I can't do it
#help-0
river fossil
start by writing down the limit definition of the derivative
river fossil
bot broken?
carmine bronze
and half the internet
river fossil
damn
carmine bronze
I tried to find stuff for polynomial derivatives and couldn't find one that helped me out
well whatever works at this point
river fossil
the question asks for the limit definition so i guess we'll continue that
carmine bronze
and I believe this is wrong
river fossil
apply the rule for every term
carmine bronze
doesn't it need exponent to work?
river fossil
and for the second question, just apply the power rule once again
carmine bronze
and for the second question, just apply the power rule once again
to -6x^2+8?
river fossil
yup
carmine bronze
river fossil
correct!
carmine bronze
cool thank you!
river fossil
there we go, wasn't so bad
though, are you sure doing it without the limit definition is fine?
carmine bronze
riemann told me to watch a bunch of basic differentiation rules stuff on khan academy
carmine bronze
I know but I don't think he explained this
maybe I skipped it
he didn't do any polynomial lessons that I saw
carmine bronze
I'm sure he did too just not on polynomials. At least none that I could find
river fossil
could be the case
river fossil
nice
carmine bronze
I have 2 channels now
river fossil
stick to this one
river fossil
do you need to show your work?
carmine bronze
Not for this assignment but I do go through all the steps on paper
river fossil
ah alright
do you wanna try to do this one with the limit definition?
or use the shortcut that is the power rule?
river fossil
well you don't have to, but it's the method you were told to use
carmine bronze
but it takes much more work doesn't it?
river fossil
it does
carmine bronze
But I guess if it says using the limit definition then it works
river fossil
ok let's do it
river fossil
so I don't have to do this?
evaluate this
river fossil
there's an h missing in the denominator
river fossil
$\frac{16h}{h(4\sqrt{x+h-4}+4\sqrt{x-4})}$
carmine bronze
see no h
ocean sealBOT
feeds
carmine bronze
mm
river fossil
right?
carmine bronze
uhh
river fossil
look at the first line
carmine bronze
ohhhhhhhhhhhhhhhh
river fossil
yeahhh
river fossil
you can cancel them now to get
river fossil
$\frac{16}{(4\sqrt{x+h-4}+4\sqrt{x-4})}$
ocean sealBOT
feeds
carmine bronze
should I learn how to type texit
river fossil
can be useful if you plan on writing math often
river fossil
I also saw 4 I could get rid of
nice
there's a litte more simplification you can do
if you combine the √x-4 together
carmine bronze
impossible
river fossil
2√x-4 😳
carmine bronze
river fossil
yup
carmine bronze
looking nice
carmine bronze
alright shortcut method time
ocean sealBOT
feeds
ocean sealBOT
feeds
river fossil
$=\frac{2}{(x-4)^{1/2}}$
ocean sealBOT
feeds
river fossil
$=\frac{2}{\sqrt{x-4}}$
ocean sealBOT
feeds
river fossil
though i advise you not to use this rule until your teacher teaches this
since chain rule can mess things up
stick to the limit definition for now
balmy warren
river fossil
$\frac{d}{dx} x^a = ax^{a-1}$
ocean sealBOT
feeds
river fossil
so you drop ½ from the exponent
river fossil
½ × 4
river fossil
yes
carmine bronze
did you get rid of the 2?
river fossil
which two
river fossil
yeah like that
carmine bronze
then wouldn't it be
oh
the exponent doesn't cover the 2
maybe that's why
ah ok makes more sense
I think the prof is making us do limit definition though so I will stick to that just to be safe
river fossil
yep
river fossil
not sure
carmine bronze
Which country are you in?
river fossil
im Indonesian
carmine bronze
Cool
river fossil
i think we're done, time to close the channel?
carmine bronze
yeah I was just working on a few problems to see if I was gonna get stuck again
Is it ok if I friend you? You seem like a cool person and you helped me a lot today.
river fossil
im sorry but i only friend irl friends
carmine bronze
alright np
river fossil
i gotta go now, good luck on your problems, see ya
steep ether
lone heartBOT
vale wigeon
the problem appears to be understated
having a website consist of only three pages (sign-in, sign-up, home, and nothing else) feels weird
it appears you were only expected to say "the vertices are the pages while the edges are links"
steep ether
the problem appears to be understated
having a website consist of only three pag...
this is what the examples says and I just want to know the three web page example is correct ?
vale wigeon
sure it works
steep ether
there is another example as well for the facebook friends
im not sure if its right cause there is a thing called mutual friends does it counts as friends?
vale wigeon
a "mutual friend of A and B" is just a person who is friends with A and with B at the same time
also i think if you're going to make concrete examples for this (which, again, i don't think is what's expected of you, but you're the one to judge)
then surely the friendship graph should be undirected
not directed with each arrow going both ways as you drew
i think you are only expected to say which objects serve as vertices and which as edges
nothing else
steep ether
also i think if you're going to make concrete examples for this (which, again, i...
oh ok so if its undirectional then I don't have to mention it twice right {(a,b),(b,a)} instead I could just say {(a,b)} right?
steep ether
yes but i think you missed my point entirely...
"I think you are only expected to say which objects serve as vertices and which as edges"?
vale wigeon
yes
and by this i mean that you are NOT supposed to give explicit examples like that
but only say things like "vertices: people, edges: friendships between people"
things to that effect
steep ether
but only say things like "vertices: people, edges: friendships between people"
ohhhhh ok
makes sense now
thank you so much, is there any pointing system to give points to the helpers?
untold sparrow
How can this type of sum be solved?
lone heartBOT
How can this type of sum be solved?
mortal trellis
alternatively from the binomial theorem, using the expansion of (1+1)^n
untold sparrow
I know how to calculate a sum but this is a sum of combination. As far as I read, this type of sum can be solved using the Leibniz Rule.
mortal trellis
I only know a leibniz rule about differentiation. I guess you can use that here somehow but seems pretty convoluted. to what rule are you referring?
you can also solve it using induction. although that is essentially the proof using pascals triangle because for that you also proof that the row sum is 2^n using induction
tawny schooner
alternatively from the binomial theorem, using the expansion of (1+1)^n
This is the easiest way really
untold sparrow
I was looking at this link https://www.cuemath.com/calculus/leibniz-rule/ .
grizzled vortex
Hi all, I'm reviewing for final and I saw that the instructor asked us to use Parseval's identity to compute the sum of an infinite series, but he did so by computing the generalized Fourier expansion and then just plugged some number in(like this⬇️). I wonder. how is this equivalent to using Parseval's theorem or am I misunderstanding something?
lone heartBOT
@grizzled vortex Has your question been resolved?
lone heartBOT
@grizzled vortex Has your question been resolved?
novel night
Been a while since I had to do anything rigorous with Fourier anything, but I agree this doesn't seem related to Parseval's theorem. The part about plugging in pi/2 is, I think, based on some version of the Fourier inversion theorem -- that f(x) is equal, point-wise, to the sum of its Fourier series.
lone heartBOT
@grizzled vortex Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
scarlet oriole
I am stuck at this problem. I've solved up until one point but I don't know how to end it tho
lone heartBOT
I am stuck at this problem. I've solved up until one point but I don't know how ...
@scarlet oriole Has your question been resolved?
lone heartBOT
@scarlet oriole Has your question been resolved?
hollow coyote
After staring at this proof for a solid amount of time, all I can prove is that triangles PRQ and SRT are similar, along with that the corresponding angles are congruent. What would be the next step?
indigo lotus
After staring at this proof for a solid amount of time, all I can prove is that ...
if PRQ and SRT are similar then ∠RPQ = ∠RTS
and since these angles also show a pair of alternate interior angles, the lines PQ and TS will be parallel
graceful mountain
This is the problem I am trying to solve.
lone heartBOT
This is the problem I am trying to solve.
graceful mountain
The solution tells me that the integral is a projection of the surface onto the xy plane. How?
Why does the integral give the area of the projection of the surface?
tacit arch
Did you try using Stokes theorem
graceful mountain
Yes
I want to understand why the integral is the area of the projection of the surface on the xy plane
I know how to calculate with the perimeter.
tacit arch
Do you know what $\hat{x} \cdot da$ is?
ocean sealBOT
riemann
graceful mountain
Not conceptually
tacit arch
What do you know about it
lone heartBOT
@graceful mountain Has your question been resolved?
wheat lagoon
I don’t know how to approach his question
lone heartBOT
I don’t know how to approach his question
wheat lagoon
vale wigeon
check your notes and/or google and/or your textbook for how to find the mean, median and mode of a dataset
wheat lagoon
I don’t have them it’s the last day
We handed in our textbooks and my notebook is at my house
vale wigeon
then google?
wheat lagoon
Oh then what’s the point of this server?
I was looking for guidance and help so I can understand in the future
vale wigeon
there isn't much guidance to be given on a problem that is almost exclusively about computation
to find the mean, find the total amount of money made from sales (taking into account the amount of each burger sold, so it's not just 4.00+6.95+7.00 and so on) and divide by the total number of burgers sold
to find the median, find how many burgers were sold in total and then find which burger type you stop at when you take all the burgers starting from the cheapest until you have exactly half of all burgers sold
to find the mode, find which type of burger has the most sales
wheat lagoon
Ah ok
vale wigeon
all of these are things which are easy to find by googling them yourself, and imo knowing how to use search engines is a very vital skill to have in this day and age
wheat lagoon
I should be fine I got a good start
Ik how lol
It’s easier when things are explain in different ways to m
Me
Not everyone learns the same.
.close
alpine sable
given $n = \sum_{i=1}^k n_i$ where each $n_i$ represents the number of repetitions of elements of type $i$ then the total number of permutations is equal to $\frac{n!}{\prod_{i=1}^{k} n_i!}$
alpine sable
how would u write this better?
ocean sealBOT
mahmooz
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
uh doesnt matter
could refer to the number i
so n_i refers to the number of repetitions of i
this is a lemma for multisets
not sets
where elements can be repeated
so say {boy, boy, boy, girl, boy, girl}
i=1 refers to girl
i=2 refers to boy
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
alpine sable
Variation with Repetition
A combination is a way of selecting k items from a collection of n items, such that (like permutations) the order of selection does matter. The repetition of items is allowed.
what does a combination have to do with variation?
don't send links
send screenshots
nice ip grabber
uh ok i linked the paragraph anyway, plus i doubt mathreference.org isnt a known website..
its not like im sending somescamurl.org/math.html
lone heartBOT
@alpine sable Has your question been resolved?
fathom hearth
'no square leaves a remainder 2 upon division by 4'
lone heartBOT
'no square leaves a remainder 2 upon division by 4'
fathom hearth
how do i prove this?
alpine sable
There's a pattern for the even and odd squares
Even squares always leave no remaider upon division by 4
And odd squares always leave a remainder 1
alpine sable
Anytime
fathom hearth
i am looking at this question
given an integer N, determine if there exists two integers a,b such that a^2-b^2=N
why is true that if N leaves no remainder 2 upon division by 4 then there does exist two integers a,b
lone heartBOT
@fathom hearth Has your question been resolved?
shadow steeple
lone heartBOT
karmic rapids
y is equal to 1 when x is equal to 6
shadow steeple
y is equal to 1 when x is equal to 6
wot
shadow steeple
what do u get
-15
shadow steeple
.close
patent swallow
the chart of
3/x is the same as the chart of 2/x or even 1/x right?
patent swallow
cause the X and Y asymptotes are 0 always
rose sigil
hey what does chart mean here?
carmine harbor
Both graphs will have the same x and y asymptotes but that doesn’t necessarily mean they are the same graphs
lone heartBOT
@patent swallow Has your question been resolved?
patent swallow
hey what does chart mean here?
graph sorry
patent swallow
Both graphs will have the same x and y asymptotes but that doesn’t necessarily m...
graphically they look the same, thats what I mean
right?
carmine harbor
graphically they look the same, thats what I mean
No they are different look on Desmos or your graphing calculator the graphs don’t intersect
abstract fractal
I guess they do look similar, though "similar" in this sense doesn't have a rigorous definition and is just based on your own perception
carmine harbor
They do however approach the same values and look very similar the further you go along both the x and y axis but they do not intersect
crystal narwhal
how do i do this question?
lone heartBOT
how do i do this question?
crystal narwhal
I did two different methods to get a>-9
then i did it a different way to get a < -9
which is the right anwser
i did a derivative to find minimum at x = -3
i substituted it back in to get - 9 - a > 0
which gave me a < -9
but why were my first two methods wrong?
the first two were about finding all values of a which yield a positive discriminant
lime bobcat
Positive discrimant means the polynomial has two real roots
You want to see when the polynomial is positive
They're two different questions
lone heartBOT
@crystal narwhal Has your question been resolved?
lime bobcat
If you solve $x^2+6x-a=0$ you get $x=-\sqrt{a+9}-3$ or $x=\sqrt{a+9}-3$.
ocean sealBOT
Categorist
lime bobcat
So we have the following factorization:
$x^2+6x-a=(x+\sqrt{a+9}+3)(x-\sqrt{a+9}+3)$
ocean sealBOT
Categorist
crystal narwhal
this was one of the ways to find the solution on the mark scheme
but they made the inequality so that the discriminant is negative being less than 0
crystal narwhal
They're two different questions
i just realized that and thought my first two methods were wrong but then the mark scheme used it to get the solution
they also used this methods but it makes no sense to me
deep mantle
hey, how do you express the amount of x in a volume at time t, when the rate of change in and out are both proportional to itself?
deep mantle
It's supposed to be a modeling question for first order differential equations
if what i said doesn't make sense I can elaborate further
deep mantle
it's oxygen in a space
basically trying to model how oxygen changes over time in a confined space with a single person in it
oxygen initially should be ~21% of the volume
the way I thought I'd express it was rate in would be the amount exhaled per hour and rate out would be the rate inhaled
i could be totally off about that tho
lime bobcat
Oh, interesant
marsh rapids
You should indeed be able to setup a differential equation with this. I'd expect an exponential decay towards 0 as the solution
marsh rapids
Is there any info given or is this a problem you came up with ?
deep mantle
It's my own question but i have more info i can share
the average person takes 960 breaths per hour
iirc the volume per breath is 380 ml
marsh rapids
I'd say you need something like: volume inhaled/exhaled per minute, percentage of oxygen inhaled that is actually consumed, volume of the room
lime bobcat
I think one can sum up inhale and exhale so the change of amount of oxigen only depends on the difference
And that is proportional bc proportional - proportional = proportional
marsh rapids
That's pretty much my "actual amount of O2 consumed" factor
lime bobcat
x'(t)=-k maybe LOL (k positive)
deep mantle
btw, the typical amount of oxygen that is exhaled is at around 15%
marsh rapids
So 1/4 of the O2 inhaled is consumed
lime bobcat
btw, the typical amount of oxygen that is exhaled is at around 15%
Oh, it's better when you say all information first
deep mantle
Oh, it's better when you say all information first
yeah my bad i thought i had mentioned it
marsh rapids
So O2/min = volume/minute * O2/volume * consumption rate
That should give you your differential equation
For the simplest reasonable model
deep mantle
So O2/min = volume/minute * O2/volume * consumption rate
do you mind expanding on this a little bit I'm a little confused
marsh rapids
That's 2 constants and 1 variable that you care about
Try to visualize the process to see what factors come into play
deep mantle
volume is and consumption rate are both constants in this case
per min so min=1 i assume
sorry
no
min is the variable
marsh rapids
So O2/min = volume/minute * O2/volume * consumption rate
More explicitly, this is:
d(mol of O2)/dt = (air intake speed in L/s) * (concentration of O2 in mol/L) * (proportion of inhaled O2 that disappears)
marsh rapids
More explicitly, this is:
d(mol of O2)/dt = (air intake speed in L/s) * (concent...
Or with mass instead of mols, idk which one is more convenient
deep mantle
yeah regardless, thanks that's a lot clearer!
marsh rapids
That's 2 constants and 1 variable that you care about
With that as I said, you get the usual equation for exponential decay (probably implement decay by having a negative proportion)
deep mantle
I see what was messing me up
deep mantle
With that as I said, you get the usual equation for exponential decay (probably ...
Alrighty cool, do you mind if i tag you if i have any questions about this?
marsh rapids
I don't intend on staying online for much longer though, so you can always try, but otherwise I'll have a bit of time in some 6 hours and then some 6 hours more
deep mantle
I see thanks
edgy flare
I need help with trying to find an algebraic expression.
lone heartBOT
I need help with trying to find an algebraic expression.
edgy flare
My professor said this:
And I did this: but I am supposed to find values for u_0, v_0, and r
This is a COMPLEX VARIABLES COURSE.
<@&286206848099549185>
lone heartBOT
@edgy flare Has your question been resolved?
edgy flare
<@&286206848099549185>
lone heartBOT
@edgy flare Has your question been resolved?
lone heartBOT
@edgy flare Has your question been resolved?
quick flower
can someone please help me pass geometry
lone heartBOT
can someone please help me pass geometry
quick flower
it makes no sense
narrow moat
can someone please help me pass geometry
I can help!
Geometry is the study of a shapes or sumfink.
.close
raven rover
can someone please help me pass geometry
golden moss
.close
quick flower
median oar
ok
so can you put the statement given in math terms?
like if it said "x is 2 times y" you would write x = 2y
oblique pier
@quick flower u still need help?
quick flower
yes please
oblique pier
like if it said "x is 2 times y" you would write x = 2y
i think he could solve this with just 1 unknown
oblique pier
Well as we know ABD is 72 degree
median oar
no but im talking about getting a math style thinking for problem solving
oblique pier
and we need to know m1 and m2
quick flower
ok
median oar
it's very helpful to write down the givens with math
so you can do operations on them
median oar
you cant do operations on english sentences
oblique pier
since we need to find m2
quick flower
k
median oar
what does "m1 is two times m2" mean in math
warm mason
Question 9. Question 9 asks in what quadrant of the argand diagram do you find z^5 if z=cos.... Motivate your answer.
tacit arch
Show your work
warm mason
It's 0 i don't know where to start i didn't study this for a while
tacit arch
Use De Moivre's theorem
warm mason
Okay 1 min
I'm just relearning it sry for taking a while
Is this the right start?
tacit arch
Question 9. Question 9 asks in what quadrant of the argand diagram do you find ...
In this case r=1
warm mason
Why?
tacit arch
You still haven't used demoivre's theorem
tacit arch
Yea you got it
warm mason
Okay
tacit arch
Your 1 looked like an r to me
tacit arch
You should know those sin/cos values from the unit circle
warm mason
Yea they are in 3rd Quadron
So both values are -
But i don't know how to answer the question?
It's 45 degrees in the 3rd Quadron
So cos 225 + i sin 225 equals to what?
warm mason
Question 9. Question 9 asks in what quadrant of the argand diagram do you find ...
How do I answer
tacit arch
https://paws.kettering.edu/~ktebeest/courses/unitcircle.html#:~:text=The unit circle (circle%20of,counterclockwise%20from%20the%20%2Bx%20axis.
warm mason
Yea but that i get
But it's i didn't finish calculating the question right but is it impossible at my stage
Because of i?
tacit arch
I don't understand what you're stuck on
warm mason
And then so i answer only sin(x) and cos(x)
Oh i think we answered the question
This is outside of the question to make me understand
Deeper
If that's okay to ask?
Cus question is cos (5π/4) + i sin (5π/4) but we only answer in what quadrant cos (5π/4) and this sin (5π/4) is. But not what happens if we actually put them together and how i affects the final answer. So i guess I'm asking can you answer the question with an i in it?
Or is this as far as i can go?
tacit arch
Yes. questions about complex numbers can have complex numbers as answers
tacit arch
Well you still didn't simplify it completely
warm mason
What else can I do?
tacit arch
https://paws.kettering.edu/~ktebeest/courses/unitcircle.html#:~:text=The%20unit%...
To do that you need to use the chart here
But you don't need to
You already found the quadrant
warm mason
But it only shows the 45° 60° and so on
It doesn't show in-between those values?
Like the values between
tacit arch
It doesn't show in-between those values?
Yes it does
Screenshot what the link looks like
tacit arch
It's the chart
5pi/4 is the same point as -3pi/4
Because cos(x + 2pi n) = cos(x) for all integers n
Similarly for sin
chilly tulip
Hello, we were given a question that involves subtracting matrices with variable exponents, while we were taught what to do with matrices with exponents, we weren't taught how to handle matrices with variable exponents. Is it literally just the same as normal matrix operations or is there some sort of special method to it?
tacit arch
Just show the problem
chilly tulip
tacit arch
That means transpose
lone heartBOT
lone heartBOT
Available help channel!
deft kettle
if i say integral of sin 90 dx, then it's gonna be 0 right?
lone heartBOT
if i say integral of sin 90 dx, then it's gonna be 0 right?
vale wigeon
neither sin(90°) or sin(90 rad) are equal to zero
median oar
and even if it was 0 it's still just + c at the end... so still not 0
deft kettle
is this correct?
median oar
uh
i dont thin kthis is the way to go
you cant just split (1-sinx)^-1 into 2 integrals
deft kettle
but thats what i did
1 is the same as x^0 and -sin x^-1 is that same as -cosec x
then i integrated both of these after splitting
median oar
1 is the same as x^0 and -sin x^-1 is that same as -cosec x
tell me how $\left(\frac{1}{1-x}\right)=1^{-1}-x^{-1}$
ocean sealBOT
Frosst
median oar
your handwriting is really badi cant tell what you're writing lol
median oar
how did you get from step 2 to step 3
median oar
1 ≠ -1
orchid python
hi
lone heartBOT
@orchid python Has your question been resolved?
orchid python
can anybody help me with that/
<@&286206848099549185> can somehow show me the direction for solving this one? the C question
lone heartBOT
@orchid python Has your question been resolved?
lone heartBOT
@orchid python Has your question been resolved?
orchid python
hi anybody
orchid python
hi
carmine shuttle
I guess that in (c), $\lambda$ is no longer in $5 unit^{-1}$,
so let $\lambda$ be mean rate of request in \textit{\textbf{0.5}} unit time.
$$P(X=\lambda) = \dfrac{e^{-\lambda} {\lambda}^0}{0!}$$
$$e^{-\lambda} = 0.9$$
$$\lambda = - \ln 0.9$$
ocean sealBOT
kelvinchan9786
final olive
mean for X1-X2 =75-70=5
and std error of X1-X2 =(s1^2/n1+s2^2/n2)^(1/2 )=4.472
a)hence P(X1-X2>4)=1-P(X1-X2<4)=1-P(Z<(4-5)/4.472)=1-P(Z<-0.2236)=1-0.4115=0.5885
b)P(3.5<X1-X2<5.5)=P((3.5-5)/4.472<Z<(5.5-5)/4.472)=P(-03354<Z<0.1118)=0.5445-0.3687=0.1758
@orchid python
final olive
whats up
orchid python
what is s12 and s22
final olive
sorry edited
final olive
thats the formula for a single population
let me find the derivation
my formula is for standard error of x1-x2
orchid python
and how do you calculate the probability from the z score, i don't know how to do it
final olive
i used the z score probability table
orchid python
how did you do it
final olive
orchid python
how did you do this part: P(-03354<Z<0.1118)=0.5445-0.3687
final olive
that is
orchid python
P(Z < 0.1118) - P (Z < -0.3354)
final olive
yeah
orchid python
so what's next
final olive
you could approximate it using a detailed table if yo have one on hand
i just used this site
where i entered the z score, and got the corresponding probablity
orchid python
so the values you give me are all correct
can you help me with this one @final olive
violet portal
orchid python
hi
orchid python
can anybody help?
for the 4-76 a, is the answer is 0.99997?
P(Z < -4) = 0.99997?
why taking the first value?
placid zinc
You're using P(x > Z) when you want to use P(x < Z)
Being 4 SD below the mean is very unlikely.
@orchid python
orchid python
yeah i'm here
for the third question i don't know why they have 2phi(x/0.1) -1
can anybody explian?
orchid python
for the a question
i need to add them together?
P(x=0) + P(x=1) + P(x=2) + P(x=3) ?
or i need to use the exponential distributed formula?
hi anybody???
carmine shuttle
(I assume that it is 4 "unit time" instead of 4 "minutes") \
... It is not how Poisson distribution works 😅 \
Let X be the random variable that represents mean rate of request in 4 minutes. \
As mean is five per unit time, $\lambda = 4 \times 5 = 20 (5 \text{unit})^{-1}$ (Don't mind the $(5 \text{unit})^{-1}$, it is just a unit) \
You should calculate $1 - P(X = 0)$, since $P(X=0)$ does not satisfy the condition that the first request is less than 4 minutes.
@orchid python
ocean sealBOT
kelvinchan9786
lone heartBOT
@orchid python Has your question been resolved?
orchid python
(I assume that it is 4 "unit time" instead of 4 "minutes") \\
... It is not how ...
but i did it with exponential distribution
is this correct?
carmine shuttle
Do you mix up Stochastic process? 😅
Exponential distribution is cont. but Poisson distribution is discrete...
@orchid python
lone heartBOT
@orchid python Has your question been resolved?
harsh girder
a+bi conjugate to a-bi
stable shore
I shall announce my question
lone heartBOT
I shall announce my question
stable shore
Okay, what was my mistake in solving this integral?
My work:
Marked in red is the final WRONG answer
I used u-substitution and integration by parts, but my answer is wrong. Here is the solution without u-substitution:
The final, RIGHT ANSWER is in white
lone heartBOT
@stable shore Has your question been resolved?
tacit arch
But this doesn't
tacit arch
Can you just show the original problem
stable shore
let me fix it
tacit arch
Screenshot or picture is best
harsh girder
stable shore
I just want to know what I did wrong. To reach the wrong integral
harsh girder
here should be -(-1)
harsh girder
The red is wrong
,w integrate x/(16*exp(x/4))
ocean sealBOT
harsh girder
it's correct
tacit arch
THIS CHANNEL IS NOW OPEN!
Type .close to close it
shell mortar
lone heartBOT
shell mortar
can someone help to solve this problem
narrow moat
Since they're consecutive, you can rewrite them as some number y, some number y+1, some number y+2, and some number y+3.
So a₁/(a₁+a₂) would be y/(2y+1).
shell mortar
yes
shell mortar
bro
harsh girder
Since they're consecutive, you can rewrite them as some number *y*, some number ...
they're consecutive terms in the expansion of (1+x)^n， not consecutive integers
shell mortar
yeah
narrow moat
they're consecutive terms in the expansion of (1+x)^n， not consecutive integers
Whateva that means!
narrow moat
Why is it on two lines?
shell mortar
Why is it on two lines?
wdym
harsh girder
Why is it on two lines?
they are the same, but the second line use ∑ sign
narrow moat
they are the same, but the second line use ∑ sign
No, why is the n and the k on different rows, but the same column?
harsh girder
No, why is the n and the k on different rows, but the same column?
it's binomial coefficient
narrow moat
it's binomial coefficient
Whateva, I'm too stupid too understand that!
harsh girder
It's okay, maybe you haven't learned this yet.
shell mortar
how can i proceed next
harsh girder
how can i proceed next
narrow moat
how can i proceed next
You do it for the rest of 'em and then simplify.
shell mortar
you can refer to https://math.stackexchange.com/questions/3986293/proof-involvin...
thanks
narrow moat
You do it for the rest of 'em and then simplify.
Stop bruhing me!
lone heartBOT
Available help channel!
wind pumice
lone heartBOT
gray ingot
Don't ghost ping helpers 🗿
lone heartBOT
@wind pumice Has your question been resolved?
wind pumice
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tacit arch
Ask in a physics server
tacit arch
<@&286206848099549185>
You have a channel already here
@wind pumice you have one here
lone heartBOT
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tribal oxide
lone heartBOT
tribal oxide
i have the domain, but in class we were told two ways to find the range for these types of questions
one method was by multiplying both sides by the denominator, and then forming a quadratic in x
and taking b^2-4ac>=0, but im not getting the answer
and the other method was by graph which im also not sure how to draw
OH the graph was for no common factors between the numerator and denominator
okay ive found the answer through the graph, but why am i not getting it through the other method?
lone heartBOT
@tribal oxide Has your question been resolved?
hazy atlas
get the quadratic in terms of y
let the funcn equal to something let sey y
denominator goes to other side, then quadratic in y generates
then simply proceed with Discriminant greater than equal to 0
tribal oxide
denominator goes to other side, then quadratic in y generates
This is still a quadratic in x, x is the one which has degree 2 right
And this is what i described
hazy atlas
then where are you getting errors
tribal oxide
From that i got y belong to R-{1/5}, but theres also supposed to be a 1 which should not be included in the answer, which i got in the graph
hazy atlas
can you show your working?
tribal oxide
Ignore the limits part, we havent done limits yet, i was just testing something 💀
Oh wait
Actually...
The last step is wrong
It should be y belong to R?💀 Which is even more wrong
hazy atlas
(5y-1)²>=0
after solving the inequality
answer should be
y>=1/5 or y<=1/5
all steps are correct imo
tribal oxide
y>=1/5 or y<=1/5
Which is y belong to R
tribal oxide
The last step in the picture is incorrect cuz i probably already knew 1/5 wasnt there in the ans cuz of my graph meyhod
So the quadratic method is giving me y belong to R
💀
tribal oxide
Domain is found
hazy atlas
then for range
tribal oxide
Domain is R-{-3,2}
tribal oxide
you can cancel that and check domain
x not -3
hazy atlas
if it is included in domain you can add that
tribal oxide
if it is included in domain you can add that
Not it was removed from before only
The thing is i can still check for the point x=2 will not give by taking the limit x tends to 2, but how will i find, that 1 is also not a part of the range without using the graph🤔
tribal oxide
also x not 2
Isnt that already assumed when ur cutting the factors
tribal oxide
Yep
Okay, ill just keep making sure i get matching answers with graphs
Thanks
.close
queen lodge
What is f(x) when f is even and x is neither
lone heartBOT
What is f(x) when f is even and x is neither
queen lodge
?
rose sigil
huh?
queen lodge
What will the fx be even or neither
rose sigil
is this something you made up or is it from a problem you saw?
queen lodge
Problem that i saw
rose sigil
can you send it?
rose sigil
,rotate
ocean sealBOT
queen lodge
?
rose sigil
I'd have to think about that one 😬
tribal oxide
is even
tribal oxide
Please explain
think of what you can the expression inside log as
queen lodge
Neither
queen lodge
It has to be +ve
tribal oxide
i mean like an actual expressio
once you find this, apply log properties, apply trig properties, then use the definition of an even function
mild otter
can someone help with q13
languid bolt
still need help?
languid bolt
try inserting the informations you have to the equation
mild otter
i tried, do i insert the raw numbers? or like 10ms^-2
languid bolt
up to you
languid bolt
$4 = 2\pi\sqrt{\frac{l}{10}}$
ocean sealBOT
MarveI
languid bolt
$\frac{4}{2\pi} = \sqrt{\frac{l}{10}}$
mild otter
oh okay i was over complicating it with the signs and units
ocean sealBOT
MarveI
languid bolt
$\frac{4}{2\pi}\sqrt{10} = \sqrt{l}$
ocean sealBOT
MarveI
languid bolt
still following until this part?
mild otter
hmm did you multiply by sqrt 10?
languid bolt
yes
languid bolt
yeah but the left side will be $\frac{160}{4\pi^2}$
ocean sealBOT
MarveI
languid bolt
i feel like it's kinda wrong
mild otter
answer in book is 40 over pi ^2
mild otter
cool ty
i was just confused cause
while you entered 10, the unit it said was 10ms ^-2
and like
idk what to do with the ^-2
languid bolt
np
mild otter
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wide raven
plug in -x and see if they fit the definition of odd or even functions
queen lodge
How to solve it then
wide raven
what do you get if you put -x
queen lodge
Cos log -x+√x²+1
queen lodge
Yes
wide raven
and also
queen lodge
But it is cos log -x√x²+1
queen lodge
-is inside log
wide raven
cos(log -x√x²+1)=cos(-log -x√x²+1)
like this
queen lodge
cos(log -x√x²+1)=cos(-log -x√x²+1)
How
wide raven
well
wide raven
and isn't cos(x)=cos(-x)?
by this
queen lodge
Oh
wide raven
and then if you reciprocate what's inside log
and then rationalize it
you get f(x) itself
so even function
queen lodge
Oh thanks
wide raven
np
queen lodge
I have one more question
queen lodge
.close
lone heartBOT
wide raven
if you want it to work
lone heartBOT
Available help channel!
random haven
sally jean wants to plant a garden with a perimeter of 40ft.what dimensions will allow the garden to have maximum area
carmine oar
a circle is the largest, tho these kinds of problems want squares or rectangles
what are you stuck with
random haven
If i want to create a circle,what dimension would i have to mention?
alpine sable
Rewriting in terms of plane algebra :
$a+b=20$
$\implies b=20-a$
so u have
Area=$a(20-a)=-a^2+20a$
ocean sealBOT
∆y/∆x=πy+π^2x
carmine oar
Rewriting in terms of plane algebra :
$a+b=20$
$\implies b=20-a$
so u have ...
don't directly give answers and too complex
alpine sable
don't directly give answers and too complex
I m not
random haven
It's pretty complex ngl
carmine oar
btw what grade is this
alpine sable
it's quite simple ig
random haven
Pre college
rose sigil
is that supposed to say plain or plane 🤔
random haven
I am dumb
random haven
So should I consider a circle, rectangle or a square?
carmine oar
it's quite simple ig
you're about to use calculus right?
carmine oar
So should I consider a circle, rectangle or a square?
circle is always the largest
but the teachers like squares
for not using pi
alpine sable
teachers like rectangles
carmine oar
but it's not necessary
right
random haven
So should I go with square
carmine oar
like just remember the fact that square has the largest areas
alpine sable
like just remember the fact that square has the largest areas
wha?
random haven
How would I solve it then
carmine oar
tho it can be false
random haven
I know perimeter of of square is 4*side
alpine sable
ig we are moving with some rough assumptions
carmine oar
but enough to solve this kinds
alpine sable
it's better to use rect ig
carmine oar
@random haven Just make sure that for quadrilaterals
square is always the largest
tho side lengths may not be integer
carmine oar
ig we are moving with some rough assumptions
I think it's good enough?
random haven
<@466568248788385805> Just make sure that for quadrilaterals
square is always th...
Ok
So what should I do ahead lol
Should I equate the perimeter to 4*side
And then when out length of the side
alpine sable
**∆y/∆x=πy+π^2x**
lemme explain this in a simpler manner let's say $a, b$ are ur dimensions
Perimeter=2(a+b)
as per condition,
2(a+b)=40
$\implies a+b=20$
$\implies b=20-a$
now we have Area=$a(20-a)$ we now want to find what a gives maximum area
random haven
Or something else needs to be done?
ocean sealBOT
∆y/∆x=πy+π^2x
random haven
**∆y/∆x=πy+π^2x**
Gotcha, thanks
alpine sable
so now try it yourself
alpine sable
I think it's good enough?
there is no need to make an assumption that's it's a square
ig
carmine oar
there is no need to make an assumption that's it's a square
I just quit
I learnt it as common sense
The teachers expected us not to proof and just use it
alpine sable
coz then u can't even solve it
u will have
side=10
now u only have 1 and only 1 area no maximisation
and the question explictly asks to maximize
carmine oar
JUST KEEP IT TO YOURSELF