So as the other guy said
#help-13
slate lintel
this was the incorrect step
that's fine but you didn't do that on the LHS
$(\log_4x)(\log_4x^2) \neq \log_4x^3$
wraith daggerBOT
Hayley
slate lintel
you can't combine them in that way
i will say i'm not sure why you are messing with x^2 here, leaving it as 2log4(x) will be more useful to you
no, you can't
well, you can write $(\log_4x)(\log_4x)$ as $(\log_4x)^2$ if you want...
wraith daggerBOT
Hayley
slate lintel
also writing $(\log_4x)$ all the time is getting really tiring try just writing $L$ or something instead
wraith daggerBOT
Hayley
cold briar
oh change of base
i don't think he did it right tho, the change of base step
slate lintel
oh yeah true they put an extra 2 in the denominator
cold briar
oh yeah true they put an extra 2 in the denominator
yes.
cedar kilnBOT
@crimson sedge Has your question been resolved?
cold briar
you shouldn't have put the coefficient (2) in the denominator when doing change of base.
brb tho, im helping someone else
cold briar
okay im back @crimson sedge
you still here?
okay so
are you done with this?
or do you still need help
okay
just do the change of base rule correctly this time
don't put the coefficient (2) at the denominator
what did you get?
ok so
what is log_4 4^2?
what is log_4 (4) = ?
??
ok lets start from the beginning then
do you understnad what log does?
okay so i'll give you an example
now with logs
wraith daggerBOT
help
cold briar
to find x, you need to find a number where
2^x = 8
you're basically trying to find a number where when the base (2 in this case) is raised to that number, it becomes the number that's inputted inside the log function (basically the number beside it, in this case 8).
yeah
so now
what is log_4 (4) equal to?
yesss
so for the numerator you have 2 * 1
which is 2
just replace it
sure
can you do it now?
okay i'll simplify it for you
lets say that log_4 x := u
,,u \cdot u + 2 = 3 \cdot u
wraith daggerBOT
help
cold briar
can you do this?
can you solve for u?
it works... you just wrote it wrong
it should be + 2
idk how but the + 2 is suddenly on the right?
yes
congrats
you did it!
it's done
now i go
byeeee
cedar kilnBOT
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Available help channel!
dire rain
How to solve this
cedar kilnBOT
How to solve this
dire rain
gritty galleon
do you know the formula for proability?
cursive escarp
p rule or c rules
dire rain
Probability of an event
P(E)=number of times event occurs/Total number of trials
gritty galleon
Probability of an event
P(E)=number of times event occurs/Total number of trial...
so total number of trials can be compaed to total num kids in this case
cedar kilnBOT
Available help channel!
slow karma
Consider the expression 𝐸(𝑋) = 1 + 𝑋^2/1−𝑋2 : 𝑋/𝑋+1. Determine the integer values of
𝑋 ∈ ℝ ∖ {−1; 0; 1}, for which the corresponding value of 𝐸(𝑋) is an integer
number.
tropic oxide
do you have a picture
slow karma
yes
tropic oxide
send it here
slow karma
rugged palm
What have you tried?
slow karma
nothing, i forgot how to do this
tropic oxide
simplifying the expression somewhat would be a good start
wonder why they said "integer values of X ∈ R \ {-1,0,1}" and not "values of X ∈ Z \ {-1,0,1}"...
but anyway yeah at least write $1 + \frac{X^2}{1-X^2} \cdot \frac{X+1}{X}$
wraith daggerBOT
Ann
tropic oxide
also for the purposes of determining integrality the 1 at the beginning can be ignored (do you see why)
tropic oxide
well do you know how to multiply fractions
and do you know how to simplify fractions
that 1-X^2 in particular looks factorizable
cedar kilnBOT
tropic oxide
was this sarcastic?
cedar kilnBOT
Available help channel!
thick kiln
Working on part b. The restriction is on repeating a resturant. I have to worry about this restriction for a few cases for the week. Like we could have Tuesday repeat Monday or Friday releat Thursday , ect. I'm sort of unsure how to account for that.
thick kiln
For the most part this is sampling with replacement right?
cedar kilnBOT
@thick kiln Has your question been resolved?
cedar kilnBOT
@thick kiln Has your question been resolved?
marble forum
For the most part this is sampling with replacement right?
Didn't you already ask it in another channel?
thick kiln
Didn't you already ask it in another channel?
I did!
marble forum
Well I believe I answered it there
thick kiln
The channel closed though before I could respond to you
marble forum
So did another guy
marble forum
The channel closed though before I could respond to you
You can still see the solution
thick kiln
I only saw yours
marble forum
The other guy said the same thing
thick kiln
Oh okay
marble forum
Did you understand my solution?
thick kiln
I did but doesn't your solution only account for repeating once?
Cause as I mentioned above, it looks like you can repeat a day in a few cases
marble forum
How could we have Tuesday repeat Monday?
Think like the man
Day 1, you haven't eaten anywhere
So you have 10 options
You pick the any one you like
The next day
You don't want to eat where you ate on day 1
So you have 9 options
Pick 1
Next day
thick kiln
Yes
thick kiln
It's 9 because we're sampling with replacement right
marble forum
Not sure what that means
thick kiln
One sec
marble forum
I am unfamiliar with the jargin
thick kiln
Right one sec
marble forum
The jargon doesn't matter
You can just think about it like I did
Every day you are "sampling" from the list that contains all - the last pick
Maybe this helps
On day 1 there is no last pick
thick kiln
Yeah!
Like with part a, it's like we were picking restaurants out of a hat and keeping that selection out of the hat after its picked. So once it's picked, I have one less day and one less resturant to pick. Without replacement. Now it's working with replacement where the resturant will be put back in the hat but we have a restriction.
I think I was having trouble thinking about this using the binomial theorem
But I don't think I need to account for double counting. Your way is clear.
I gotta think better..
thick kiln
On day 1 there is no last pick
Ty for your help
cedar kilnBOT
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Available help channel!
crimson sedge
Hello, the answer in the book is 10, I do not understand why this answer is wrong. Can someone please explain it to me?
crimson sedge
crimson sedge
Yeah
Basically I interpreted bc as the sums of the radius of the circles.
And ab is 6, and ac is 5, so I thought that a is 1, b is 5, c is 4, and 5 + 4 is 9, so bc is 9
tropic oxide
"A is 1"?
crimson sedge
No
tropic oxide
so I thought that a is 1, ...
crimson sedge
What I mean is that the line segment outside of the circle
Is 1
That’s what I meant, not like in linear equations and variables
slate lintel
bc is indeed the sum of the radii of circles B and C
crimson sedge
can you name the segment whose length you're saying is 1
It’s not necessarily a segment
tropic oxide
then what is it that has a length
crimson sedge
More like an unnamed section of the radius
crimson sedge
Oh I realized my mistake but now I’m utterly confused
tropic oxide
...sorry now i'm confused as to what the fuck you're talking about anymore
crimson sedge
Same
tropic oxide
may i suggest acknowledging two things:
- AX = AY
- CB = CQ + QB = CY + BX
instead of finding AX find AX+AY, which is exactly twice as much
crimson sedge
may i suggest acknowledging two things:
1. AX = AY
2. CB = CQ + QB = CY + BX
That makes sense
slate lintel
may i suggest acknowledging two things:
1. AX = AY
2. CB = CQ + QB = CY + BX
(CB = CX + BY? doesn't sound right...)
crimson sedge
Yeah that does rise a point
tropic oxide
got that bit backwards sorry
crimson sedge
I’m now genuinely confused as fuck on a. What the fuck my logic was
b. How to solve this problem, the book explanation is genuinely fucking confusing
tropic oxide
do you want me to elaborate on what i wrote or to explain what the book wrote
crimson sedge
do you want me to elaborate on what i wrote or to explain what the book wrote
By all means both
tropic oxide
which one first
crimson sedge
Also i realized my logic
crimson sedge
which one first
book
tropic oxide
ok then show what the book writes
crimson sedge
Give me five minutes I’m in the car
By then I’ll explain my logic
The circles are one unit away from the radius of the circle
tropic oxide
... how can i explain the book's solution to you if i don't have the book's solution on hand
crimson sedge
And now i realized my logic is so dumb
crimson sedge
do you want me to elaborate on what i wrote or to explain what the book wrote
ok then what you wrotw
by then I’ll be home
crimson sedge
... how can i explain the book's solution to you if i don't have the book's solu...
Please explain what you wrote
tropic oxide
no need to say it twice.
crimson sedge
ok
tropic oxide
as i said before, instead of finding AX, i will find AX + AY, which is exactly twice as large as AX. once AX+AY has been found, AX can be found by halving it.
do you follow thus far Y/N
@crimson sedge
tropic oxide
AX = AB + BX, and AY = AC + CY.
agree or disagree?
crimson sedge
agree
tropic oxide
CY = CQ, and BX = BQ.
agree or disagree?
crimson sedge
Agree
crimson sedge
agree
tropic oxide
therefore AX+AY = AB+AC+BC
all of the stuff on the right hand side is known
do you see how to proceed from here?
crimson sedge
one sec i need to go back to everything you said
but i most likely will
ok i understand now
thanks
so ax + ay = 6 + 5 + 9
so ax = 10
thanks
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
mortal frost
I'm trying to self learn some multivariable calculus and I just started working through "calculus a complete course" by Adams. But I have gotten stuck on example 5 from section 12.1. Specifically how the derivative of d/dt (x^2 j) = 2x * dx/dt j. We aren't taking the derivative with respect to x but we get a result as if we do.
mortal frost
x is just a function with t as a parameter. And I have never heard of d/dx (f(x))^2 = 2f df/dx being a thing
OH WAIT ITS THE CHAIN RULE
dire geode
,rotate
wraith daggerBOT
dire geode
yes it is chain rule
mortal frost
What about the next step. If v = dx/dt is v = abs(dx/dt)???
dire geode
it's confusing, but $\textbf{v}$ = velocity, while $v = |\textbf{v}|$ = speed
wraith daggerBOT
rie.mann
mortal frost
Yes, and u get that by taking the size of the vector v right?
How does the size operator work on dx/dt?
dire geode
,tex .abs def
wraith daggerBOT
rie.mann
mortal frost
So the size operator turns into absolute value? The book kinda says so ig (right is the positive direction ig)
,rotate
wraith daggerBOT
cedar kilnBOT
@mortal frost Has your question been resolved?
bold lotus
So the size operator turns into absolute value? The book kinda says so ig (right...
it doesn't turn anything into absolute value when you are calculating magnitude/size you just end up with the abs of dx/dt
Since they are assuming the object is always moving right then the x co-ordinate is always increasing so the derivative of x(t) is always gonna be positive hence the absolute value is redundant
cedar kilnBOT
cedar kilnBOT
✅
mortal frost
Hmm okay, so if I am taking the size of a vector function with dx/dt or some other derivative in it I just take the abs of the derivative and go on with my day?
bold lotus
Hmm okay, so if I am taking the size of a vector function with dx/dt or some oth...
No it has nothing to do with the fact that it's a derivative
It just happened to be that way when calculating the size
mortal frost
Like if v = dy/dx × (3i + 4j) then |v| = |dy/dx| × sqrt(9+16) ???
bold lotus
You know how to calculate size right so try doing it for vector v and see what you get
bold lotus
Like if **v** = dy/dx × (3**i** + 4**j**) then |**v**| = |dy/dx| × sqrt(9+16) ??...
Not at all
mortal frost
You know how to calculate size right so try doing it for vector v and see what y...
Well I would say its sqrt( (dy/dx)^2 + 3^2 + 4^2)
Do they just pull dy/dx out?
bold lotus
Well I would say its sqrt( (dy/dx)^2 + 3^2 + 4^2)
Should be times 3^2
but other than that it's good
mortal frost
Yeah the example wasn't the best
bold lotus
Do they just pull dy/dx out?
And yes but this was only possible because the dx/dt was multiplied by both terms
So then you can factor it out and use square root laws to put it in its own square root
bold lotus
But the conclusion is then that |dy/dx| = sqrt((dy/dx)^2)
Applies for any value not just derivative
bold lotus
sqrt(x^2) = |x|
See here
mortal frost
Ig not, just gotta get it into my brain
bold lotus
and then undoing it you get the original value but it's always the positive one cause that's how the square root function works
So you basically just turn the value positive
which is exactly what the absolute value function does
It's midnight in Greece gn
mortal frost
Gn!
Well I do have one more question, let's see if someone responses.
What happens between step 2 and 3 here?
From my understanding it looks like d/dt = d/dx * dx/dt? Did they just multiply by dx/dx?
Feels wacky but ig I see no reason why you can’t do that, treating derivatives like ratio's feels illegal but we did it physics so ig we can do it anywhere lol
dire geode
From my understanding it looks like d/dt = d/dx * dx/dt? Did they just multiply ...
No this is nonsense. This only makes sense in your head
mortal frost
Though so hahaha
dire geode
Feels wacky but ig I see no reason why you can’t do that, treating derivatives l...
This is also generally wrong, but sure do it in your physics classes
mortal frost
But okay, what's the solution then? How does it actually work?
Is it something to do with x = x(t)?
mortal frost
Yeah
dire geode
then dx^2 / dt^2 = 6t
mortal frost
Yeah
dire geode
but if dx/dt = f(x)
and x = x(t)
then dx/dt = f(x(t))
so find dx^2 / dt^2 using chain rule
cedar kilnBOT
@mortal frost Has your question been resolved?
mortal frost
I got it!!!! Let y = f(x) = 5/sqrt(1+4x^2)
Then the chain rules gives dy/dt = dy/dx × dx/dt.
Substitute in y = 5 sqrt(1+4x^2) and we done!
I'm used to Lagrange notation so all of this is a little new hahaha
Never really got the chain rule good enough to be able to used it fluidly and the new notation is a little confusing at first
But I got it!
slim grail
is this even possible if not why?
cedar kilnBOT
is this even possible if not why?
slim grail
<@&286206848099549185>
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
bold vine
To compute by hand?
slim grail
like can you get a real number
bold vine
,w Calc (1.728)^(2/3)
wraith daggerBOT
violet flume
3/2 *
slim grail
yea
violet flume
slim grail
1.5
violet flume
ur right
slim grail
so the ans is 1.44
violet flume
,w pfactor 1728
wraith daggerBOT
violet flume
yes 
bold vine
@slim grail Need anything else?
cedar kilnBOT
@slim grail Has your question been resolved?
cedar kilnBOT
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Available help channel!
hollow patrol
can someone explain this to me? how did they get the answer?
dire geode
can someone explain this to me? how did they get the answer?
Where exactly do you get lost first
hollow patrol
like literally the first step
dire geode
Show the question
hollow patrol
am i supposed to simplify the 1/3(3x/7x-5) first?
dire geode
Write y = in terms of u
hollow patrol
can someone explain this to me? how did they get the answer?
i think the first step would be to make 1/3(3x/7x-5)^-2/3 into the 1/cube root of 3x/7x-5 to the power of 2/3
right? @dire geode
hollow patrol
well how do i find that in terms of u?
hollow patrol
can someone explain this to me? how did they get the answer?
and is this going to help me solve this faster?
cuz this is where im at rn
where do i go from here?
or is this the wrong step?
dire geode
You're doing it a different way from the solution
dire geode
like literally the first step
The first step is to express y in terms of u
But you don't have to do it that way
hollow patrol
But you don't have to do it that way
which way? my way or ure way?
hollow patrol
can someone explain this to me? how did they get the answer?
also which one is the y?
cuz i wasn't taught to do anything like y in terms of u after doing all of the previous steps
dire geode
I was explaining it then you went off and did your own thing
dire geode
Yes
hollow patrol
ok so whats the next step?
dire geode
can someone explain this to me? how did they get the answer?
Did you follow the first equation
hollow patrol
yes, i understand how they got dy/du and du/dx
i just dont know how they got their answer
hollow patrol
i should've clarified then, my bad. what i meant is how to find the answer from dy/du and du/dx
because ik how to get those but what do i do next?
how do i get from here
to here
sorry i didn't clarify
wraith daggerBOT
rie.mann
hollow patrol
i see where to apply the rules but can you walk me through it?
cedar kilnBOT
@hollow patrol Has your question been resolved?
hollow patrol
.close
dreamy zenith
If you do long division for a polynomial to get a rational function into y=mx+b
and the final result is y=mx-b does that mean there is no oblique ?
dire geode
If you do long division for a polynomial to get a rational function into y=mx+b ...
Show exactly what you mean with specific polynomials
fading summit
I think that sound right. The rational function will just have holes.
cedar kilnBOT
@dreamy zenith Has your question been resolved?
coarse sable
Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 16,$ and $CF$ is a positive integer, then find the largest possible value of $CF.$
wraith daggerBOT
funwiththepros
coarse sable
!help
cedar kilnBOT
Please read #❓how-to-get-help
sick ledge
cedar kilnBOT
sick ledge
Could I walk through this problem with someone
I have a answer for the max
but I am not to sure about the min
talking it through with a helper would be great
cedar kilnBOT
@sick ledge Has your question been resolved?
sour jetty
guys i need help on question 17, i do not know if the point the question is the minimum point or not so i do not know if i can just put the numbes in.
What i did was -p=2p^2-15
and what i got was p=2/5 or p= -3zzz
and q= 2 im not sure if that is correct or not
cedar kilnBOT
guys i need help on question 17, i do not know if the point the question is the ...
@sour jetty Has your question been resolved?
cedar kilnBOT
@sour jetty Has your question been resolved?
Show your work, and if possible, explain where you are stuck.
Available help channel!
civic eagle
what does this mean? in the green dialog.
cedar kilnBOT
what does this mean? in the green dialog.
civic eagle
is the constant C dependent on the factors of each term when using an antiderivative, so any change in a factor of an antiderivative can be "adjusted for" with C?
slate lintel
any constant C is allowed to make it a valid antiderivative
civic eagle
would a professor mark this wrong?
slate lintel
eg $x^2 - 7$ and $x^2 + \pi$ are both valid antiderivatives of $2x$
wraith daggerBOT
Hayley
slate lintel
well... usually you'll have a $+C$ on the end of any antiderivative for that reason
wraith daggerBOT
Hayley
civic eagle
but what about 3x^2 - 7 as an antiderivative of 2x?
civic eagle
looking at the two different results in the picture, would you mark that as wrong if the calc answer was the book answer?
slate lintel
both of them should have a +C unless there's some initial value ($f(0) = 1$ for example)
wraith daggerBOT
Hayley
slate lintel
and if there is an initial value then at most one of them will be correct
with +Cs on both they would both be valid
civic eagle
sorry, there's more to this. i didn't realize i'd need to explain more for this.
this is the original integral
i used tan sub
slate lintel
yeah they should both have a +C on the end of them then
it's common to knock off a point or two for forgetting that
civic eagle
well, i didn't forget + C
but i was wondering if my answer was equivalent to the book answer
slate lintel
well, i didn't forget + C
I don't see it in your answer though?
they differ by a constant 
it's common for that sort of thing to happen particularly with trig subs
civic eagle
the green was one small part of a much bigger problem
its the middle two terms
omg it is equivalent, i think i see how they simplified the log now
civic eagle
yeah idk actually. i thought maybe square the dividend and bring it into the root
slate lintel
,tex .log rules
wraith daggerBOT
Hayley
slate lintel
ok yeah they differ by $\ln(3)$
wraith daggerBOT
Hayley
civic eagle
make it ln( sqrt( (x^2+9)/9 ) ) -> 1/2 ln ( (x^2+9)/9 ) ?
slate lintel
yeah
slate lintel
what's the difference between them?
like if you took one and subtracted the other what would you get?
civic eagle
so.. when finding an antiderivative, i should cancel out any constant factors like that since C can always replace them?
the ln 3 you spoke about earlier specifically
slate lintel
you are free to add or subtract any constant that you'd like from your antiderivative
civic eagle
so my above answer, since i had that /3 inside the log, i could such separate it into -ln 3 and then toss that into C and forget about it?
slate lintel
yep
civic eagle
mind. blown.
how did i get this far
in life i mean, without knowing this
500 pages deep into textbook i never needed this?
thanks, i appreciate the epiphany
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sharp shoal
cedar kilnBOT
sharp shoal
I'm not too sure what I should use here. A little assistance would be much appreicated
dreamy sleet
this is the same as how many ways to choose 3 T’s from a set of 7 letters
because you’re choosing the positions
sharp shoal
this is the same as how many ways to choose 3 T’s from a set of 7 letters
but can't we also say that this is the same as to choose 4H's from a set of 7 letters?
dreamy sleet
but can't we also say that this is the same as to choose 4H's from a set of 7 le...
Yes, that’s also the same
sharp shoal
But then do we doo 7 choose 4 or 7 choose 3?
dreamy sleet
But then do we doo 7 choose 4 or 7 choose 3?
Both are the same
Because when you choose 4, you are also choosing which to leave behind
crystal raptor
Alternative counting: find the number of ways to permute if everything was distinguishable, then divide out by the number of ways to permute the Hs and by the number of ways to permute the Ts
dreamy sleet
(I did that in my head first and then realized it was the same as combination)
the same expression
sharp shoal
Because when you choose 4, you are also choosing which to leave behind
oh yeah you're right
sharp shoal
Alternative counting: find the number of ways to permute if everything was disti...
im sorry im a beginner i didn't understand this
dreamy sleet
im sorry im a beginner i didn't understand this
find the way to permute 7 objects, then realize that since all the H’s are the same, you overcounted by a factor of 4!
same for the T’s
crystal raptor
See if it agrees with the other method
crystal raptor
There are usually different ways to count things so always good to see if the ones you can come up with agree:)
sharp shoal
yeah
thanks both a lot. it really means a lot you guys taking out the time to help begineers like me 🙂
.close
cedar kilnBOT
sharp shoal
.reopen
cedar kilnBOT
✅
sharp shoal
i had another doubt
how do we know the answer to this is 0?
it was there in a lecture that this is equal to 0 but I didn't understand the reason
crystal raptor
Did they prove it or just state it?
You will be integrating an odd function over a symmetric interval which in general is zero
sharp shoal
Did they prove it or just state it?
stat
sharp shoal
You will be integrating an odd function over a symmetric interval which in gener...
oh yeah wait something like this was said
sharp shoal
You will be integrating an odd function over a symmetric interval which in gener...
how do we just look and thell that this is an odd function?
sharp shoal
You will be integrating an odd function over a symmetric interval which in gener...
rigght. to find expectation we integrate x f(x) from negative infinity to positive infininty
crystal raptor
A function is odd if g(-x) = -g(x) for all x
crystal raptor
Is f(x) odd?
sharp shoal
I think it's the later.
crystal raptor
Test the condition
crystal raptor
Good, but xf(x)?
sharp shoal
it is odd
sharp shoal
is this true for any odd function?
crystal raptor
Yep!
crystal raptor
Thanks, you have a great attitude to being helped 
cedar kilnBOT
@sharp shoal Has your question been resolved?
safe violet
is this answer corrrect?
cedar kilnBOT
is this answer corrrect?
dreamy sleet
Yes
dreamy sleet
Yes
dreamy sleet
thank you so much
Has your question been resolved?
safe violet
Has your question been resolved?
yeah I guess
can I get an explanation for what is the upper number and the lower number?
here
dreamy sleet
choose 8 from 8(order matters)
safe violet
so since jim and Anne wanted to stay together you took substract them from the group and show it separately
then show the Permutation with upper 8 and lower 8
dreamy sleet
so since jim and Anne wanted to stay together you took substract them from the g...
The reason why it is 2 x 8! is because Jim and Anne want to stay together, so they can be treated as one “person”, so that explains the 8!
the 2 is because Jim can sit to the left of or to the right of Anne
cedar kilnBOT
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peak salmon
cedar kilnBOT
peak salmon
could someone please explain this to me in other words?
I don't understand how they get to one
and is the interval (1, 3) just an arbitrary decision?
tropic oxide
sure is
peak salmon
Also, I put that answer knowing it was wrong, I just didn't know where to go from there
without having to draw a graph
tropic oxide
when doing this kind of problems you should try to look for factorizations
peak salmon
yeh i did that part
tropic oxide
to cancel out the parts that make the top and bottom go to 0
or ∞ as the case may be
tropic oxide
you mean x^2/(x+2)?
peak salmon
yeh
tropic oxide
parentheses...
well, what's the problem? aren't you able to plug in x=2 at that point?
peak salmon
well plugging it in gives 4/0
exotic acorn
you would factor and cancel
exotic acorn
yeah
exotic acorn
so you would take out x^2 from the top to be left with x^2(x-2) on the numerator
and the denominator will be (x+2)(x-2)
then the (x-2)'s would cancel each other
leaving you with
[x^2] / [x+2]
peak salmon
then shouldnt the rule be
exotic acorn
from there you could just plug in and get 4/4 which is indeed be 1
peak salmon
x != -2 ?
exotic acorn
yes
peak salmon
from there you could just plug in and get 4/4 which is indeed be 1
yeh thats where i messed up
exotic acorn
because then you would get an error
peak salmon
but on the page it says x != 2
peak salmon
how would i be able to tell without having to draw the graph?
peak salmon
i imagine its for the main equations aswell
exotic acorn
i think it means the original function
exotic acorn
not the simplified one
exotic acorn
like if you can plug straight in or not?
peak salmon
imagine plugging in both 2 and -2 would give proper results
how would I know which is correct
exotic acorn
you plug in what ur limit approaches
peak salmon
because the graph of this function does have an asymptote at -2
and it seemed u knew wihtout having seen it..
peak salmon
peak salmon
exactly
and is there a way to ever tell that
without having to draw it?
because u guessed so before
peak salmon
thats why i thought ud maybe know
exotic acorn
you would look at
ur highest exponent in ur denominator
and then find that in ur numerator
and lets say
if its
2x^2 / 3x^2
ur asymptote lies at 2/3
exotic acorn
correct
peak salmon
i c
i dont think ive ever heard of this rul before
interesting
thanks both of you
exotic acorn
if N = D = n/d
if N>D = 0 (Note: if it is greater by at least one there also could be a slant asymptote but i dont think that youll ever need to know that for limits)
N<D = DNE
i believe
cedar kilnBOT
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crimson sedge
Hi, I basically made a box plot using the following info:
The average (X mean) of your data is 5.678571429.
The sum of all the data (ΣX) is 159.
The sum of the squares of the data (ΣX^2) is 959.48.
The standard deviation (σ X) of the data is 1.421608029.
The number of data points (n) is 28.
The minimum of the data (min X) is 3.4.
The first quartile (Q1) is 4.4.
The median (Med) is 5.75.
The third quartile (Q3) is 6.6.
The maximum of the data (Max X) is 8.7.
Now the question is:
F) Your numbers will most likely not be exactly normally distributed but may be close to the normal distribution. Assume your numbers are normally distributed. Then calculate the interval within which 95% of all your numbers lie. Does this also correspond to reality?
cedar kilnBOT
Hi, I basically made a box plot using the following info:
The average (X mean) ...
@crimson sedge Has your question been resolved?
bold kettle
Hi, I basically made a box plot using the following info:
The average (X mean) ...
For that question, you just need to use the normal distribution with the given mean and standard deviation. If they're asking for the middle 95%, that means you have 2.5% on either end of the normal curve missing (because 2.5%+2.5%=5%). Do you know how to get the bottom 2.5% or top 97.5% of the normal distribution?
crimson sedge
For that question, you just need to use the normal distribution with the given m...
Hi! Thank u for this, I’m just confused because it apparently has some kind of formula
bold kettle
Hi! Thank u for this, I’m just confused because it apparently has some kind of f...
Yes, there's a general way to do percentiles like here: https://www.statology.org/calculate-percentile-from-mean-standard-deviation/, or in this special case you could also use the 68-95-99.7 rule if you've learned that (if not just go off the link, it's the general way to do it)
cedar kilnBOT
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royal loom
Let ${x_n}$ be a bounded sequence, prove $$\lim_{n \to \infty} x_n=0 \iff \lim_{n \to \infty} \sup{|x_n|}=0$$
royal loom
I've proven one direction, I'm hoping someone can check my proof, and then I will probably need a hint for the other direction
wraith daggerBOT
austinu
violet flume
wraith daggerBOT
austinu
royal loom
So this is my work for going in the one direction
If it checks out (?) then I need help figuring out how to go the other direction
crimson sedge
You mean Let ${x_n}$ be a bounded sequence, prove $$\lim_{n \to \infty} x_n=0 \iff \lim_{n \to \infty} \sup_{k \geq n} {|x_k|}=0$$ ?
wraith daggerBOT
sugaku3460
royal loom
if that is the proper notation, then yes
the limsup of |x_n|
but I wrote the question exactly as it was written in my HW
crimson sedge
Yes so there is no space between lim and sup
royal loom
latex issue
crimson sedge
Okk
solid juniper
$\limsup_{n\to\infty}$ is a thing
wraith daggerBOT
slayyla
crimson sedge
So what you have to say is that over N all |x_n| are <= eps is the same thing to say that sup k>= N |x_n| <= eps
Do you see why ?
royal loom
I don't really even understand what you mean by what you wrote
crimson sedge
If $N \in \mathbb{N}$ and $\epsilon > 0$ then $\forall n \geq N |x_n| \leq \epsilon$ \iff sup_{k \geq N} |x_n| \leq \epsilon$
wraith daggerBOT
sugaku3460
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
solid juniper
i'm just gonna add this is not written right
solid juniper
yes, don't put the for all epsilon > 0 at the end
crimson sedge
**sugaku3460**
Compile Error! Click the <:errors:504266556054962196> reaction fo...
Do you agree ?
royal loom
sure
solid juniper
If $N \in \mathbb{N}$ and $\epsilon > 0$ then $\forall n \geq N |x_n| \leq \epsi...
i think there's a typo on the sup here
crimson sedge
And $\forall n \geq N \sup_{k \geq n} |x_k| \leq \sup_{k \geq N} |x_k|$
royal loom
sure
wraith daggerBOT
sugaku3460
crimson sedge
So you can write it well now
With writing what means $\lim{n \to \infty} x_n=0$ and $\lim{n \to \infty} \sup_{k \geq n} {|x_k|}=0$
wraith daggerBOT
sugaku3460
solid juniper
carry on on but austin is there any chance you have the theorem that says if a sequence converges then its lim, limsup, and liminf are all equal?
royal loom
I do!
solid juniper
that makes that direction pretty trivial then
royal loom
what about the absolute value?
solid juniper
lim x_n = 0 iff lim |x_n| = 0
royal loom
right
and then since lim | x_n | converges
the sequence given by |x_n| converges
and since the sequence converges its limsup is equal to its limit
which is 0
that's the idea right?
solid juniper
what you said is a little weirdly wordy but sure
royal loom
I get that a lot
solid juniper
llol
blazing fern
cedar kilnBOT
hoary chasm
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
blazing fern
Don't have a clue how to start
hoary chasm
Heard of communtativity
vestal wolf
We don't even need to proove communitativity to solve this, do we
hoary chasm
But some sample values and assume theta
vestal wolf
Also what is a and b here
blazing fern
Not given
hoary chasm
But some sample values and assume theta
Put a=1i,b=1j
vestal wolf
Is the period supposed to be a dot product
hoary chasm
Yea
vestal wolf
I don't understand what the instructor here is up to
blazing fern
The answer says it's 0
vestal wolf
How is a dot product with a scalar and a vector possible
vestal wolf
Put a=1i,b=1j
Your logic is not fully applicable here in case of a= 2i+j and b= i+2j
hoary chasm
Your logic is not fully applicable here in case of a= 2i+j and b= i+2j
Yea ryt I was just tryna get it into one of the options
So the wrong question
hoary chasm
Lolmao
blazing fern
Oh is the question not clarified?
hoary chasm
Ysa
vestal wolf
A dot product is supposed to be with vectors
Not scalars
Like seriously
What was he up to when making this problem
And why is he qualifed for making this problem
hoary chasm
Which country
blazing fern
Nepal
hoary chasm
Ahh goverment content
vestal wolf
I'm very sorry to hear about that
cedar kilnBOT
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Available help channel!
safe violet
can I get an explanation to this answers?
cedar kilnBOT
can I get an explanation to this answers?
safe violet
crimson sedge
35^75/37, remainder=?
tropic oxide
@crimson sedge please open your own channel. #❓how-to-get-help
@safe violet which part do you want explained? if both, which one first?
tropic oxide
A and B have 4 seats available for them to sit in
the boat is (presumably) symmetrical so 4 of its seats are on its port side and 4 are on the starboard
safe violet
tropic oxide
is that meant to counter my point?
safe violet
not sure I just googled what's a port side of a boat
tropic oxide
when facing the 'front' (bow) of a boat,
port is on the left, and starboard is on the right.
safe violet
ok
tropic oxide
in nautical usage these terms are preferred over left and right as they can be treated as absolute when you're on a vessel
tropic oxide
like this, more like.
but it doesn't actually matter what the 'geometric' placement of these seats is.
safe violet
ohhhh ok
safe violet
ok so A & B and sit on the port side
so 4 chances 2 humans?
4P2
and
Boy W can site on the starboard side
so 4 chances 1 human
4P1
now we have to think about the rest
5 Chances(Seats) remaining 3 Humans
so
5P3
so the total is
4P2 X 4P1 X 5P3
tropic oxide
don't use the letter x or X for multiplication
also i think phrasing these as "chances" is weird
but yes
tropic oxide
yeah sure w/e
cedar kilnBOT
Available help channel!
jolly sable
How to check whether a number is prime or not?
cedar kilnBOT
How to check whether a number is prime or not?
crimson delta
the dumb way is to just divide it by all numbers smaller than its sqrt and check whether those are factors
crimson delta
well which number did you have to check
crimson delta
well eg 171 is obviously divisible by 3
cause of divisibility rules
dont friend request me
jolly sable
well eg 171 is obviously divisible by 3
I know
But here the question is how to check?
Do you have any idea? I choose options by elimination method
crimson delta
apply divisibility rule for the first few numbers
winged wharf
if the number is 56 i think checking all the way to 28 is good
crimson delta
after that, long division by the prime numbers smaller than the sqrt
jolly sable
Damn no this is going to take time. We have nearly 30 seconds only
crimson delta
if the number is three digit, then the sqrt is at most 32 so there isnt that much to check
well presumably the number is easy
and you will get a result soon
for 171 you have to check until 13 only
2,3,5,7,11,13
each of those doesnt take longer than a few seconds
winged wharf
Step 1: First find the factors of the given number
Step 2: Check the number of factors of that number
Step 3: If the number of factors is more than two, it is not a prime number.
jolly sable
for 171 you have to check until 13 only
Hmm right
How will you identify a big number that is divisible by 7?
E.g. 39361
crimson delta
well there is a divisibility rule which you could practice if you wanted to
otherwise, just long division
jolly sable
My focus is to learn short methods
crimson delta
that really doesnt take that long either
jolly sable
I found something to subtract method
crimson delta
not for every problem there are short methods
jolly sable
39361-35000=4361
jolly sable
not for every problem there are short methods
So what is your method?
crimson delta
39361-35000=4361
that is literally the first step of long division
crimson delta
yes
granite eagle
/text how do i write the integral of root(1+a/x^2) in latex?
crimson delta
$\int \sqrt{1+\frac{a}{x^2}} dx$
south tundra
[ \sqrt{1 + \frac{a}{x^2}}?] Although this question belongs to #latex-help
wraith daggerBOT
denascite
alonelybean
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
granite eagle
oh the integral itself is the question too
crimson delta
with maybe some extra command for the d in dx
south tundra
\dd{x}
south tundra
/text how do i write the integral of root(1+a/x^2) in latex?
Don't put text in $$
granite eagle
this came out crappy
south tundra
If you have to, then use \text
crimson delta
(you should very rarely have to do that)
crimson delta
only put the math bits in $
that said, we gave you the answer for the tex part already
south tundra
You don't need \text here
granite eagle
the integral is the actual question tho
south tundra
The integral of that is $\int\sqrt{1 + \frac{a}{x^2}}\dd{x}$
wraith daggerBOT
alonelybean
granite eagle
huh'?
💀
also some hints would be better have been racking my brain all day but nothing
slate lintel
some trigonometric substitution might work
i'd start by doing $\int \sqrt{1+\frac1{x^2}}\dd{x}$
south tundra
You want to solve the integral or type it in latex?
wraith daggerBOT
Hayley
granite eagle
something like acos(z) = x?
crimson delta
you can simplify to $\int\frac{\sqrt{a+x^2}}{x} \dd{x}$
wraith daggerBOT
denascite
south tundra
No, looks like tan or cot
crimson delta
and then the sqrt might give a better idea on what to sub
crimson sedge
how do I do this
cedar kilnBOT
how do I do this
tropic oxide
which part?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
which part?
part a
tropic oxide
do you know how radians work in general
if not i have something to show you
@crimson sedge
crimson sedge
do you know how radians work in general
yes i do
tropic oxide
ok then what's troubling you with part a
you're told arc AB, taken from a circle of radius r, has length 1.45r
crimson sedge
idk how to get AOB out
oh
wait
fuck
i got it
i didnt notice the arc length was 1.45r i didnt notice the r
thank u ann
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
Multiple correct
cold briar
sorry for asking but, is that log_(2/5) or (log_5 )^2?
cosmic steppe
(Log base 5) squared
cosmic steppe
Yeah I'm looking at it
crimson sedge
I think x is in multiplication with log 2 with base 5
cosmic steppe
Uh if it helps, rewrite each log in terms of ln
livid hound
$(\log_5(x))^2$
wraith daggerBOT
ℝamonov
vagrant elbow
$(\log_5 x)^2 + \log_{5x} \left ( \frac 5x \right ) = 1$
cosmic steppe
Yeah but $\log^2_5(x)$ is cleaner
wraith daggerBOT
umbraleviathan
cosmic steppe
That's how I write it anyways
wraith daggerBOT
neonperseus
vagrant elbow
Helper spam I'm out
crimson sedge
👁👁 what
First of all, i dont what does wuestion really meant by first term
Is x is in multiplication? Or x is the number of log?
crimson sedge
Helper spam I'm out
What happened? You fine?
vagrant elbow
I'm fine there were too many people so I peaced out
But it appears everyone else thought the same as well
vagrant elbow
Is x is in multiplication? Or x is the number of log?
Where?
crimson sedge
But it appears everyone else thought the same as well
Lol, this is most weird and awkward moment
vagrant elbow
Umbra be nice now
vagrant elbow
But yes that would probably be the best move
You can rule out A and D since that really doesn't make for a nice integer
crimson sedge
And see which ones are true
Seems reasonable in this one, but might not be a good one if this was integral type or smth else tho
But is x still in multiplicatipn or smth else?
vagrant elbow
Meh I think you need to break up the second log using log properties and then assume log_5 (x) = u
crimson sedge
Hmmm
cosmic steppe
You can rule out A and D since that really doesn't make for a nice integer
Don't rule out a
Would a work lol
5/1 = 5
vagrant elbow
A does work
wraith daggerBOT
crimson sedge
This way?
cosmic steppe
Don't change base for log_5^2(x)
I mean you could but like
$\log_5^2(x) = \parens{\frac{\log(x)}{\log(5)}}^2$
wraith daggerBOT
umbraleviathan
amber pier
A Ferris wheel has 20
carts that are evenly spaced around the wheel. The wheel rotates at a constant speed and it takes 5
minutes to complete a full revolution. The total height of the Ferris wheel is 200
meters and customers enter the carts at the lowest point, which is 2
meters above the ground.
What is your distance from the ground after riding the wheel for 4
minutes and 10
seconds? Give an exact and fully simplified answer.
amber pier
could someone please explain why do we calculate the equilibrium and amplitude like that
like the logic behind it
cedar kilnBOT
@amber pier Has your question been resolved?
amber pier
.close
iron knot
hey
iron knot
i have a doubt in linear algebra
cold briar
cedar kilnBOT
@iron knot Has your question been resolved?
cold briar
i also have doubt in linear algebra