled H
and the other half are labeled T
about how many H should we expect to see if we roll the dice 1000 times?
fathom cairn
so you mean there are 3 H‘s and 3 T‘s because a dice has 6 sites. So it would be 333
simple totem
why 333?
fathom cairn
1000/3?
simple totem
why are you dividing by 3
fathom cairn
Should not?
simple totem
what are your chances to land on an H?
fathom cairn
okey 500
simple totem
yes
so if instead of H and T
we say the dice has 3 sides with the number "4"
and the other 3 with a different number
how many times should we expect to see the number "4" if we roll the dice 1000 times
fathom cairn
500?
simple totem
yes it's exactly the same
fathom cairn
yea okey now in relation to my task
simple totem
now if instead we had 2 sides labeled "4", and the other 4 sides labeled something else
this is all in relation to your task
hopefully you see the dice they gave you have exactly the sides im describing
fathom cairn
ye
simple totem
now if instead we had 2 sides labeled "4", and the other 4 sides labeled somethi...
consider this (this is just the first dice they gave you)
we have 2 sides labeled "4"
and 4 sides labeled something else
fathom cairn
Hmh
simple totem
so 2/6 sides are labeled "4"
that is
1/3 of the sides
so we should expect to see "4" 1000 * 1/3 times
what's 1000/3?
fathom cairn
333
simple totem
which number is closer to 324, 500 or 333?
fathom cairn
324
simple totem
the choices are 333 or 500
simple totem
so then which dice was probably rolled?
fathom cairn
Ye okey number 1
okey wait a minute
I have to learn more about that…
(Maybe do you know some good websites..?
simple totem
i dont
torn jolt
let x be the number of students in the class
bcuz u want to find it
what can u say about the women in the class?
onyx glen
@torn jolt do you know in general how percentages work?
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young bramble
can i use universal generalization to proof that odd+odd=even
for examplr:
1+1=2
% for modulo
1%2=1 1-> 1 is odd
2%2=0 -> 2 is even
warm abyss
And how does this prove that odd + odd = even?
young bramble
idk
that was my question if this is enough to prove
I wasnt sure if just adding any 2 arbitrarily chosen odd numbers and having an even number as sum was enough
warm abyss
No. Two examples are not a proof
You can make it like this:
Let a, b be arbitary odd numbers
Then a mod 2 = b mod 2 = 1
What is a + b mod 2 then?
young bramble
but this isnt universal generalizazion right?
idk im probably just mixing up stuff
warm abyss
Wdym with universal generalization? You were just giving an example for which it is right
young bramble
Wdym with universal generalization? You were just giving an example for which it...
"If P(u) is true for an arbitrarily chosen u in domain D then we can generalizr that for all x in domain D, P(x)"
warm abyss
"If P(u) is true for an arbitrarily chosen u in domain D then we can generalizr ...
You need to prove this for an arbitary number though
warm abyss
You can make it like this:
Like it did it here
young bramble
oh ok
warm abyss
It does mean that you can just chose a random example
warm abyss
Sorry, I'm not a native. Obviously 😂
young bramble
alles gut
warm abyss
Haha
young bramble
weiß ich noch nicht
würde eher informatik aber hab noch zeit
studierst du mathe?
warm abyss
Yes
warm abyss
Ist nicht einfach. Der Unterschied zur Schule ist, das es jeder kann. Aber, wenn man Spaß an der Mathematik hat, ist es durchaus machbar
young bramble
Was kann man mit Mathe nach dem Studium außer Forschung eigentlich machen?
warm abyss
Mathematik kannst du durchaus auch im Versicherungswesen oder auch in der Wirtschaft verwenden (Risikomanagement). Auch kannst du (zumindest) in Bayern Mathe nur mit Integriertem Anwendungsfach (Informatik, Physik, Chemie, ...) studieren.
warm abyss
Was kann man mit Mathe nach dem Studium außer Forschung eigentlich machen?
Von den Inhalten her wirst du recht wenig nach dem Studium weiter verwenden. Das ist aber bei fast jedem Studium so. Ist bei meinem Bruder als Maschinenbauer genauso. Viel mehr geht es um das Skillset, wie die Fähigkeit zum Abstrahieren, das Einarbeiten in komplexe Themenbereiche und die hohe Frustrationstoleranz, das man sich im Verlaufe des Studiums aneignet
restive hawk
i have not seen a differential equation question like this
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vapid pivot
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vapid pivot
How do I plot the eigenvectors? Will it just be one vector with a direction on matlab?
I have this scatter plot.
And this is my calculated eigen vector on the covariance.
fast peak
plot([0,0], [x,y]) or some variation of that
vapid pivot
Like this?
fast peak
something like that, yes. but that vector looks wrong
vapid pivot
my values change when I run the code
that's the new values
What does it mean by "length given by the square root of the eigenvalues" Is it sqrt(.9633+17.0006)?
fast peak
how are you using the eig command
it should give you two things
a list of eigenvalues
and a list of eigenvectors
vapid pivot
Oh okay I have two 2x2 matrices now
fast peak
the first has as columns the eigenvectors with norm 1
the second has on the diagonal the eigenvalues
vapid pivot
Ohhh okay. Thank you so much!
fast peak
you should read the documentation
vapid pivot
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jolly dirge
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jolly dirge
Help plz
runic bloom
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glossy valveBOT
hushed raft
Do u know the sin cos tan?
jolly dirge
Yeah
jolly dirge
Ok
hushed raft
What trigonometric u gonna use?
Remeber, SQ is the opposite from the point of view of the angle
jolly dirge
Tan
hushed raft
Not really
twilit barn
tan(x) = opposite /adjacent
hushed raft
U want a relation between opposite side and hypotenuse
jolly dirge
Sine
hushed raft
Sine is for opposite and hypotenuse relation, yes
twilit barn
Sine is for opposite and hypotenuse relation, yes
are you sure?
jolly dirge
Sine is opposite/hypotenuse
twilit barn
Do you know the length of QS? @ The guy
jolly dirge
8m
hushed raft
Sorry, it's 0:45 here xD
jolly dirge
I see
twilit barn
haha thats all good
hushed raft
So, u can now apply the sin formula
jolly dirge
I tried but the answer was too small
twilit barn
Lets see your working out?
hushed raft
Is your calculator mode in degrees?
hushed raft
So, u have SQ and you have PQ
jolly dirge
Yeah
jolly dirge
I'm not sure
hushed raft
Look at this
jolly dirge
Tan
hushed raft
Yep
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frail perch
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frail perch
why is this wrong?
i guess if we take the slope of each line and plug it into the equation we get -4 but -4 isnt a answer
hot herald
show full work
frail perch
hey ramonov 🙂
hot herald
which equation are you plugging into
you should be at some point applying something like quotient rule
frail perch
i didnt do any work for it i just tought about it
hot herald
i didnt do any work for it i just tought about it
not a good idea, always do the work
you got it wrong because you didn't do the work
frail perch
i did QR earlier but the answer wasnt right
lemme try one more tim e
it should be 0
but its not correct
or wait
should it be -2x/(1/2)x?
hot herald
the question wants P'(2),
so you'd want to slope where x=2
frail perch
Like I'm confused about the approach
hot herald
considering the quotient rule and not being lazy with notation
$$P'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}$$
$$P'(2) = \frac{g(2)f'(2) - f(2)g'(2)}{(g(2))^2}$$
$f'(2)$ is the slope of $f(x)$ where $x=2$ \
$g'(2)$ is the slope of $g(x)$ where $x=2$ \
$f(2),g(2)$ can be read directly off the graph
glossy valveBOT
ℝamonov
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Jshy <3
lyric cargo
rocky vale
That's right, but are you sure you want 2 decimal places and not 2 significant figures?
Usually if you're using scientific notation, you'd be concerned with sig figs.
well then yeah, given that wording, 7.16 * 10^-10
glossy valveBOT
Jshy <3
astral lotus
-_-
3^3 and (squr 2)^3 and then multiple the numbers. Easy
What you can do it in your head 3^3 is 27. Squr 2^3 is 2root2 and multiple together is 54root2
Dude I'm not annoyed calm down.
I go do other stuff now
torn jolt
please help with 55a, tag me when responding
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please help with 55a, tag me when responding
lunar iris
please help with 55a, tag me when responding
Show your work.
buoyant tinsel
What is (1-0)^2?
I think you've misunderstood where your region is
it's always the bounded region
so your drawing in the top right would be correct
buoyant tinsel
yes
torn jolt
@buoyant tinsel could u help me visualize 55b?
buoyant tinsel
55b would be the same thing, except your axis of rotation is just moved up one unit
something like that
buoyant tinsel
where's the hole?
buoyant tinsel
oh sorry I misread
torn jolt
no worries
buoyant tinsel
yeah then I guess you would have a gap
torn jolt
so it would be like a split up ball?
buoyant tinsel
it would be a silo shape with a hole through the center
buoyant tinsel
I like to think of it as subtracting two disc methods (which it is)
it just combines the integral, which might make it confusing for some people
torn jolt
it just combines the integral, which might make it confusing for some people
i dont really understand that part
so lets say we are doing 55c
if we basically subtract 2 discs methods, bigger radius minus smaller
why isnt it 1^2 - (x^2)^2?
@buoyant tinsel
buoyant tinsel
that would be correct if your axis of rotation were y = 0
torn jolt
wait mb
so that means R is 2^2 in this case?
like i dont understand how to determine whats big R and whats little r
buoyant tinsel
yeah
buoyant tinsel
your axis of rotation is y = -1, so you need to add 1 to your radius
so (x - (-1))^2 = (x + 1)^2
that would be your little r
buoyant tinsel
well no, it's all relative to your function
torn jolt
can i pick an example and u go through it with me please
buoyant tinsel
sorry it's very late here so I gotta head out soon, but basically it's just the distance from your function to the AOR
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wraith ivy
Hey can someone explain me how to do this ?
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Hey can someone explain me how to do this ?
wraith ivy
the last part is the awnser
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wraith ivy
<@&286206848099549185>
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@wraith ivy Has your question been resolved?
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sacred cove
Hey can someone explain me how to do this ?
Sure! I'll explain each part of the task.
a) The distance between two numbers in the respective formats in the interval [0, 1.4] and [10, 100] can be calculated as follows:
For the decimal floating-point format G(10, 3), the distance between two numbers is given by the smallest representable difference, which can be calculated as:
G(10, 3) = 0.001
For the decimal fixed-point format F(10, 2, 2), the distance between two numbers is given by the smallest representable difference, which can be calculated as:
F(10, 2, 2) = 0.01
b) The upper limit of the absolute error, which is determined by G and F in the intervals [0, 1.4] and [10, 100], can be calculated as:
For the interval [0, 1.4], the upper limit of the absolute error is given by the smallest representable difference, which is:
G(10, 3) = 0.001
F(10, 2, 2) = 0.01
For the interval [10, 100], the upper limit of the absolute error is given by the smallest representable difference, which is:
G(10, 3) = 0.001
F(10, 2, 2) = 0.01
c) The upper limit of the relative error, which is determined by G and F in the intervals [0, 1.4] and [10, 100], can be calculated as:
For the interval [0, 1.4], the upper limit of the relative error is given by the ratio of the smallest representable difference to the value being represented, which is:
G(10, 3) = 0.001 / 1.4 = 0.0007143
F(10, 2, 2) = 0.01 / 1.4 = 0.007143
For the interval [10, 100], the upper limit of the relative error is given by the ratio of the smallest representable difference to the value being represented, which is:
G(10, 3) = 0.001 / 100 = 0.00001
F(10, 2, 2) = 0.01 / 100 = 0.0001
I hope this explanation helps! If you have any further questions, feel free to ask.
wraith ivy
Sure! I'll explain each part of the task.
a) The distance between two numbers i...
TY SOOOO MUTCH ❤️
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torn jolt
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torn jolt
How wrong am I
short siren
First you had to divide because the power of the numerator is bigger than the power of the denominator
hollow grove
Convert the improper fraction to proper fraction
torn jolt
Photo math says Im missing like x^2/2 -5x
torn jolt
Why
short siren
Because the numerator is $x^3 +4$ which has a bigger degree than $x^2 +5x+6$
glossy valveBOT
VulcanOne
torn jolt
Does that give the remainder I guess?
short siren
Yeah
torn jolt
Thanks that makes sense
short siren
You do the polynomial division
Then you get a remainder
Then you do partial fractions on the remainder
torn jolt
I did partial fractions on the original prompt right
But that’s not the remainder of poly div
short siren
Yep
torn jolt
So I’m confused as to why I got half the answer if thag makes sense
trim hinge
Can I drop the bases and just compare exponents at this point?
sharp flame
Well a^{\lim_{n \to \infty} (\log_2 n \times \log_a n) - n}
Well $a^{\lim_{n \to \infty} (\log_2 n \times \log_a n) - n}$
glossy valveBOT
NEONPerseus
sharp flame
You can do this
trim hinge
Can I get that to converge to 0?
and are you saying to pull the a in front of the limit
gritty rose
and are you saying to pull the a in front of the limit
yes that's what the symbols mean
you should understand how neon got to that expression. follows from power rules
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viral plume
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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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
torn jolt
sounds like pigeonhole principle
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viral plume
sounds like pigeonhole principle
yes maybe but i didnt get any success by that
torn jolt
what have you tried?
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Show your work, and if possible, explain where you are stuck.
viral plume
i tried to solve it with pigeonhole principle
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winged lava
Hey, just a quick question, what does triviality for intersection mean? thx :)
spice orchid
you need to provide more context
solar river
Hey, just a quick question, what does triviality for intersection mean? thx :)
Triviality for intersection refers to a property of two sets in mathematics, where the intersection of the two sets is an empty set, i.e., the two sets have no elements in common. This is also known as "disjoint sets." When two sets are trivial for intersection, they are considered to be non-overlapping and disjoint. In this case, the intersection of the two sets is said to be a trivial one.
copied from my maths book, can't explain it further myself
winged lava
haha thx a lot, i've tried to google it, idk why i didn't find the definition @solar river
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torn jolt
hello
torn jolt
I need help finding the complex numbers of a poly function
the question is x^4+5x^2+4
Since its a 4th degree im not sure how to aprocche it
I tried the rational zeros test. got nothing
Hello?
spice orchid
this is a quadratic equation in disguise, try a substitution
spice orchid
we have not done U subsition yet
if you're referring to the integrating technique then that is not what I'm referring to, just a general substitution
torn jolt
oh
spice orchid
can you do long division?
divide what by what?
torn jolt
(x+4) and (x+1) by the whole thing
spice orchid
why?
torn jolt
idk lol
ok so im guessing we need to make it into a quatratic before we can work with it correct?
its missing 2 terms
so
spice orchid
well you dont want to pull it out thats not going to help you
but you should notice that it is a quadratic in the variable x^2
spice orchid
I have not idea what you've done
torn jolt
I dont know how to make it un hidden.
(x^2+4)(x^2+1)
becasue it add to give u 5 and times to give u 4
spice orchid
that is a correct factorisation yes
torn jolt
so so we set them to zero
spice orchid
if you're trying to find the roots then yes
torn jolt
so the roots are x=2,1
how do we find the complex zeros with that
can you just tell me how the hidden quad lookslike
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torn jolt
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mental creek
we can set these function equal to zero since f(-5)=f(4)=f(0)=0
When we solve for x then it produces the (x+5)(x-4) and x=0 which is where we get x(x+5)(x-4)
from there we plug f(3) into that function and we get -24 but since we know that f(3)=96 then dividing by what we got means that we plug the -4 in front of the initial x
mental creek
f(4)=0 and f(-5)=0, therefore we can set both equal to 0. The inside of the f(x) is x, so x+5=0 ---> x=-5. same with f(4), x-4=0 ----> x=4
torn jolt
how did you make f(3)=(3+5)(3-4)
mental creek
the f(3) means that we plug 3 into all terms of x, so we took the x(x+5)(x-4) and plugged 3 into all terms
leaving us with 3(3+8)(3-4)
remember that f(x)=y, all the f(x) means is that whatever number is on the inside of the parenthesis is being substituted for x
for example f(x)=x then if we had f(4) it would be f(4)=4, also f(-4)=-4
torn jolt
well your way is much easier than what i was trying to do
where did i go wrong with my attempt?
mental creek
Well to be completely honest I see the direction you were taking but I personally do not know how to get the values that way. You have the right track with the cubic function but instead of having the entire formula equal to the value it would often be best to figure out what it means when f(x)=0. Like how f(-5)=0 can be represented as x+5
mental creek
and similarly for f(3), once we figure out what the other terms are represented by then we can just plug in the value get our solution and figure out the value that gives us what f(3) equals by dividing the actual value by the value we plugged in
Did that solve everything?
eager falcon
Is a group with order 3 represented as Z3?
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Is a group with order 3 represented as Z3?
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slate meteor
can i assume angle BCD is a right angled triangle ?
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can i assume angle BCD is a right angled triangle ?
sly frigate
slate meteor
ah ok thanks and i was wondering for part 3
in order to prove it i need the angle ABC but i dont know how to get it
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slate meteor
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safe onyx
How do I get a numerical value for b and a ? For x and n I'd know the values beforehand, say 10 and 1 as an example, but I'd want to be able to set different values to them depending on the situation.
I need a way to solve for an approximate value of b so that x is as close to equal it's input value as possible.
a = (x - b) / 0.3659 / 0.0011
b = 0.001 * (a * 0.3655) + ((a * (1 + 0.00031)^n - a) * 0.3395)
safe onyx
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tardy halo
Hi guys, working on this and I'm really stuck. I actually have a answer sheet but I don't want to see the full answer, I just want a nudge to be able to figure it out:
https://i.imgur.com/MY4XtOm.png
tardy halo
First question is, in $y^{(p+q)} the $(p+q)$ means p+q-th derivative. But inside of the function $y = x^p(1 + x)^q$ the p and q seem to be regular exponents. Am I right in this?
glossy valveBOT
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spice orchid
Where ever they appear p and q are just numbers
They appear as exponents and in "how many times to differentiate"
tardy halo
I see, yeah that's what I figured
but then the lectures / reading never went over how to take the
nth derivative of something...
spice orchid
There is literally a formula for it directly above
tardy halo
haha well ok applying it for the product rule
I can do
but how do I take the p+qth derivative of one of th eterms like x^p
wait is it just nested leibniz?
spice orchid
Just think about what repeated applications of the power rule does
tardy halo
I can see it I think even for a regular nth derivative but p+q is really throwing me off
is this actually a hard problem or am I being dense?
like how far into calculus do you need to be to see this as easy?
spice orchid
tell me what happens when you do repeated application of the power rule to x^p
calculate the first few derivatives and notice a pattern
tardy halo
I wrote it out here and deleted it 😭
it would be $px^{p-1} then p(p-1)(x)^{p-2} then p(p-1)(p-2)(x)^{p-3}$
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math
tardy halo
but here I just decided to stop at the 2nd derivative
how do you know when to stop at the p+qth derivative
tardy halo
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dreamy cradle
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dreamy cradle
Hello could you please help
frosty geyser
Hello could you please help
can you translate the task?
grave elm
can you translate the task?
[Translated task]
In dependence on parameter p/=1, solve the system of equations. If you don't suceed for general p, solve for p=2 (half points)
frosty geyser
ty
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calm kiln
Hi. Last week, I was sick and I missed a lot of lessons, now I don’t really understand how to do this
torn jolt
suggestion: multiply by the common factor between the fractions for both equations to get a system of two linear equations
stable heart
i think in this particular case they want you to add the two together to cancel out the y terms
torn jolt
then you can solve the system of linear equations the standard way you would do
torn jolt
i think in this particular case they want you to add the two together to cancel ...
ah i guess thats possible too
torn jolt
suggestion: multiply by the common factor between the fractions for both equatio...
thats what u end up doing here, eventually too
stable heart
yes both will work. but i believe teachers generally want the add/subtract method if the problem really suits it as it shows you know both methods
in this particular case it is much easier to do so
calm kiln
So if I do equation 1 - equation 2 i’ll have
y/3 - - y/3 = -2 - 12 so,
y/3 + y/3 = -14
but what do I do after and is this even correct ?
stable heart
that can for example work yes, now you have $$\frac{y}{3}+\frac{y}{3}=-14$$you can combine the two $y$ terms to get $$\frac{2y}{3}=-14$$and then you can multiply both sides by $\frac{3}{2}$, do you think you can take it from here?
glossy valveBOT
Duh Hello
stable heart
well theres an equal sign there, to preserve it yes you must do it to both sides
stable heart
correct
now you can simply plug that into either of the other formulas and solve for x from there
acoustic frost
so y = -21
👍
calm kiln
x/2 - -21/3 = 12 for instance?
stable heart
for example that yes
doesnt matter which one
you will get the same answer no matter what
calm kiln
x/2 - -7 = 12
x/2 + 7 = 12
x/2 = 5
x = 5x2 = 10?
stable heart
also in this particular problem i just want to note one thing. it would be a bit faster to instead of subtracting the 2 equations you could instead add them. once you do you would simple get $$\frac{x}{2}+\frac{x}{2}+\frac{y}{3}-\frac{y}{3}=12-2$$ which would then get $x=10$ and then you could plug in $y$, looking at each option to see which is faster might save you some time
glossy valveBOT
Duh Hello
calm kiln
but why do I get x and not y? that’s what I don’t get
stable heart
the y's cancel out in this case since we add instead of subtract. in your case you cancelled the x's so we get y' instead. either way it does not matter which one you choose, but a lot of the time one is more convenient than the other
peak dome
how do i know its A or D
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how do i know its A or D
peak dome
u cant sqrt a negatice number
misty raft
wait so -1 is i right?
misty raft
so there is sqrt-5 so its 5i?
misty raft
oops sorry @peak dome lol didnt notice this was used
viral jasper
@misty raft this help channel is occupied, @peak dome do not encourage helping other people in your channel. It sets a bad precedent
Oops locker already acknowledged. Thank you
torn jolt
you got that the free coefficient is c
peak dome
<@463009283249012737> this help channel is occupied, <@1032004384311214210> do n...
ok np
torn jolt
it cant be bx+c
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dense edge
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dense edge
How is this the same thing as slope formula?
[1,3]
Isn’t 1 the input and 3 the output? Or am I misreading this set notation for [1,3]?
small pier
(x+1)^2-(x^2+2x+1) factor this expression
nova basin
[1, 3] just the closed interval. So you're just taking the slope between the endpoints, which is the average slope
dense edge
displacement used the functions, time uses the inputs.. but they are using the exact same numbers somehow
nova basin
what do you think you're computing here ?
nova basin
s(t) is your position as a function of time
dense edge
Normally I see [1,3] and think of it as a single coordinate (1 is input, 3 is output)
nova basin
find the average speed between t = 1 and t = 3
dense edge
Normally I see [1,3] and think of it as a single coordinate (1 is input, 3 is ou...
But this is incorrect, yeah?
nova basin
I invite you to think about what the problem might represent
dense edge
Or is it just a number line?
nova basin
or the y axis
and whether this would make any sense
as an interpretation of the meaning of this sentence
dense edge
Alright, if it’s just the number line.. I suppose that would mean x axis