Isn't it always a constant but different constant for different intervals?
#help-27
quiet delta
lost laurel
Isn't it always a constant but different constant for different intervals?
yes , and d(c)=0
where c is a constant
quiet delta
So the answer should be 0 right?
lost laurel
so the answer should be 0, I think
quiet delta
so the answer should be 0, I think
Yeah me too
lost laurel
I'm not sure only know HS level maths as of now
quiet delta
I'm not sure only know HS level maths as of now
Same
tiny bay
I only understand d(c)=0
fervent sundial
lost laurel
Maybe we should use [x]=x-{x}
that's still 0. The slope of {x} is 1
fervent sundial
in the conventional case, you have the differential dy = y(x+dx) - y(x) so if y = x (like here) then you'd have x + dx - x = dx
but in the case of y = [x], you have dy = [x + dx] - [x] = 1 so d[x] = 1
quiet delta
that's still 0. The slope of {x} is 1
Yeah but the answer should be greater than 0 for the whole
fervent sundial
i guess you can see that if you map x to x - a where a is some infinitesimal
x maps to x-a
so dy = [x-a + a] - [x-a] = [x] - [x-a] = 1
the answer should be like 0 * 1 + 1 * 1 + 2 * 1 + 3 * 1 + 4 * 1 ( i think)
since this is more of a discrete sum than integrals at this point
quiet delta
Wait i got the solution
Use x=[x]+{x}
And when you get int xd{x}
You just consider a new variable t with t=x-1 then x-2 till 4
Answer is 0
I calculated
Put [x]=x-{x} in the differential
Then seperate it
xdx-xd{x}
quiet delta
You just consider a new variable t with t=x-1 then x-2 till 4
Then use this technique
Hey @tiny bay can you tell me the source of this question
tiny bay
Hey <@1186149220160381102> can you tell me the source of this question
Sorry i found the question from a friend
quiet delta
Sorry i found the question from a friend
Ok if you can ,plz ask him which book it is and can you plz dm me the name of the book?
tiny bay
Sure let me ask them
quiet delta
Sure let me ask them
Thanks man
quiet delta
xdx separately then xd{x}
For xd{x} break it into 4 parts
0 to 1 1 to 2 2 to3 and 3 to 4
For 0 to 1 int normally as x={x} for 0 to 1
Then convert the other limits into 0 to 1 too
As {x+1}={x}
So just use x=t+i for rest of them
I can be 1 to 3
To adjust the limits of integral to 0 to 1
After solving i got 0 as the answer
quiet delta
dx-d{x}
quiet delta
Yes
quiet delta
For xd{x} break it into 4 parts
Isse aage ka padle bhai vapas nhi likha jaayega mai mar jaaunga
quiet delta
Multiply by x?
Yeah
tiny bay
Acha theek hain bhai🙏
quiet delta
Acha theek hain bhai🙏
Bhai kitaab ka source bhi batade
tiny bay
English se acha hindi sahi hain yar
quiet delta
Itni mahenat ki hai🥲
quiet delta
English se acha hindi sahi hain yar
Sahi mein
quiet delta
Jab maine tiranga dekha teri dp mein tab Hindi hi bol li
quiet delta
Source jarur bataunga apko bhai vo dost reply ni de rha
Thank you bhai batadiyo👍
tiny bay
JEE?
tiny bay
Picture is not clear
devout snowBOT
@iron vessel Has your question been resolved?
red viper
they just expressed x in terms of y so they could use condition x != 8
strange nimbus
Solve the equation for x.
What do you get?
No, that's wrong.
You need to do the same thing to both sides until you get x = something without x.
Draw what?
The way which thing would be written?
woven radishBOT
Chai T. Rex
strange nimbus
What can you do to both sides to get x closer to being on the left by itself?
You almost have it here ^
That's incorrect, though.
Show your work.
What did you do to both sides to get from the first line to the second line?
woven radishBOT
Chai T. Rex
strange nimbus
But that isn't what you got.
What did you do to both sides to get from the first to the second line?
OK, getting better, but it would look like this:[\frac{y}3 = \frac1{x - 8}]
woven radishBOT
Chai T. Rex
strange nimbus
Dividing by 3 would put 3 on the top and on the bottom, and they'd cancel, leaving 1 on the top.
woven radishBOT
Chai T. Rex
strange nimbus
Dividing a fraction by 3 means multiplying the bottom by 3.
Multiplying a fraction by 4 means multiplying the top by 4.
Does that make sense?
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sudden canopy
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sudden canopy
Hey, so I’m not confident in the centering and normalization process or how to involve central limit theorem
devout snowBOT
@sudden canopy Has your question been resolved?
sudden canopy
<@&286206848099549185>
pulsar sand
It helps if you define what the meaning of pn you wrote even is. Don't use new notation and skip writing down what it means to you
restive river
n most likely refers to number of terms
like it normally does
np is number of terms * probably
pn is the probability of a certain term
most likely
sudden canopy
It helps if you define what the meaning of pn you wrote even is. Don't use new n...
Sorry I actually did, I think I forgot a page
sudden canopy
pn is the probability of a certain term
Yes I have it here now
pulsar sand
You are making it harder to see what is happening by redefining your variables in terms of a new variable $P_n$. You have from the Central Limit Theorem that $$\frac{ \frac{S_n}{n} - p } { \frac{\sqrt{p(1-p)} } {\sqrt{n}} }$$ is standard normal
woven radishBOT
JessicaK
pulsar sand
Now, having established that is standard normal, you want the distribution of just S_n. So your problem is the S_n/n term needs to be just S_n
sudden canopy
Now, having established that is standard normal, you want the distribution of ju...
Thank you, I’m not seeing the relationship between the calculations and the standard normal distribution from googling I see it should be so but I’m not seeing it not sure what rule I’m missing
pulsar sand
I don't understand what you mean, I wrote the relationship down
sudden canopy
I don't understand what you mean, I wrote the relationship down
What formula for a standard normal distribution does it resemble?
pulsar sand
What do you mean by resemble? The distribution is unique. There is only one
sudden canopy
What do you mean by resemble? The distribution is unique. There is only one
Because when I type the standard normal distribution on google im not able to look at this and see that they are the same
pulsar sand
The theorem says that the quantity I wrote down converges in distribution to the standard normal
If you want to make it look the same, you are rederiving the CLT in the special case of a bernoulli distribution, which involves a bit more work than what you are asked
The point being that you are not supposed to be able to clearly see that they are the same. The theorem tells you they are the same after you take the limit as n tends to infinity.
sudden canopy
Ok, what is what we calculated called?
Like the standard normal would be the asymptotic distribution
sudden canopy
**JessicaK**
and what is this called
pulsar sand
It doesn't have a special name, that's just a probability distribution
sudden canopy
It doesn't have a special name, that's just a probability distribution
Like separate from the Bernoulli?
Thanks
.close
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sage socket
I'm sort of confused by the numerator here
devout snowBOT
I'm sort of confused by the numerator here
sage socket
First picture for context. Second picture for what I'm talking about.
I don't understand why we're using addition instead of multiplication. If some assumption of the multiplication rule is violated, what is it?
I don't understand why we can't just do 5^12 + 5^11.
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@sage socket Has your question been resolved?
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@sage socket Has your question been resolved?
sage socket
<@&286206848099549185>
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@sage socket Has your question been resolved?
gloomy spire
Hey 🙂
small jackal
this is quite unclear ngl
small jackal
this is quite unclear ngl
wait
gloomy spire
I don't understand why we're using addition instead of multiplication. If some a...
The reason you can't just do $5^{12} + 5^{11}$ is that your set of 12 dice is ordered, however when you count how many 6's you have, there is no ordering, so $\frac{5^{11}}{6^{12}}$ undercounts the number of ways of rolling just one dice by a factor of $\binom{12, 1}$.
small jackal
I don't understand why we're using addition instead of multiplication. If some a...
the events are mutually exclusive i guess
thats why you add
woven radishBOT
Corpuscular Crow
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
gloomy spire
thats why you add
that's right! otherwise you have to subtract their intersection
small jackal
👍
gloomy spire
sorry for the formatting btw
small jackal
sorry for the formatting btw
np
sage socket
Wait why is it ordered?
It doesnt matter if the first die is a 6 or the last.
I just need two 6's to show out of 12 die
sage socket
the events are mutually exclusive i guess
I knew I should have draw a venn diagram
gloomy spire
when you count the total number of events in your system, you have $6^{12}$, in other words, the events ${6,1,1,1,1,1,1,1,1,1,1,1}$ and ${1,6,1,1,1,1,1,1,1,1,1,1}$ are counted as distinct
woven radishBOT
Corpuscular Crow
gloomy spire
but when you are counting up the 6's, the order doesn't matter anymore, so you have to multiply by the ways of changing the order of your 6's
in the case of P(getting one 6), you have $\binom{12}{1}$ places where that 6 could be
woven radishBOT
Corpuscular Crow
sage socket
in the case of P(getting one 6), you have $\binom{12}{1}$ places where that 6 co...
Oh
sage socket
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General_Jacob
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@restive river Has your question been resolved?
restive river
Trying to figure out where to put stuff if the formula here is $\beta_2-\beta_1=10log(\frac{I_2}{I_1})$
devout snowBOT
Trying to figure out where to put stuff if the formula here is $\beta_2-\beta_1=...
restive river
$\beta_2-\beta_1=10log(\frac{I_2}{I_1})$
woven radishBOT
mj
restive river
this is the part b of the question above ^^
so intensity is 316 times less, I assume it's either -316 or something/316
can't be -316 because log can't be -ve
so my guess is the 2nd one?
if intensity initially is 69
$\beta_2-69=10log(\frac{\beta_2}{316})$
woven radishBOT
mj
nova whale
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nova whale
how do i sovle tihs?
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uncut yew
How would i solve this?
devout snowBOT
How would i solve this?
crisp niche
you must first raise the integral expression to the 7th power
uncut yew
I have to expand?
uncut yew
is there a way to do it without expanding, as its kinda tedious
crisp niche
$5^{7}\int_{}^{}\left( x^{2}+1 \right)^{7}dx$
woven radishBOT
Joanna Angel
crisp niche
is there a way to do it without expanding, as its kinda tedious
no, to make other trick
you wud need to have other form of an integral of yours
for example:
$\int_{}^{}x\left( x^{2}+1 \right)^{7}dx$
woven radishBOT
Joanna Angel
crisp niche
it is very simialr but you can solve it very fast
using substituion
but it is not your case
uncut yew
Would reversed chain rule work?
crisp niche
it is an integration not differentation
but it is simialr
though perosanlly i do not call it this way
there are analogies
uncut yew
What would it be called when u have a composite function and you have to integrate it
uncut yew
alr
crisp niche
this
$\int_{}^{}f\left[ g\left( x \right) \right]g'\left( x \right)\text{ }dx=\t=g\left( x \right),dt=g'\left( x \right)dx\\=\int_{}^{}f\left( t \right)dt$
woven radishBOT
Joanna Angel
crisp niche
In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variable
uncut yew
**Joanna Angel**
is this sub?
uncut yew
I see
crisp niche
uncut yew
**Joanna Angel**
and this wouldnt apply in my equation as there isnt a g' right
crisp niche
yes
but for now
you cant
since
your integral misses it
because yoru teachers
wanted you
to work more
suign expansion
to 7 power
crisp niche
crisp niche
Would that work?
no
crisp niche
Would that work?
becasue you wud add x but insa me tiem you wud add 1/x
so that is ineffective
sad but true
uncut yew
becasue you wud add x but insa me tiem you wud add 1/x
What if i used integration by parts after
would that still
or
crisp niche
What if i used integration by parts after
no, by parts needs other classes
of functins
like:
sand meteor
multiply times 3 for every 1 that’s multiplies
crisp niche
$\int_{}^{}x^{n}\sin\left( ax \right)dx,\int_{}^{}x^{n}\cos\left( ax \right)dx,\int_{}^{}x^{n}e^{ax}dx$
woven radishBOT
Joanna Angel
crisp niche
and fwe other too
crisp niche
multiply times 3 for every 1 that’s multiplies
mayeb it is not my photo, it is wikipedia 🙂
sand meteor
cap
uncut yew
no, by parts needs other classes
wdym
oh like 2 functions in 1
but if i multiply by 10x * 1/10x times the other stuff
wouldnt that be able to
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crisp niche
wouldnt that be able to
unfortunately, not, well do not waste the time and expand it to the 7-th power, no other way
crisp niche
yw )
lost laurel
What exactly is the "Moving point " of a parabola, or any function for that matter?
devout snowBOT
What exactly is the "Moving point " of a parabola, or any function for that matt...
lost laurel
just $y= \sqrt{4ax}$?
woven radishBOT
Why am. I here
thin inlet
i think 'moving point' just means the set of all midpoints of line segments connecting from the parabola itself to the focus
like this
(drawn poorly)
@lost laurel
supple knot
Linear algebra, reflection matrices
delicate river
do you know how matricies work?
do you know what the columns of a matrix represent?
like for example if you consider the first column of a matrix as a vector
what does that vector tell you?
delicate river
?
oh I meant in general
do you know what the first column vector of a matrix tells you
ok
each column vector is where the matrix will map the corresponding standard basis vecotr
vector*
so for example
the first column of a matrix is the vector that the matrix will map (1, 0) to
then the second column is where it will map (0,1) to
$\begin{bmatrix}a&b\c&d\end{bmatrix}\begin{bmatrix}1\0\end{bmatrix}=\begin{bmatrix}a\c\end{bmatrix}$
woven radishBOT
qianqian07
delicate river
$\begin{bmatrix}a&b\c&d\end{bmatrix}\begin{bmatrix}0\1\end{bmatrix}=\begin{bmatrix}b\d\end{bmatrix}$
woven radishBOT
qianqian07
delicate river
so what this tells us
is that if we know how a linear transformation acts on the vectors (1, 0) and (0, 1)
then we can just use those to determine the matrix
wdym
?
we can't multiply two vectors
when we multiply the matrix on the left
by the vector (0, 1)
it turns out to be (b, d)
which is the second column of the matrix
so basically
the second column of the matrix is the vector which (0, 1) gets mapped to
does that make sense?
👍
now to answer the question
what vectors will (1, 0) and (0, 1) get mapped to?
when we reflect them through the origin
I mean with the transformation described
"the reflection of the point P(x, y) through the origin"
what point does (1, 0) become when reflected through the origin?
yes
yes
and then what does (0,1) get reflected to?
yes
so now
to find the matrix
yes that is correct
👍
slate stump
its a list of transformations
so each of those matrices do what the description says
delicate river
👍
that is correct
actually you don't even need to multiply it out
you can just see where (0, 1) gets reflected
and that is automatically the second column
that might make the problem slightly quicker to solve
but your method works too
you could consider (1, 0) and (0, 1) again
where does (1, 0) get rotated to?
frosty cradle
you could consider (1, 0) and (0, 1) again
should, not could
delicate river
are you sure?
when we rotate by theta
if you start with (1, 0)
and then you rotate it counterclockwise by theta
what does it become?
it might help to think about it using the unit circle
frosty cradle
draw a picture
frosty cradle
yes but FYI they usually are referring to counterclockwise rotation in these problems. unless they state otherwise
delicate river
can you think of a way to write out the vector (1, 0) gets mapped to in terms of theta
(using trig functions)
exactly
so that will be the first column of the matrix
not quite
it will prob help to draw a picture like cwatson suggested
yes
oh wait
sorry I misread
(-1,0) is (-cos(theta),-sin(theta))
that is correct
but you don't really need that
to find the matrix
we want to consider where (0,1) gets mapped
not (-1,0)
close but not quite
the diagram looks right, but check your work
are you sure the cosine goes in the x component?
👍
sorry it's a bit blurry
but you can just consider the right triangle made with the y axis
👍
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kind cave
does integrating f(c+x) also give F(x)?
where all notations hold the usual meaning.
frozen aurora
does integrating f(c+x) also give F(x)?
where all notations hold the usual mean...
do you see why?
kind cave
no...
I was looking at a solution online and couldn't get how that happened
oh...
Just read it again, and I guess I get how this step happened here :p
frozen aurora
do you know u substitution?
kind cave
no...
frozen aurora
okay
well
you kinda just discovered it lol
since it's an indefinite integral, instead of F(x) you get F(x+c)
kind cave
do you know u substitution?
Is it different from substituting t?
kind cave
then why the "u"?
frozen aurora
some places just have different variable names
in my country we do the same thing but instead of t=.. we say u=..
but the technique it equivalent
kind cave
then why the "u"?
I just learned it as "substitution" so I didn't knew :p
frozen aurora
if you were to substitute, idk, u=1+t, du=dt
kind cave
So it's just skipping steps
frozen aurora
then you get $\int \frac{1}{(1+t)^2} dt = \int \frac{1}{u^2} du$
frozen aurora
So it's just skipping steps
yeah
woven radishBOT
artemetra
frozen aurora
$=-\frac{1}{u} = -\frac{1}{1+t}$
woven radishBOT
artemetra
kind cave
thank for the explanation
frozen aurora
no problem
frozen aurora
thank for the explanation
if you are done, type ".close"
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restive river
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near stone
!status
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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 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
Oh sorry
I'm supposed to solve for x
but I have no idea how, I've tried factoring out an x from the first two terms
but I'm not sure if it's legal to use zero property
to remove the x
and even then, I'm left with x^2-5=0
near stone
have you tried gcf
restive river
there isn't any common terms here though
restive river
can you do that with cubes?
near stone
cubes?
restive river
like x^3
near stone
you can
restive river
are you sure? I thought quadratic formula was only for quadratics
because then we have an a, b,c, and d value
prime hollow
are you sure? I thought quadratic formula was only for quadratics
Yes, it is only for quadritcs. It does not work for cubic equations.
Like this one
restive river
yeah I had a feeling, would be weird putting a 0 in there
prime hollow
I would try some small values for x and see if some of them are roots.
restive river
and then doing synthetic division?
prime hollow
In general, cubic equations are very hard to solve so usually, you have to assume that it's a nice one.
restive river
2 is a root here
prime hollow
Yes!
near stone
because then we have an a, b,c, and d value
the only left is, you can factor it by grouping
prime hollow
and then doing synthetic division?
Sounds like a great idea
restive river
the only left is, you can factor it by grouping
the easiest way is probably guessing and checking I suppose
.close
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trail eagle
It is true for any vector.
lusty sapphire
trail eagle
Yes. Only, you'll have only 2 components to square.
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muted blaze
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muted blaze
Need help with first step
muted blaze
no
pseudo basin
mileage is how many miles your vehicle can travel by burning 1 gallon of fuel
in other words mileage (in MPG) is distance (in miles) divided by fuel consumption (in gallons)
(the same way speed is distance divided by time)
muted blaze
in other words mileage (in MPG) is distance (in miles) divided by fuel consumpti...
so then
i would do
pseudo basin
this is something that you yourself could have (and imo should have) looked up
zenith vortex
the units are literally saying the answer
pseudo basin
also tbh "see unknown word => ask explicitly about unknown word, or google it yourself"
muted blaze
,calc 385 / 22
woven radishBOT
Result:
17.5
like you could say "what the fuck is mileage" or something
pseudo basin
you thought that you knew, but then i asked you if you knew, and you answered no. what gives?
muted blaze
but english remains hard for me too
muted blaze
czech
pseudo basin
ok
pseudo basin
muted blaze
because i wasnt sure
pseudo basin
ah...
muted blaze
So do I need to do something else to the 17.5
dusky drift
What grade are you in?
muted blaze
9
pseudo basin
So do I need to do something else to the 17.5
you'd need to round it to the correct number of significant digits
which is 2 here if we look at it strictly and formally
but just 17.5 might be fine too
muted blaze
Rounded to correct number would be 18 then
pseudo basin
seems so
agile narwhal
The problem states that a sailor takes steps in such a way that with a probability of 1/2, he takes one step forward, and with a probability of 1/2, he takes a step 0.5 meters backward. Using a normal approximation to the binomial distribution, determine the probability that after 300 steps, the sailor will be at a distance of less than 105 meters from his starting point. Express the result using the cumulative distribution function of the normal distribution N(0,1).
devout snowBOT
The problem states that a sailor takes steps in such a way that with a probabili...
agile narwhal
can someone check whether this response is correct?
https://chat.openai.com/share/7966cb74-c213-48f4-853a-ef1ad3284405
i came up exactly with the same solution but it seems too easy
devout snowBOT
@agile narwhal Has your question been resolved?
jade oak
can someone check whether this response is correct?
https://chat.openai.com/shar...
The question is a bit unclear. Is it 1/2 that he takes a 1m step forward or a 0.5m step forward? Either way gpt is giving the incorrect mean (it is assuming a step backwards is 0 meters back). You should not use gpt for math
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agile narwhal
The question is a bit unclear. Is it 1/2 that he takes a 1m step forward or a 0....
It's 1/2 that he takes 1m forward
agile narwhal
The question is a bit unclear. Is it 1/2 that he takes a 1m step forward or a 0....
How to fix it?
I thought it is correct since I came up with exactly the same solution
jade oak
$E[X]=\sum_{x\in \text{Im}X}xP(X=x)$
woven radishBOT
Cure Grace
jade oak
Use that to find the mean for 1 trial, and the variance for 1 trial, then multiply by n to get the mean and variance for 300 trials
agile narwhal
To approximate binomial with normal you can use formulas
expected value of binomial = np
Variance = np(1-p)
And then you can plug it in into normal distribution
jade oak
To approximate binomial with normal you can use formulas
I do not think you can use a binomial here (maybe if you transform the problem you can). Binomial distributions give the probability of k success of a Bernoulli rvs. The issue is that right now each step is not a bernoulli trial (since instead of 0 and 1 the possible values are -0.5 and 1)
agile narwhal
I do not think you can use a binomial here (maybe if you transform the problem y...
It's mentioned in problem assignment that it's binomial
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@agile narwhal Has your question been resolved?
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@agile narwhal Has your question been resolved?
topaz axle
i can't open the link
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@agile narwhal Has your question been resolved?
desert yew
I do not think you can use a binomial here (maybe if you transform the problem y...
You can use the binomial, since the function of the random variable is so simple.
I.e. define a forward step as a success
Then if you have k successes in n steps, you move a distance of 1*k-0.5(n-k) meters forward
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sturdy yew
is xy=1 a rectangular hyperbola?
devout snowBOT
is xy=1 a rectangular hyperbola?
thin inlet
are the asymptotes perpendicular?
do you know that xy=1 is a hyperbola? if so, that's all you need :)
prime egret
If you rotate the coordinates system 
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restive river
I got question i but I am stuck on ii. The answers are provided but I cannot seem to get to the general solution. I did find the characteristic equation with the the 2's but cannot seem to figure out how to get 2+t with the particular solution
devout snowBOT
I got question i but I am stuck on ii. The answers are provided but I cannot see...
@restive river Has your question been resolved?
magic thicket
you're expecting a polynomial, so look for a polynomial particular solution
And you can easily argue that it must be of degree 1
restive river
I am not sure on how to solve it then because I tried ct^2
magic thicket
that's not a general polynomial
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@restive river Has your question been resolved?
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mortal sky
hello I have to draw this graph
devout snowBOT
hello I have to draw this graph
mortal sky
could anyone help me on how to do that
I firstly started with the graph of e^x
and then got the graph of e^|x| by reflecting the graph in the +ve axis wrt to y axis
however I am stuck on how to get graph of e^-|x|
gusty shale
I mean e^x and e^-x aren't that similar. May I suggest plotting a few points to get an idea of what you're looking at?
mossy gale
mortal sky
well I was planning to first draw the graph of y and then get of |y| from that
mortal sky
I mean e^x and e^-x aren't that similar. May I suggest plotting a few points to ...
can't we transform f(x) into f(-x) by just reflecting through y-axis
gusty shale
I don't think so. Are you sure you don't mean f(x) and -f(x)
gusty shale
Ah, OK. But remember |x| is always at least 0, so you just have the lower parts of those two graphs
e^-|x| will always be less than 1
mortal sky
hm ye
mortal sky
Ah, OK. But remember |x| is always at least 0, so you just have the lower parts ...
why only lower parts?
|x| is greater than zero in above parts too
gusty shale
Are you sure? Remember, we're looking at -|x|
So, you can never get e^2 for example because that would mean -|x| = 2 or |x| = -2
gusty shale
So you can draw e^-x on the right side and then flip around the y axis to get e^-(-x) on the left side
mortal sky
and that should just give me e^-|x|
after that I can shift it down by 1/2
I think I will be able to do it
thanks
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near belfry
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near belfry
i know what the taylor series is but i cant seem to get a correct answer
can someone tell me the correct answer please
supple knot
i know what the taylor series is but i cant seem to get a correct answer
Just find the Taylor series for all the options
graceful cosmos
Note you should be able to eliminate b and d right away. Why?
restive river
the first term being 1 eliminates 2 of the choices from the get go
restive river
Note you should be able to eliminate b and d right away. Why?
yeah exactly
devout snowBOT
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wary sapphire
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lyric marlin
Hello guys, can somebody please help me understand how my teacher get this answer
devout snowBOT
Hello guys, can somebody please help me understand how my teacher get this answe...
lyric marlin
while if i use wolfalpha i get a different answer (of even if i use my own calculator)
The strange part is that the answer my teacher gets is excactly double what my calculator/wolframalpha gets
If it helps this is G(s):
$G(s)=\frac{1-s}{s^2+2+s}$
woven radishBOT
Lyuka
lyric marlin
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desert arch
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candid tapir
simplifying u get 100x + z = 27y
then just put in random values
oh wait nahh im stupid
i found a better way to do it
ok so yyy can be 000, 111, 222, ..... , 999
so when u divide it by 3, the middle digit should still be same
cuz 3 * (xyz) = yyy
i believe thats uh
444
yeah 444
444/3 = 148
x = 1, y = 4, z = 8
devout snowBOT
@desert arch Has your question been resolved?
wheat pawn
well, you can think of more restrictions first.
Since the result is a number of 3 digits, x has to be lower or equal to 3.
south bison
It is given that f is differentiable, f(a)=b and f(b)=a with a<b and I have to show that an x at (a,b) exists so that f(x)=x
south bison
If I use the Bolzano theorem I can prove that there’s an x so that f(x)=0
But idk what to do about f(x)=x
plush knot
I think in this case the intermediate value theorem is going to work much better
Bolzano's theorem can be deducted from the intermediate value theorem, but to use it you have to know that a and b have opposite signs
south bison
What if I use the proof of the intermediate value theorem?
Which is basically Bolzano
I let f(x)-x=g(x)
I figured it out thanks for the help!
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restive river
I have 2 quizzes tomorrow. one in limits and continuity, the second is in inverse functions, exponential and logarithmic functions. I know little about them, not much
I have around 4 hours of potential studying
one quiz is optional
could you guys give me some guidance if any?
devout snowBOT
I have 2 quizzes tomorrow. one in limits and continuity, the second is in invers...
restive river
I want to pass one with a good grade if possible
its only calc1 so it shouldnt be that complicated
which quiz is easier to get comfortable with, understand and get good enough at in this period of time?
or/and can I get good enough at both in this short period of time?
also. do you guys have any good resources for quiz material like those? ones I could get good info from within 4 hours
arctic silo
you can prob learn limits and continuity in the next hour
restive river
wow
arctic silo
or next 2 hours if you include practice problems
restive river
thats really good.
arctic silo
inverse functions, exponential and logarithmic functions
does this including integrating/differentiating them?
restive river
it doesnt
arctic silo
or just the algebra of them
arctic silo
maybe optimise for the second quiz then
that stuff is ezpz
im sure you can get an A in the second with only 4 hours
- get a B/A in the first
arctic silo
like infinite limits?
arctic silo
are those included in the 2 hours?
but yeah
restive river
Oh wow
arctic silo
are you doing limits at infinity?
restive river
thats so nice
arctic silo
as well?
restive river
are you doing limits at infinity?
Not fully sure yet
arctic silo
what about infinite limits at infinity?
restive river
my teachers notes arent that good either
they feel difficult to understand
all over the place
handwritten
restive river
I'm not, no
arctic silo
okay you can just have my notes if you want
restive river
first semester actually
arctic silo
like my professor's notes for calculus 1
restive river
I would love that.
arctic silo
okay dms
devout snowBOT
@restive river Has your question been resolved?
wise mauve
why cant you do division on both sides of a modular congruence
devout snowBOT
why cant you do division on both sides of a modular congruence
restive river
why cant you do division on both sides of a modular congruence
because dividing both sides of a congruence by a number may not always have a unique solution due to the presence of modular inverses and whatever
If the divisor and the modulus share a common factor, it can lead to multiple solutions or no solution at all for example
wise mauve
is that the same as multiplicative inverses?
restive river
wdym
wise mauve
modular inverse?
wooden veldt
Yes division is multiplying by multiplicative inverse. Issue is not everything has an inverse mod n
pseudo basin
why cant you do division on both sides of a modular congruence
in limited circumstances you can.
restive river
modular inverse?
yeah basically
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rugged sparrow
Okay so idk where am I going wrong in the problem:
devout snowBOT
Okay so idk where am I going wrong in the problem:
rugged sparrow
for a,b in $\mathbb R$ find the maximum value of $\left(\left(1-a\right)\left(1-b\right)+\left(1-\sqrt{1-a^{2}}\right)\left(1-\sqrt{1-b^{2}}\right)\right)$
woven radishBOT
B-eard
rugged sparrow
I let:
topaz beacon
Oh hell naw
rugged sparrow
$a=\sin\theta,\ b=\cos\theta$\$⇒\left(1-\sin\theta\right)\left(1-\cos\theta\right)+\left(1-\sin\theta\right)\left(1-\cos\theta\right)$\$=2\left(1-\sin\theta\right)\left(1-\cos\theta\right)$\$\sqrt{2}\cdot\frac{1-\sin\theta+1-\cos\theta}{2}\ge\sqrt{2}\cdot\sqrt{\left(1-\sin\theta\right)\left(1-\cos\theta\right)}$\$\left(\frac{2-\sqrt{2}}{\sqrt{2}}\right)^{2}\ge2\left(1-\sin\theta\right)\left(1-\cos\theta\right)$\$⇒2\left(1-\sin\theta\right)\left(1-\cos\theta\right)\le3-2\sqrt{2}$
rugged sparrow
Oh hell naw
That was exactly my reaction when this question was given to me on a co-ordinate test
grand siren
well presumably the maximum is some (a,b) that can't be expressed as (sin(theta),cos(theta))
grand siren
well you can still get some of the convenience of the sqrt(1-sin^2) trick by a = sin(theta), b = cos(some other letter)
since that covers all (a,b)
rugged sparrow
would it tho?
grand siren
i don't know how much that actually helps but it does at least get rid of the square roots
finite briar
**B\-eard**
couldnt u try diff?
it might seem impossible
but actually doesnt look that tough
rugged sparrow
couldnt u try diff?
sure I would try that on a 1hr test with 20 qs
finite briar
💀
grand siren
for sqrt(1-a^2) to exist we do need -1 <= a <= 1, so it is valid to assume it's sin or cos of something
rugged sparrow
since that covers all (a,b)
cos(x) is limited to the interval [-1,1] so like if b=2 then idt I would be able to express it as cos(x)
rugged sparrow
for sqrt(1-a^2) to exist we do need -1 <= a <= 1, so it is valid to assume it's ...
Oh okay I see
grand siren
if b=2 then you have $(1-a)(1-2) + (1-\sqrt{1-a^2})(1-\sqrt{-3})$
woven radishBOT
bee [it/its]
rugged sparrow
Yeah yeah I get it
finite briar
cos(x) is limited to the interval [-1,1] so like if b=2 then idt I would be able...
u can but then x isnt real
rugged sparrow
so maybe try with cos(x) and sin(y)?
grand siren
yeah
finite briar
so maybe try with cos(x) and sin(y)?
by assuming sin x and cos x
u made the hidden assumption that a^2 + b^2 = 1
so u maximised the expression w.r.t. to that assumption
grand siren
yeah making it sin and cos of x gets you just points on the unit circle
when we actually want an entire square region around the origin
finite briar
when we actually want an entire square region around the origin
huh?
grand siren
-1 <= x <= 1, -1 <= y <= 1, is a square
finite briar
-1 <= x <= 1, -1 <= y <= 1, is a square
oh rightttt
grand siren
blue = what you get with (sin theta,cos theta)
red = all the actually allowed points
finite briar
yes yes I got that
finite briar
wait what if we view this as a transformation?
what about this??
grand siren
wait what if we view this as a transformation?
i guess you could do that but i don't really see how it would make the computation any easier
finite briar
i guess you could do that but i don't really see how it would make the computati...
Idk LA shit methods?
grand siren
well it's not linear so applying linear algebra would be difficult
finite briar
well it's not linear so applying linear algebra would be difficult
well i dont remember exactly but I remember micheal penn turning a function into a matrix
rugged sparrow
well I end up with a mess
$1-\left(\sin x+\cos x+\sin y+\cos y\right)+\sin x\cos y+\cos x\sin y$
I dont see a way to get further
finite briar
identities 🙂
grand siren
hm
ok yeah that's less helpful than i was hoping
woven radishBOT
B-eard
finite briar
**B\-eard**
notice that sin x cos y + cos x sin y is sin(x+y)
rugged sparrow
sure
finite briar
and then
sin x + cos x is equal to sqrt(1+2sin2x)
so
$1- (\sqrt{1+\sin 2x} + \sqrt{1+\sin 2y}) + \sin(x+y)$
wait shit fuck that doesnt lead anywhere
woven radishBOT
ItzKraken
finite briar
hmm I havent done SHM properly
late rose
hmm I havent done SHM properly
oh okay
rugged sparrow
aparently this is a thing
well you are going into shit that idt should be brought in
finite briar
well you are going into shit that idt should be brought in
hmm
well theres one only 1 thing left i can think of
speed calculus
rugged sparrow
**B\-eard**
this poc is a symmetric multivariable function, and symmetric functions generally have their maxima when all the variables are equal.
so on setting x=y, I get
3-2(sinx+cosx)
now for this to be maximum, sinx+cosx should be minimum which is -sqrt(2)
so effectively i get the maximum as 3+2sqrt(2)
which is indeed the answer
finite briar
Hmm
finite briar
this poc is a symmetric multivariable function, and symmetric functions generall...
'generally' I think u would need to have the conditions set
finite briar
im just too exhausted
eh if it was a MCQ it doesnt even matter ig
silk hill
**B\-eard**
Is this the whole problem?
rugged sparrow
yeah
it was an objective question with four options
excluding the options, this exact thing was the question, the same wording, the same font and the same spacing
devout snowBOT
@rugged sparrow Has your question been resolved?
silk hill
OK, I got the answer
Use AM GM on 1-a and 1-b let it be eqn 1
and then on 1-sqrt(1-a^2) and 1-sqrt(1-b^2) let it be eqn 2
then take the square of eqn1 and eqn2
then add both eqns
I am way too lazy to write in latex
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lethal citrus
okay just a quick something, when i'm using the bisection method, I index the iterations right? I write the iteration number in the table I'm doing, well I've seen some people start with the iteration indexed 1, while I start with the iteration indexed 0, because in my head I'm thinking that I already have the initial values and since I'm using the bisection method I'm already gonna be doing at least one iteration so the initial should be 0, but then a friend of mine said well we're searching for the root, which can turn out to be found through the initial values if f(xM) = 0 so it would make sense to start from index 1, so I'm here to ask about which index I should start with
devout snowBOT
okay just a quick something, when i'm using the bisection method, I index the it...
@lethal citrus Has your question been resolved?
lethal citrus
<@&286206848099549185>
frigid jetty
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@lethal citrus Has your question been resolved?
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@lethal citrus Has your question been resolved?
soft nest
okay just a quick something, when i'm using the bisection method, I index the it...
I don’t think this matters? Are you looking for search depth? Otherwise the result is just the result of the bisection
lethal citrus
I know it doesn't matter that much but I really want to know which is more correct with good reasoning
soft nest
Then I would say step zero is before the main loop and step one is the first round of bisection, but I think it’s up to you.
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quiet delta
Hey I wanna ask a question of physics if that's ok as no one is online in the physics server.
Question: Why does current not depend on the speed of electrons?
devout snowBOT
Hey I wanna ask a question of physics if that's ok as no one is online in the ph...
lavish knoll
Because what matters is the net flow of the electrons, not the individual speed of each one
Each electron flows randomly through the cable (assuming a cable), so it can go in any direction inside the cable in a random way, for up, down, back instead of only forward through the cable
quiet delta
What about photo electric current?
lavish knoll
Wdym?
quiet delta
I mean what if we place a positively charged sheet in front of it wouldn't it give them a direction?
lavish knoll
It would lead to a repulsive attraction
quiet delta
Let's just consider a straight electric field in the wire then wouldn't all electrons flow opposite to the electric field in a straight line?
Then the motion of electrons wouldn't be random would it?
In this case if we can increase the speed of electrons in the wire would the current be affected?
And i am not talking about increasing the voltage just increasing the speed of electrons
lavish knoll
The motion of electrons are almost always random
quiet delta
The motion of electrons are almost always random
Even in a straight electric field?
Wouldn't they be attracted to the opposite of the electric field if the direction of the electric field is straight then wouldn't they all travel in a straight line?
lavish knoll
In this case if we can increase the speed of electrons in the wire would the cur...
I mean... mathematically yeah, because I = dC/dt, and since more loads are going through a cable section in the same time interval (more Coulombs) so yeah I would increase
But i don't have sure if it's as linear as it seems like
quiet delta
I mean... mathematically yeah, because I = dC/dt, and since more loads are going...
Yeah I was thinking about the same thing
lavish knoll
Even in a straight electric field?
Yep
quiet delta
But i don't have sure if it's as linear as it seems like
Even if it's not the ideal case it should have some effect
lavish knoll
Wouldn't they be attracted to the opposite of the electric field if the directio...
But even with that, there are random motion
quiet delta
I was studying photo electric current where we strike photons on a metal sheet to produce electricity
lavish knoll
Even if it's not the ideal case it should have some effect
But did u see anywhere that speed doesn't affect the current?
quiet delta
There it is given that photo electric current doesn't depend on the frequency
lavish knoll
I was studying photo electric current where we strike photons on a metal sheet t...
Oh
quiet delta
But then I thought if we increase the frequency of striking photons wouldn't the speed of electrons increase?
So is the magnitude of current really independent of the speed of electrons?
lavish knoll
I can't answer with 100% sure, but I think it depends on the speed
quiet delta
But then I thought if we increase the frequency of striking photons wouldn't the...
If we increase the frequency of striking photons then energy given to electrons will increase in the form of kinetic energy hence increasing speed
quiet delta
I can't answer with 100% sure, but I think it depends on the speed
But in books it's written it doesn't depend on it's speed
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restive river
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pseudo basin
,rccw
woven radishBOT
pseudo basin
did you mean $\frac{1}{2-\sqrt{3}}$?
woven radishBOT
Ann
pseudo basin
cause you wrote $\frac12-\sqrt{3}$, and that wasn't what you intended
woven radishBOT
Ann
pseudo basin
anyway: 1/(2 - sqrt(3)) is the correct value but it isn't in the right form.
pseudo basin
do you know how to rationalize denominators like this one?
restive river
oh yh i do
okay let me try that
Alright i got the right answer
But ive also tried the second part
And i got (cos^2A) / (2 - sqrt(3))^2
because i squared it , then divided it by cos^2A and then flipped it to get cot^2A to equal to my answer
but its wrong
nvm i got it
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steel halo
im seeing conflicting opinions: are preimages and inverse images (not inverses!) the same?
devout snowBOT
im seeing conflicting opinions: are preimages and inverse images (not inverses!)...
lime stream
im seeing conflicting opinions: are preimages and inverse images (not inverses!)...
i would say they're two words for the same thing, in my experience. what would the difference be? 
woven radishBOT
woven radishBOT
steel halo
notice the usage of preimage and inverse image separately
lime stream
oh, so they use preimage to mean an element of f^{-1}({y})
i guess they like to do that
steel halo
even that part is confusing
lime stream
i don't think most people make the distinction, and it doesn't matter so much since you can phrase this def of preimage in terms of inverse images anyway
steel halo
because they write ALL preimages as f^-1(y)
not one!
i changed it myself to be f^-1(Y) because i thought it makes abs no sense
lime stream
that seems right. instead of f^{-1}({y}) they write f^{-1}(y)
sorry, was doing a covid test 
steel halo
lol nice
but what do u mean
its not right
f^-1 of a single image giving ALL preimages?
lime stream
of a single element, you mean. yeah. like take the function f(x) = x^2. they are saying that f^{-1}(1) = {1,-1}; they're writing f^{-1}(1) instead of the more annoying f^{-1}({1}). so i guess that part is "wrong". but they're saying thats what theyre going to do to spare your eyes from tons of parenthesis
so now its right 
since they defined the notation to mean that
worthy girder
because they write ALL preimages as f^-1(y)
note how a function is not necessarily bijective. Hence "all preimages"
just because f(x_0)=y_0 does not mean f(x_1) couldn't also be =y_0
yet for any g:=f^{-1}, g(y_0) must be defined as one SINGLE value
steel halo
aaaaaah
i see now
there could be more preimages
but
it's not all the preimages of the set Y
worthy girder
the point is that the preimage js not necessarily uniquely defined
steel halo
yeah
worthy girder
take for example f from R->R with f(x)=x²
steel halo
exactly
worthy girder
what's f^{-1}?
worthy girder
but for any inverse you define, you can only have one value for f^{-1}(4)
thus we simply define "the square root is the positive inverse of the function x²"
-root(x) is also an inverse of x² though
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potent ether
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potent ether
whenever im given two points like this here (A and B)
and i want to find the vector AB
does the order matter when i do x2-x1 , y2-y1 , z2-z1
like if a vector AB is asked to find, do i only have to write x2 from B and x1 from A because its AB (B is after A hence indicating that the vector is going from A to B)
arctic temple
Suppose $(x_1,y_1) , (x_2,y_2)$ be two points
woven radishBOT
.doc
arctic temple
If you want you tip of the vector to be at (x_2,y_2)
you will make the vector as $<x_2-x_1, y_2-y_1>$
potent ether
okay so the order does matter
woven radishBOT
.doc
potent ether
my friend kept saying it doesnt
arctic temple
indeed it does
potent ether
indeed it does
can i dm you with a specific part of a video its in hindi so ig you'll understand can u just confirm if he did it wrong or correct cuase its really conflicting
arctic temple
my friend kept saying it doesnt
You can easily verify this by taking some examples
Eg: A=(2,3), B=(5,2)
<3,-1> is different from <-3,1> right?
one vector is a flipped of the other one
arctic temple
can i dm you with a specific part of a video its in hindi so ig you'll understan...
I sadly don’t know hindi
I can try
potent ether
I sadly don’t know hindi
ahh man
its just the calculation tho
you'll be able to understand
potent ether
one vector is a flipped of the other one
yeah ik this but idk why that other person did it like that
devout snowBOT
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@potent ether Has your question been resolved?
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@potent ether Has your question been resolved?